dynaflow lecture: buried piping - dynaflow research

Dynaflow Lecture: Buried Piping Rotterdam, 8 March 2012

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Contents Introduction to Buried Piping

!  Introduction to Buried Piping

!  Soil Properties & Classification

!  Some Principles of Soil Mechanics

!  Rigid Pipe - Soil Interaction

!  Flexible Pipe - Soil Interaction

Copyright 2011 @ Dynaflow Research Group

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Why burying a pipe? Advantages of burying a pipe

!  Reduces plant congestion and avoids existing above ground obstructions.

!  Allows for shorters route (fewer bends).

!  Soil can be used as uniform supporting, no above ground supports and constructions are needed.

!  Protection from ambient temperature changes.

!  Protection from wind loads.

!  Long stretches of buried pipe act as a virtual anchor and the need for large axial restraints or expansion loops is eliminated.

Copyright 2011 @ Dynaflow Research Group 4

Why burying a pipe? Disadvantages of burying a pipe

!  Piping has to be designed for soil and surface loads, which makes the stress and flexibility of the piping more complex.

!  Careful trenching and backfill is required to avoid excessive soil settlement.

!  There are some ‘uncertain’ parameters involved in the design of buried piping.

!  Identification and repair of failures is more problematic (quality control is very important for buried systems).

!  Corrosion challenges, coathing/cathodic protection might be required.


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Soil-Pipe Interaction It is useful to have a basic understanding of the fundamental principles


!  Soil is an earthen material consiting of loose solid particles with water in between. When burying a pipe, soil is effectively used as a construction material.

!  Soil is not a distinctly defined material with constant properties. Soil has a variety of appearances with widely varying properties.

!  The mechanical behavior of soil (soil mechanics) on its own is a very specialized field of study.

!  Buried pipelines are for their strength and stability behaviour dependent on the support and resistance of the surrounding soil.

!  Deformation of the pipeline can also deform the soil. Additionally, external influences may cause the soil to deform as well, causing additonal loads on the pipe.

!  All in all, there is a complex and continuous interaction between a buried pipe and the soil and therefore soil-pipe interaction should be considered in any buried pipe design.

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Underground Failure Mechanism Examples of typical failures in buried piping

!  Buried steel pipe failures are most often corrosion related – a good coating is the first line of defence.

!  If soil and surface loads are excessive the pipe cross-

section can buckle or crack. !  The moving portion of a pipe will generally be resisted

by the soil, creating significant bending stresses at changes of direction, e.g. elbows and tees.

!  Upheaval buckling due to a high water table or

buckling due large thermal expansion.

!  Fiberglass (FRP/GRP) pipes are more flexible than steel pipes and therefore very senstive for abrupt changes in soil settlements.


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Underground Failure Mechanism High bending stresses in elbows and tee’s


Underground Failure Mechanism Steam line failure in New York City


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Underground Failure Mechanism Steam line failure in New York City

Copyright 2011 @ Dynaflow Research Group 10 Copyright 2011 @ Dynaflow Research Group

Underground Failure Mechanism Pipe upheaval due to high water table

11 Copyright 2011 @ Dynaflow Research Group

Underground Failure Mechanism Various “bad” design solutions

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Relevant Design Codes Codes and manuals that touch on the subject of buried piping Buried pipelines are not extensively covered by the ASME B31 codes. Some of the B31 codes have additional requirements for buried pipes such as: !  ASME B31.4 (Liquid Petroleum Transportation Piping) !  ASME B31.8 (Gas Transportation Piping) !  ASME B31.1 (Power piping) Often codes refer to “competent engineering judgement”. However, the following codes and standards address the issue of buried pipe lines in detail: !  NEN3650 !  AWWA M11 and M23 (American Water Works Association) !  ASCE (American Socitiey of Engineers) !  German ATV-DVWK

Apart from these codes there are well-known publications about this matter by: !  L.C. Peng, Stress Analysis Methods for Underground Pipelines ( Peng’s papers are also added to the course material) !  G. Kruisman, Influence of the Soil in Avanced Buried Pipeline Flexibiltiy Analysis


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Contents Soil properties & classification







Soil Classification According to Grain Size Soils can be classified according to the size of the grains

!  Most basic classification of soil is based grain-size.

!  Soils with large grains are called “gravel” and soils with small grains “sand”.

!  Internationally it is defined that sand contains grains larger than 0.063mm and smaller than 2mm.

!  Gravel contains grains with sizes between 2mm and 63mm.

!  Grains smaller than 0.063mm are called “silt”.

!  Grains smaller than 0.002mm are called “clay”.


0.063 mm

2 mm

63 mm

0.002 mm

300 mm

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Soil Classification Diagram The grain-distribution diagram contains the distribution of the various grain sizes

!  A steep curve indicates that the soil grains are similar of size (uniform soil).

!  A flat curve means that the soil consits of various grain sizes.

!  For grains larger than 0.05mm the distribution diagram may be determined by means of seaves.

!  The uniformity coefficient is defined by the following ratio:

!  Values of Cu < 2 indicate that the soil is bad or discontineously “graded”.


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60

DDCU =

well graded

bad graded

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Porosity, Void Fraction & Water Saturation Parameter Fundamental soil composition parameters

!  “Porosity of Soil” (n): void volume between the grains devided by the total soil volume:

Most soils have porosity numbers between 0.30-0.45. When porosity is small soil is “closely packed”, when large soil is “losely packed”.

!  A similar parameter to describe the porosity of the soil is “Void Fraction” (e):

!  Water Saturation Parameter (S) is the water volume devided by the void volume:

soil

void

VV

n =

5236.0=n

2595.0=n


grain

void

VV

e =

void

water

VV

S =

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Classification According to Soil Density Dry, wet, grain and total soil density

!  Dry soils have a dry density (ρdry) and wet soils have a wet density (ρwet) .

!  The dry density should not be confused with the density of the grains (ρgrain) itself.

!  To illustrate this sand for instance has a grain density typically around: ρgrain=2650 kg/m3. The dry density of sand as a bulk itself is typically ρgrain=2000 kg/m3.

!  Based on earlier defined parameters the total density (ρ) of the soil can be expressed as:


ρdry ρwet

gngnS grainwet ⋅⋅−+⋅⋅⋅= ρρρ )1(

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The Relative Soil Density The relative soil density is a measure how well soil may be compacted

!  The relative density (RD) is an indicator of the “compaction ability” of the soil and depends on the void fraction:

!  Soils with values of (RD) < 0.5 can easily be compacted.

!  Tests may be used to determine the relative density of the in-situ soil. Example os such test is the “Proctor Test”.


( )( )min,max,

min,max,

minmax

max

drydry

drydry

eeeeRD

ρρρ

ρρρ

−⋅

−⋅=

−

−=

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Other Soil Parameters & Properties Chemical composition and soil cohesion

!  Chemical composition of the soil (content of minirals; organic

particles, ect). Sands and gravels consit for instance out of quartz, felspar, mica spots. Clays contain next to above mentioned minirals also so called clay minirals (kaoliniet, montmorilloniet, illiet).

!  Cohesion is another property of the soil. Cohesion indicates that loads may be transferred by for instance roughness or attraction forces between grains in the soil. Examples are:

1.  Electrostatic forces in stiff clays, 2.  Root cohesion (which may be caused by vegetation). 3.  Negative capillary pressure


International Soil Classification Table Examples of international soil classifications

!  Classification attempts have been made to derive a “global” soil classification table.

!  A well known (international) classification system is shown in the table on the top right; for which a two letter designation is given to the soil.

!  More extended classification tables give also measures for: the compaction properties of the soil and other useful guidelines.

!  Classifications tables are found in ASTM D2487, NEN3650, DIN18196.


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Contents Some basics of soil mechanics







Macroscopic Stresses on Soil Elements Soils can only be loaded by compression

!  On soil stresses can work similar to other materials. !  Soils however can only accomodate “compression”

stresses not tensile stresses. !  For wet soils it is true that a large part of stresses are

accomodated by the water content in the soil. !  The water content inside the soil cannot accomodate

shear stresses; however the soil itself can.

!  Typical (macroscopic) stress tensors working on an arbitatry soil element are shown on the right.


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Microscopic Soil Stress Distribution Loads in a wetted soil are transferred by the water and contact between grains

!  When a soil element is subjected to a uniform normal stress (σ) as shown in the figure on the right stresses can be accommodate by two effects:

1.  water pressure 2.  soil contact force

!  The nett stress is:

!  p is the fluid pressure in between the voids

!  σ" is called the “effective (grain) stress”

!  Formulas were first derived by “Terzaghi”

p

p p

p Fcontact = σ”*A

σ σ

σ σ p−=σσ"


Example of Vertical Stress in a Soil Layer Application of Terzaghi’s formula

!  According to Terzaghi the effective grain stress in a soil can be found as the difference between total stress and water pressure.

!  The total weight of the soil below the “freatic surface” is: ρwet*Hwet. In which ρwet is the volume weight of the wet soil and Hwet is depth of the wet soil layer.

!  The total weight of the soil above the freatic surface is: ρdry*Hdry. In which ρdry is the volume weight of the dry soil and Hdry is depth of the dry soil layer.

!  The effective grain stress then becomes:

Hdry

Hwet


wetwaterwetwetdrydry HgHHgp ⋅⋅−⋅+⋅⋅=−= ρρρσσ )("

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Shear Stress in Soils The ability to resist shear stresses depends on the friction and cohesion

!  When cohesionless soils are poured to the ground from above it will spread due to gravity. Because of friction the area of spread is limited creating an angle of repose (φ) at the balanced state.

!  From this experiment the friction force that resists the shear loads may be calculated and the internal friction coefficient (µ) of the soil may be determined:

!  The friction resistance (s) of any soil in any plane is then expressed as:

!  The angle (φ) is also called the soil angle of internal friction.

ϕµϕµµ tancos =→⋅⋅=⋅= wnf

cns +⋅= )tan(ϕ

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The Horizontal Stress in a Soil at Rest The horizontal stress in a soil is directly related to the vertical stress

!  At rest the vertical soil load induces also a horizontal load due to contraction effect.

!  The ratio σ’’h/σ’’v is a constant known as coefficient of neutral earth pressure at rest (K0).

!  Values for K0 are typical between 0.5 and 1.

!  Sometimes Jaky’s correlation is used:


)sin(10 ϕ−=K

σ’’h σ’’v

''0

''vh K σσ ⋅=

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The Max Horizontal Soil Stress Nnar a Retaining Wall Rankine determined the relation between max horizontal and vertical soil stress

!  When a burried object start to move the horizontal soil pressure changes.

!  Based on Rankin’s Theory (1857) the maximum increase and decrease in horizontal soil pressure on each side of the object may be calculated.

!  The active coefficient of soil pressure is: !  The passive coefficient of soil pressure is:


σ’’h+∆σ’’h σ’’v σ’’v

σ’’h-∆σ’’h

)2

45(tan2 ϕ−=AK)2

45(tan2 ϕ+=PK

''''''vAhh K σσσ ⋅=Δ− ''''''

vphh K σσσ ⋅=Δ+

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Contents Some basics of soil mechanics







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Modeling Soil – Pipe Interaction Soil stiffness & ultimate soil load are key parameters for a proper soil model

!  A buried pipeline is continuously supported and restrained by the soil.

!  When the pipe line moves inside the soil the soil exerts a reaction force counteracting the movement of the pipe.

!  The soil itself has a certain stiffness which describes the relation between applied load and displacement as in a regular material.

!  Another important property is the ultimate load which it can accomodate before it fails/collpases .

!  Knowing both soil properties are crusial when one is aiming to estimate soil pipe interaction and resulting pipe stresses.

!  Rigid buried pipe theory addresses longitudinal pipe deformations only.


Modeling Soil – Pipe Reaction in a Pipe Mechanical Model Soil reaction is often represented by spring type elements in a mechanical model

!  It is custom practise to approximate soil-pipe interaction by means of spring elements; which are applied along a mechanical model of the piping system.

!  These spring elements are placed along the “wire” model to simulate the distributed reaction of the soil.

!  The spings carry both information regarding the stiffness of the soil and the ultimate load it may accomodate.


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Representation of Maximum Soil Loads Three different soil loads may be developed

!  Generally pipe experiences 3 types of soil loads:

1.  Vertical Soil Load (Upward & Downward) 2.  Horizontal Soil Load 3.  Axial Soil Load (Friction)

!  When the pipe is in rest and does not move the loads extered on the pipe are in balance and are normally called: “neutral soil loads”

!  When on the pipe another external load is exerted neutral soil loads modify to balance the external loads: we then talk about: “active and passive soil loads”


Vertical Upward

Vertical Downward

Horizontal

friction

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Upward Soil Resistance Depending on Soil Prism Marston’s load theory may be used for vertical soil resistance

!  Vertical soil resistance can be described by the application of the “soil prism theory” also know as “Marston’s load theory”

!  This theory states that the soil resistance is determined by (a) the weight of a soil prism above the pipe and (b) the shear forces exerted on either sides of the prism.

!  The shear conditions depend on the installation layout of the pipe and soil; but in this case negative shear will be assumed.

!  Next to the soil prism the weight of the pipe needs to be taken into consideration as well.


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Derivation of Upward Soil Resistance Shear effects are found by integration of the loads on both sides of the prism

!  Shear stresses can be found by intergrating the friction along both side surfces of the prism.

!  Let’s assume cohesionless soil (c=0, e.g. sand); ϕ is the friction angle of the soil.

!  The upward soil resistance q [kg/m] is:

!  The weight of the prism is:

!  The shear along the prism is calculated using Rankine’s theory:

DHHKWSq AS ρρϕ +⋅=+= 2)tan()(


)tan(2 2 ϕρµ ⋅⋅=⋅⋅= HKNS A

N N

Hv ρσ =''

HDWS ⋅⋅= ρ

2

21 HKN A ρ⋅=

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Upward Soil Resistance for Deep Buried Pipes Marston theory does not apply for deep buried pipes

!  Marston’s method assumes that the “friction planes” run from the outer edges of the pipes towards grade level.

!  For deep buries pipes (H > 5*D /10*D) this is not true anymore.

!  The failure mechanism for deep buried pipes can be determined according to deep burried foundations; which is beyond the scope of this course.

!  These failure planes do not strech until the grade surface.


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Downward Vertical Soil Resistance Downward soil resistance requires the definition of the soil bearing capacity

!  When the pipe moves downwards the soil resistance can be determined from the “vertical bearing capacity”.

!  Detailed geotechinical evaluation is required to determine the vertical bearing capacity.

!  For a general idea the downward resistance can be roughly estimated to be as twice the horizontal resistance.

!  The vertical bearing capacity is the vertical load required to break the soil underneath the pipe over the full width of the pipe.

!  The failure mode is illustrated in the figure on the right.


Lateral Soil Resistance Lateral soil resistance restrains the pipe to move laterally

!  When a structure is buried it experiences lateral (horizontal) soil loads at rest.

!  There are numerous theories to describe the relation between the lateral load and the soil reaction.

!  We will discuss Rankine’s Method developed for retaining walls.

!  When the structure moves horizontally when buried the equilibrium loads change.

!  Also for buried non-pipe structures lateral soil pressure is of great relevance.


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Soil in Equilibrium without Lateral Movement In equilibrium there is a balanced lateral load called the neutral lateral load

!  When a pipe is buried it also experiences a horizontal soil load at rest.

!  The horizontal equilibrium loads (qneutral) at rest are called the “neutral horizontal loads”.

!  Netto no horizontal force works on the pipe.

!  Lateral loads can be represented by 2 symmetric “wedges” shearing along planes A-A.


qneutral qneutral

A-A A-A

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Passive & Active Lateral Soil Resistance When the pipe moves laterally the neutral soil load is altered in an active and passive load

!  To move the pipe horizontally inside the soil a load (Q) is required.

!  In front of the pipe the neutral load increases to resist this movement; “passive soil resistance”.

!  At the back side of the pipe the neutral soil load decreases: “active soil resistance”.

!  In most cases the active soil load (qactive≈0) can be ignored; since a void is created direclty next to the pipe and no load is transfered to the pipe.

!  Lateral stresses can be represented by 2 asymmetric “wedges” shearing along planes A-A & B-B.

qpassive qactive

activepassive qqQ −=

Q

A-A B-B

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Lateral Loads and “Wedge Effect” Example of an experiment


Maximum Passive & Active Lateral Soil Resistance Mohr-Coulomb theory may be used to calculate the passive and active loads

!  To calculate the maximum active and passive horizontal loads the equilibrium of the forces along the shear planes of the wedge may be determined.

!  Theory assumes that the soil fails at a friction surface planes Ѳ.

qpassive qactive

Q

S = shear force (friction) N= normal force Ws= prism weight load Ѳ = slip plane


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Determining the maximum lateral soil load Maximum soil load is found by differentiation

( ) )2

45(tan21 22 ϕγ ++= DHqpassive

qpassive


θθ sincos0: NSqF passive −−=→Σ

θθ cossin0: NSWF S −+=↑Σ

( ) )tan(*cot21 2 ϕθγ −Θ+= DHqpassive

(B) Solving for qpassive:

(C) Determining Maximum qpassive

Expressed as Rankine’s Coefficient Kp:

(A) Load Equilibrium: :

)2

45(tan2 ϕ+=PK

θ

( ) )tan(21 2 Θ+= DHWS γ

( ) ppassive KDHq 2

21

+= γ

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Lateral Soil Resistance For Deep Buried Pipe Rankine’s model is not valid for deep buried pipes

!  The wedge model is valid only when the depth of the cover is less than the diameter of the pipe.

!  When it is applied to larger cover depths it over estimates the lateral resistance.

!  However for a cover depth equal to 3 times the diameter of the pipe the overestimate is only 10%.

!  For deeper buried piping the failure mode is tunneling and pipe punching.

!  For this case the soil resistance is typically much smaller than according to the wedge theory.

!  Special theory is required to define the ultimate load for this cases, which beyond the scope of the training.


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Axial Soil Resistance Axial soil resistance is caused by the effects of friction

!  Axial loads are generated by the shear resistance developed over the pipe outer surface.

!  Shear resistance comprises two parts: 1.  cohesive forces 2.  friction forces

!  A typical soil pressure distribution on a pipe is

shown in the figure on the right.

!  A more practical approach is to idealize the methodology and determine the axial friction based on the vertical loads as shown in the figure on the right.


An Equation for Axial Soil Resistance Axial soil resistance is proportional to the weight of the soil cover and pipe

!  In the case of an idealized model the axial resistance (f) can be determined by the following expression:

!  The active soil force is defined as:

!  The resulting axial resistance force is than:

!  (µ) is called the friction coefficient (not to be confused with the soil friction coefficient).

( )pS WWf += 2µ

DHWS ρ≈

( )pWDHf += ρµ 2Typical friction values of µ:

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Pipe/Soil Stiffness Definition Pipe/Soil stiffness defines the interaction stiffness between soil and pipe

!  Stiffness describes the amount of soil displacement that is required to reach ultimate soil load.

!  As can be seen from the stress-strain curve the behavior is generally non-linear.

!  Soil stiffness values may be determined from soil investigation.

!  In pratise the non-linear behavior is approximated by a so-called bi- or tri-linear curve as can be seen from the graph on the right.

!  The strain at which maximum (ultimate load) is reached is also called the “yield displacement”. Some sources report that this value is about 1.5 – 2% of the pipe bottom depth.


eq d

qK =

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The Axial Pipe/Soil Stiffness The definition of the axial pipe stiffness is similar

!  Axial friction can also modelled as a bi-linear curve as is shown on the right.

!  The movement before full fracture is reached, is considered to me small or instantenous in most mechanical representations of axial friction.

!  After reachring full axial load the load remains unchanged.

!  The relation between load and displacement in the linear part is desribed by:

ef d

fk =


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Contents Flexible pipe – soil interaction







Flexible Pipe – Soil Interaction Ring deformation is especially relevant for flexible pipes

!  Flexible Pipes can also experience significant circumferential deformation effects due to soil load.

!  Exessive circumferential deformation of the pipe may lead to collapse/fracture of the pipe.

!  Determining the amount of ring ovalisation is therefore a key factor in the design of a flexible pipe.


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Pipe Ring Deformation and Stresses Ring deformation is especially relevant for flexible pipes

!  M. Sprangler (student of Marston) observed that Marston Theory for vertical loads on buried pipes was not adequate for flexible pipes.

!  Flexibile pipes provide little inherent stiffness in comparison to rigid pipes, but still perform remarkably well when buried.

!  The ability of flexible pipes to support vertical loads is dervied from:

1.  The redistribution of loads around the pipe 2.  It generates passive pressures at the sides of the pipe

when it moves outward against the earth

!  His derived formula is called “Sprangler’s” or “Iowa“ formula which relates ring deflection (∆X) to the vertical soil loads.


∆X

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Some Notes on the Iowa Formula The Iowa formula includes 2 stiffness effects

!  If one studies the Iowa equation one can note that the ring deflection is resisted by 2 effects:

1.  Pipe ring stiffness 2.  Stiffness of the surrounding soil

!  The bedding constant (K) accounts for the the supporting “bed” underneath the pipe.

!  Typical values for different bedding angles are shown in the table on the right.

!  Since soil consolidates at the sides of the pipe over time the factor (DL) is used to account for the additional ring deflection.

(A) Pipe ring stiffness (B) Soil lateral stiffness


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Contents End






!  End


Dynaflow Buried Piping Training


!  Two days buried lines with CAESAR II training course.

!  17 - 18 September 2012.

!  You can register using our webpage. www.dynaflow.com

53 Copyright 2011 @ Dynaflow Research Group

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dynaflow lecture: buried piping - dynaflow research

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