annex xii final report effects of loads on asset ... · 3. critical aspect iii: transferability of...

International Energy Agency Technology Collaboration Programme on

District Heating and Cooling including Combined Heat and Power

Annex XII final report

Effects of Loads on Asset Management of the 4th

Generation District Heating Networks

Date of publication: 31.03.2020

Authors: Ingo Weidlich, Gersena Banushi, Nazdaneh Yarahmadi, Ignacy

Jakubowicz, Jan Henrik Sällström, Alberto Vega, Jooyong Kim, Yeon Soo Kim,

Øyvind Nilsen, Thomas Grage, Georg Schuchardt, Fang Yang


Effects of Loads on Asset Management of the

4th Generation District Heating Networks

2

This project has been independently funded by

the International Energy Agency Technology Collaboration Programme on

District Heating and Cooling including Combined Heat and Power

(IEA DHC).

Any views expressed in this publication are not necessarily those of IEA DHC.

IEA DHC can take no responsibility for the use of the information within this publication,

nor for any errors or omissions it may contain.




3

Executive Summary

This research project investigates the influence of future mechanical and thermal load

spectra on the service life of pre-insulated bonded single pipes, representing the

majority of currently operating DH pipelines, based on the 3rd generation technology

(3GDH). To minimize heat losses, these pipes have a composite cross-section with

three different material layers, including the steel pipe for the water supply, the

insulation foam of polyurethane (PUR), and an outer coating of High Density

Polyethylene (HDPE), interacting with the surrounding soil. The stiffness of the PUR

foam and its constant adhesion to the steel pipe are essential to properly transmit at the

HDPE coating the friction stresses from the surrounding soil. 3GDH pipes undergo

large temperature variations, associated with significant cyclic loading at the soil-pipe

interface, as well as within the pre-insulated DH pipe system, leading to accumulated

material damage and ageing.

Conversely, 4th generation DH networks (4GDH) operate at lower temperatures, also

integrating renewable energy sources, that are more volatile than the traditional ones,

based on 3GDH technology. The lower levels of operating temperature and the

increased amount of cyclic loading influence ageing and the service life of 4GDH

networks, requiring proper analysis of the system performance. This is fundamentally

important, in order to guarantee an efficient operation of DH networks, optimizing the

durability of the thermal insulation and the mechanical strength of the piping system.

Moreover, the elevated levels of operating temperature in 3GDH had led to the

development of pipe materials with worse thermal properties, able to sustain the high

temperature of the accelerated ageing tests, required by the European standards.

These do not address either the testing nor the design of 4GDH, highlighting the need

to further investigate the combined effect of increased volatility, and decreased thermal

loading associated with the integration of renewable energy sources in the DH network.

This research project aims to investigate the lifetime of 4GDH pre-insulated bonded

single pipes, developing a new approach as a function of the increased cyclic

mechanical and thermal loads, and the decreased thermal ageing.




4

The present report is structured in different chapters, describing the research carried

out within each workpackage of the research project.

Chapter 1 reports the fatigue analysis of the steel service pipe according to the

Palmgren-Miner rule implemented in EN 13941, considering temperature history data

collected from traditional and 4GDH pipe networks in Germany, Sweden, Norway, and

South Korea.

Chapter 2 describes the state-of-the-art on fatigue and damage accumulation theories

for the steel pipe material, identifying critical aspects in using linear and non-linear

theories. Moreover, the axial shear strength from naturally aged pipes is analyzed,

identifying the main parameters influencing the shear strength degradation of pre-

insulated piping systems.

Chapter 3 reports the experimental investigation of the adhesion strength of straight

pipes under the combined effect of thermal ageing and cyclic mechanical loading. The

adhesion strength of the aged pipes was evaluated using the plug method introduced

by RISE, while the degradation of the PUR material of some samples was analysed

further, using the Fourier transform infrared (FTIR) technique.

Chapter 4 reports the results of the tests performed on naturally aged pipes specimens,

gathered from four DH branches of KDHC in Korea, for measuring the adhesion

strength of the PUR foam.

Chapter 5 examines the consequences of the research project outcome for improving

the current network design, and asset management of 4GDH systems.

The analysis results indicate that the lifetime of 4GDH pipelines is expected to increase

due to the lower operating temperature, and the low impact of thermal loading volatility

in the network, compared to conventional DH. To accurately estimate the fatigue

damage, the measuring time interval in the temperature data should be sufficiently

small, highlighting the importance of data logging process. The performed accelerated

ageing tests demonstrated that the combined effect of mechanical loading and thermal

ageing accelerates the rate of chemical degradation of the PUR foam, leading to a

faster deterioration of the mechanical adhesion strength. The analysis of the naturally

aged DH pipelines showed that, in addition to the ageing time, the shear strength of DH

pipes depends on the temperature history, decreasing with the level of operating

temperature and amount of fluctuation. Finally, it is recommended to document the




5

operating temperature history and the most important properties of the pipe system

before installation, as well as during operation, contributing to better predictive

maintenance, and subsequent reduction of economic risks for replacement and repair.

In conclusion, the obtained results give a better understanding of the performance of

traditional and 4GDH pipelines in operation, that need to be suitably considered in the

engineering design standards of DH networks, contributing to a more sustainable and

energy efficient infrastructure.




6

Table of Contents

Executive Summary ....................................................................................................... 3

1 Identification of load characteristics and estimations of future conditions................ 9

1.1 Fatigue analysis of the steel service pipe .................................................... 9

1.1.1 The Palmgren-Miner rule ........................................................................... 13

1.2 Cycle counting methods ............................................................................ 15

1.2.1 Rainflow counting algorithm....................................................................... 16

1.3 Fatigue analysis of the collected sample data ........................................... 17

1.4 Results and discussion.............................................................................. 24

2 Investigation of fatigue theories and shear strength experience ............................ 28

2.1 Comparison of fatigue theories for steel .................................................... 28

2.1.1 State of the art – linear fatigue theories for ductile materials ..................... 29

2.1.2 Non-linear fatigue theories for ductile materials......................................... 31

2.1.3 Summary and evaluation of different theories of fatigue accumulation...... 34

2.2 Estimating fatigue resistances for future load conditions........................... 35

2.2.1 Definition of illustrative mechanical load spectrum .................................... 36

2.2.2 Quantification of fatigue resistances.......................................................... 43

2.2.3 Summary on the quantification of fatigue and interpretation of results ...... 44

2.2.4 Interpretation of results and evaluation of usability – critical aspects ........ 48

2.3 Compilation of shear strength data from naturally aged pipes................... 49

2.3.1 Naturally aged pipes.................................................................................. 50




7

2.3.2 Artificially aged pipes................................................................................. 55

2.3.3 Summary ................................................................................................... 57

3 Investigation of thermal ageing in combination with cyclic mechanical loads ........ 58

3.1 Background ............................................................................................... 58

3.2 Choice of objects and conditions ............................................................... 59

3.3 Selection of mechanical loading ................................................................ 59

3.4 Experiments............................................................................................... 61

3.4.1 Mechanical testing..................................................................................... 63

3.4.2 Fourier Transform Infrared spectroscopy................................................... 64

3.5 Results....................................................................................................... 65

3.5.1 Mechanical adhesive strength ................................................................... 66

3.5.2 Fourier-transform infrared spectroscopy.................................................... 69

3.6 Interpretation of results and evaluation of usability.................................... 73

4 Field tests .............................................................................................................. 74

4.1 Field selection and data acquisition........................................................... 74

4.1.1 Selecting and test preparation of naturally aged DH pipes........................ 74

4.1.2 Measuring the shear strength .................................................................... 79

4.2 Results....................................................................................................... 80

4.2.1 Shear strength of naturally aged DH pipes................................................ 80

4.2.2 FTIR analysis of naturally aged DH pipes.................................................. 95

5 Consequences for network design and asset management strategy..................... 97

5.1 Analyze consequences and impacts of future loads on the service pipe... 97




8

5.2 Consequences and impacts of future loads on the adhesion between

service pipe and insulation........................................................................................ 97

5.3 Recommendations concerning network design and asset management of

4th generation DH systems....................................................................................... 98

Concluding remarks ..................................................................................................... 99

Acknowledgments ...................................................................................................... 100

Bibliography................................................................................................................ 101

Appendix A: fatigue analysis results of the temperature data..................................... 105




9

1 Identification of load characteristics and estima tions of

future conditions

First, this section introduces the fatigue analysis of the steel service pipe, using the

failure criterion given by the Palmer-Miner rule, implemented in the European Standard

EN 13941, and the different cycle counting methods, including the rainflow counting

algorithm. Second, the fatigue analysis is performed considering the collected

temperature history data of 3GDH networks from different countries, provided by the

project partners. These results are then compared with those obtained from the

collected temperature history data on 4GDH pipes, in order to estimate the trend for

future load spectra, characterizing the energy transition in the heat sector.

1.1 Fatigue analysis of the steel service pipe

Fatigue is defined as material failure, caused by crack initiation and progressive growth,

due to repeated cyclic loading. At present, there are three major approaches for fatigue

design and analysis, like the traditional stress-based approach, strain-based approach,

and fracture mechanics approach (Dowling, 2013). The design standard of DH pipes

(EN 13941) uses the stress-based approach for the fatigue analysis of the steel service

pipe. Herein, the lifetime of a test specimen or an engineering component, subjected to

fully reversible cycle of stress range S, is measured in terms of the corresponding

number of loading cycles to failure N. Thus, the material fatigue performance is

characterized by the SN curve, also known as a Wöhler curve, representing the

magnitude of a cyclic stress, in terms of stress range (S) versus the number of cycles to

failure (N).

The lifetime where High-Cycle Fatigue (HCF) starts varies with material, typically in the

range 102 to 104 cycles, characterized by small elastic stress amplitudes. Conversely,

Low Cycle Fatigue (LCF) is caused by a relatively small number of cycles, on the order

of 102, associated with significant amounts of plastic deformation. Repeated heating

and cooling can cause a cyclic stress due to differential thermal expansion and

contraction, resulting in thermal fatigue (Dowling, 2013; Frederiksen and Werner, 2013).

In contrast to classical high or low cycle fatigue (Figure 1.1), steel structures subjected

extreme loading conditions, like earthquakes, may experience Ultra Low Cycle Fatigue

(ULCF), involving fewer than ten cycles with large strain amplitudes, on the order of ten

or more times the yield strain (Kanvinde et al., 2013; Fernandes et al., 2018).




10

Figure 1.1: Definition of the material failure mechanism as a function of the number of cycles (Bleck et al., 2009).

Fatigue strength is expressed in terms of series of SN curves (Figure 1.2), representing

the relationship between the stress range (S) and the number of cycles to failure (N).

Each SN curve refers to a particular construction detail, considering the effect of local

peak stresses (EN 13941, 2019).

Figure 1.2: SN curve for for steel service pipe components with butt weld and fillet weld (EN 13941, 2019).




11

The SN curves have been derived from fatigue test data obtained from appropriate

laboratory specimens tested under stress control or, for applied strains exceeding yield

(low cycle fatigue), under strain control. Continuity from low to high cycle regime is

achieved by expressing low cycle fatigue data in terms of the pseudo-elastic stress

range (i.e. strain range multiplied by elastic modulus, if necessary corrected for

plasticity).

Generally, SN curves vary with the material and its pre-processing. They are also

affected by mean stress, member geometry, especially the presence of notches,

surface finish, frequency of cycling, residual stress, thermal and chemical environment

(Dowling, 2013). The latter can cause stress corrosion cracking (SCC), initiating fatigue

earlier than expected, if the steel undergoes variable thermal loading. The presence of

water within a fatigue crack, as well as low-frequency temperature variations, typical of

district heating, adversely impact fatigue crack growth rates, by increasing the time for

environmental interactions per stress cycle (Christensen et al., 1999).

Most piping standards (EN 13941; EN 13480-3; ASME 31.1; ASME 31.3) are based on

the full-scale fatigue tests performed by Markl in the 1950's on a limited number of pipe

components, including straight pipes, bends and tees (Markl, 1952; 1955). The results

were a set of SN curves referring to an equivalent straight pipe, and the flexibility and

stress concentration factors for different pipe components. These factors, since their

introduction in the piping standards, have remained unchanged up to date. However,

full-scale fatigue tests are very expensive, requiring a considerable number of test

specimens to determine a statistically reliable SN curve. On the other hand, the stress

concentration factors can be evaluated by analytical and numerical methods, as hot-

spot values, and further compared to SN curves obtained from small scale material test

specimens. The latter must be further corrected for practical use with a number of

coefficients, taking into account the effects of rougher surface finish, temperature,

mean stress level, plastic strains, and electro-chemical environment (Randløv et al.,

1996; Christensen et al., 1999; Penderos, 1996).

The current design standard of DH systems (EN 13941, 2019), proposes the following

expression to evaluate the SN curve for the steel service pipe, based on the

aforementioned Markl's experimental work (Markl, 1952; 1955):




12

mNkS /1−⋅= (1.1) m

S

kN

= (1.2)

For low alloyed carbon steel (σy ≤ 360 N/mm2) normally used for preinsulated pipes the

factors k = 5000 N/mm2 and m = 4 can be used giving:

4/15000 −⋅= NS N/mm2 (1.3) 4

5000

=S

N (1.4)

Clearly, the SN curve should be used in combination with stress intensification factors

calculated or measured as hot-spot values. The curve includes the effect of a butt weld,

as well as reductions for rolled skin, temperature, and plastic yield (Figure 1.2). The

effect of the electro-chemical environment is not included, although a combination of

plastic strains and high pH-values of the heat carrier, characterizing district heating,

may severely reduce the fatigue life of DH pipelines (Christensen et al., 1999).

The curve presupposes that the stress range is calculated assuming a linear elastic

material behavior for the steel, also above yield.

The safety factor is applied by dividing the calculated number of cycles with γfat (Table

1.1), as a function of the project class, depending on the risk and consequences of

damage to the society or environment.

Table 1.1: Partial safety factor for action cycles

Project class A Project class B Project class C

γfat 5 6.67 10

The failure criterion is expressed by the Palmgren-Miner hypothesis:

fatfi

i

N

N

γ1≤∑ (1.5)

where:

Ni is the number of cycles with stress range Si during the required design life;

Nfi is the number of cycles of stress range Si to cause failure.




13

1.1.1 The Palmgren-Miner rule

Considering a situation of variable amplitude loading, (Figure 1.3), where a certain

stress amplitude σai is applied for a number of cycles Ni, and the number of cycles to

failure from the SN curve for σai is Nfi, then the fraction of life used is Ni/Nfi. The

Palmgren–Miner rule states that fatigue failure is expected when the life fractions

(Ni/Nfi), corresponding to all levels of stress amplitudes σai, sum to unity:

13

3

2

2

1

1 ==+++ ∑fi

i

fff N

N

N

N

N

N

N

NL (1.6)

Figure 1.3: Use of the Palmgren–Miner rule for life prediction for variable amplitude loading which is completely reversed (Dowling, 2013).

This simple rule was used by A. Palmgren in Sweden in the 1920s for predicting the life

of ball bearings. However, it was not widely known until its appearance in 1945 in a

paper by M. A. Miner (Dowling, 2013), subsequently finding large application in the

fatigue analysis and design of railways, bridges, aircraft and offshore structures.

In the design of district heating pipelines, the temperature history is used to calculate

the stress history. For simplicity, it is assumed that the stress variation Si is proportional

to the temperature variation ∆Ti:

ii TcS ∆⋅= (1.7) m

ifi Tc

kN

∆⋅= (1.8)

where, k and m are the constants defining the SN curve (Equation (1.1)), while c is the

proportionality constant between stress range (Si) and temperature variation (∆Ti):




14

( )i

T

T

i

i

T

dTE

T

Sc

i

∆

⋅=

∆=

∫0

α (1.9)

where the Young's modulus E and the linear thermal expansion coefficient α vary

linearly with the operating temperature, according to EN 13941 (2019). Consequently,

also c increases with temperature, but for simplicity in the design calculations, it can be

assumed as constant, equal to c = 2.505 N/mm2/K, considering an installation and

operation temperature equal to T0 = 10°C and Ti = 120°C, respectively.

The Palmgren-Miner rule can be expressed as:

∑∑ ∆⋅

= mii

m

fi

i TNk

c

N

N (1.10)

Moreover, the temperature history is simplified by calculating the number of full

temperature cycles N0, for the reference temperature ∆Tref, giving the same

accumulated damage as the temperature history presumed for the system:

mref

mm

ii

m

fi

i TNk

cTN

k

c

N

N ∆⋅

=∆⋅

= ∑∑ 0 (1.10)

∑ ∆⋅∆

= miim

ref

TNT

N1

0 (1.11)

therefore, the number of full temperature cycles N0 only depends on the coefficient m,

the reference temperature ∆Tref and the temperature history (Randløv et al., 1999;

EN 13941, 2019).

The design standard EN 13941 (2019) assumes as a reference temperature

∆Tref = 110°C, corresponding to a maximum number of equivalent load cycles N0,max, for

a straight pipe, given by:

fatfatfat

m

mreffi

i

m

mref c

k

TN

N

c

k

TN

γγγ1084121

2.505

5000

110

11114

4max,0 =⋅

=⋅

∆=⋅

∆= ∑ (1.12)




15

Clearly, the design standards of DH systems, must take into account their typical

mechanical behavior, that differs from other types of pipelines, such as the elevated

axial stresses due to the soil resistance, counteracting pipe thermal expansion.

According to EN 13941 (2019), the number of full action cycles, chosen in the

calculation for pipelines in normal operation, should not exceed the lowest number of

equivalent full action cycles indicated in Table 1.2 for the relevant years in operation.

Table 1.2: Equivalent full action cycles for m = 4 and ∆Tref = 110°C (EN 13941, 2019).

Number of full action cycles N 0 Pipeline characteristics 30 years operation 50 years operation

Transmission pipelines 100 to 250 170 to 420 Distribution pipelines 250 to 500 420 to 840 House connections 1000 to 2500 1700 to 4200

1.2 Cycle counting methods

Various counting methods have been developed to reduce cyclic time histories to some

simple form of cycle count for analysis and testing purposes. Two parameters counting

methods, such as range-pair-range, rainflow, and racetrack methods, have been

developed, reflecting some aspects of loading sequence. Rainflow counting is perhaps

the most widely accepted method for the identification of fatigue critical events and is

useful when pursuing a basic understanding of material behavior (Rice, 1997).

Most practical rainflow counting algorithms are based either on the 'availability matrix'

or the 'vector' mathematical concepts (Dowing and Socie, 1982). The 'availability

matrix' algorithm, developed by Wetzel (1971), requires the input signal to be divided

into a finite number of bands, used to define the numerical value of the range and mean

of each reversal. Corresponding to each band is an element in the availability matrix.

'Vector' based rainflow counting algorithms use a one dimensional array to keep track

of those peaks and valleys which have not formed a closed loop. In other words, once a

closed loop has been determined, the peak and valley associated with it can be

eliminated from the vector. First proposed by Matsuishi and Endo (1968), this approach

is generally regarded as the method leading to the best estimation of fatigue life. Due to

its importance, many other procedures, essentially equivalent, have been proposed in

literature (Downing et al., 1976; Okamura et al., 1979).




16

Finally, the ASTM standard E1049-85 reports a compilation of acceptable procedures

for cycle-counting methods employed in fatigue analysis (ASTM, 2011). The latter is

also referenced in the ISO 12110-2 (ISO 12110-2, 2013), presenting cycle counting

techniques and data reduction methods used in variable amplitude fatigue testing.

1.2.1 Rainflow counting algorithm

In performing a rainflow cycle counting, a cycle is identified and if it meets the criterion

shown in Figure 1.4. A peak-valley-peak or valley-peak-valley combination X-Y-Z in the

loading history is considered to contain a cycle if the second range, ∆σYZ, is greater

than or equal to the first range, ∆σXY. If the second range is indeed larger or equal, then

a cycle equal to the first range (∆σXY) is counted. The mean value for this cycle,

specifically the average of σX and σY, is also an important parameter.

The complete procedure is described as follows, using the example of Figure 1.5:

Rainflow counting starts at the beginning of the recorded temperature variations, using

the criterion illustrated in Figure 1.4. If a cycle is counted, this information is recorded,

and its peak and valley are assumed not to exist for purposes of further cycle counting,

as illustrated for cycle E-F in (c). If no cycle can be counted at the current location, it is

proceeded until a count can be made.

Counting is complete when all of the history is exhausted. For this example, the cycles

counted are E-F, A-B, H-C, and D-G, with ranges and means as tabulated at the

bottom of Figure 1.5. For lengthy histories, it is convenient to present the results of

rainflow cycle counting as a matrix giving the numbers of cycles occurring at various

combinations of range and mean.

Figure 1.4: Condition for counting a cycle with the rainflow method (Dowling, 2013).




17

Figure 1.5: Example of rainflow cycle counting (Randløv et al., 1996; Dowling, 2013).

Commonly, the rain flow cycle counting for DH pipes is calculated considering directly

the temperature history, instead of the stress history, due to the assumed linear

relationship between the stress and temperature variations (Randløv et al., 1996).

1.3 Fatigue analysis of the collected sample data

First, this section presents 19 pairs of temperature history data from conventional DH

networks (in supply and return), gathered in different countries from the project partners.

Specifically, the Korea District Heating Corporation (KDHC) collected data from the two

locations of Goyang and Daegu Branch in South Korea, the Research Institutes of

Sweden AB (RISE) from the Gothenburg Energy company in Sweden, the Fortum Oslo

Varme AS (Fortum) from the Vika heat plant as well as different house connections in

Norway, and the German District Heating Research Institute (FFI) from the DH heating

network in Germany. Table 1.3 summarizes the characteristics of the pipe samples,

where the collected temperature data have been recorded, numbering the measured

points from 1 to 19, and indicating the supply and return pipe with "S" and "R" before




18

the number. Table 1.4 reports the information on the measured time period, including

the recording time interval ∆t, corresponding to each measured point.

For these temperature data, the measuring time ranges from 1 year to 11 years, except

for the single pair of data (S18/R18) collected in Germany, at the HKW network in

Hannover in 2011, over a period of 4 months. Moreover, the temperature data gathered

in South Korea and Sweden are recorded every hour (∆t = 60 min), while those in

Norway and Germany every 5 min and 15 min, respectively (Table 1.4).

Second, the section presents temperature data measured at different locations of a

4GDH network in Germany, heated with solar energy, as indicated in Table 1.5 and

Table 1.6. These temperature data have been collected within the recent German

research project "Solar district heating for the Brühl district in Chemnitz –

accompanying research (SolFW)" in 2018. The measured points regard different

locations the system including the main (S20/R20) and distribution (S21/R21) pipelines,

the two-zone thermal energy storage, the two solar collector fields (S22/R22; S23/R23),

and a house connection (S24/R24), illustrated in Figure 1.6 (Shrestha et al., 2018). The

measuring time for these data is one year, and the corresponding recording frequency

is one minute (∆t = 1 min), but for the house connection (∆t = 5 min).

This solar 4GDH system, is regulated so that the supply temperature in the distribution

network ranges between 75°C and 90°C, depending on the outdoor temperature. When

the solar heat is not sufficient to satisfy the consumers demand, the required heat

generation is complemented with a combined heat and power (CHP) plant, feeding the

heat directly into the distribution DH network.

The gathered temperature history data have been processed in Matlab (Mathworks,

2019), using the implemented rainflow cycle counting algorithm, for the fatigue analysis.

Then, the resulting rainflow cycle matrix, is used to evaluate the number of equivalent

full temperature cycles N0, using the Palmer-Miner rule. The latter is calculated for two

different values of the reference temperature ∆Tref, ∆Tref = 110°C, and ∆Tref = Tmax -

10°C (maximum temperature at the measuring point - 10°C), as also assumed in

Randløv et al. (1996).

Appendix A reports in detail the evaluated rainflow cycle matrix, as well as the number

of equivalent full temperature cycles N0 corresponding to each temperature history data.




19

Table 1.3: Characteristics of the measured points for the collected temperature history data regarding the steel pipe in conventional DH pipelines (3GDH).

Temperature history data

DH pipe Category N. mes. point *

Direction DN [mm]

OD [mm]

ts [mm] H [m]

S1 supply 65 140 4.5 1.6 Daegu branch House connection

R1 return 65 140 4.5 1.6

S2 supply 80 160 4.5 2.1

KDHC (South Korea)

Goyang branch House connection R2 return 80 160 4.5 2.1

Main S3 supply 200 315 4.5 1.7 Danska vägen

Main R3 return 200 315 4.5 1.7

Main S4 supply 400 630 6.3 2.5 Hisingsbron

Main R4 return 400 630 6.3 2.5

Main S5 supply 500 710 6.3 2.0-2.5 Marieholm

Main R5 return 500 710 6.3 2.0-2.5

Main S6 supply 300 500 5.6 1.5-2.0

RISE (Sweden)

Falutorget Main R6 return 300 500 5.6 1.5-2.0

S7 supply 50-500 125-710 0.6-1.5 Vika 2013 Main, Distribution

House connection R7 return 50-500 125-710 0.6-1.5

S8 supply 50-500 125-710 0.6-1.5 Vika 2016 Main, Distribution

House connection R8 return 50-500 125-710 0.6-1.5

S9 supply 65 76.1 2.9 0.6 Soerengkaia 153 Substation

R9 return 65 76.1 2.9 0.6

S10 supply 50 60.3 2.9 0.6 Brobekkveien 80 House connection

R10 return 50 60.3 2.9 0.6

S11 supply 100 114.3 3.6

Fortum (Norway)

Skøyen Terrasse 4 House connection

R11 return 100 114.3 3.6

Main S12 supply 300 323.9 5.6 0.6-0.8 COCA 2010

Main R12 return 300 323.9 5.6 0.6-0.8

Main S13 supply 900 914.0 10.0 - GKH 2010

Main R13 return 900 914.0 10.0 -

Main S14 supply 400-600 406.4-610 6.3-7.1 in conduit HKW 2010

Main R14 return 400-600 406.4-610 6.3-7.1 in conduit

Main S15 supply 200-700 219.1-711 4.5-8.0 0.6-0.8 KWH 2010

Main R15 return 200-700 219.1-711 4.5-8.0 0.6-0.8

Main S16 supply 300 323.9 5.6 0.6-0.8 COCA 2011

Main R16 return 300 323.9 5.6 0.6-0.8

Main S17 supply 900 914.0 10.0 - GKH 2011

Main R17 return 900 914.0 10.0 -

Main S18 supply 400-600 406.4-610 6.3-7.1 in conduit HKW 2011

Main R18 return 400-600 406.4-610 6.3-7.1 in conduit

Main S19 supply 200-700 219.1-711 4.5-8.0 0.6-0.8

FFI (Germany)

KWH 2011 Main R19 return 200-700 219.1-711 4.5-8.0 0.6-0.8

* N. mes. point = number of the measured point for the temperature data




20

Table 1.4: Characteristics of the collected temperature history data regarding the steel pipe in conventional DH pipelines (3GDH). N. mes. point* Start date Finish date Number of days

start-finish Number of

days recorded Number of

days missing Measuring

interval ∆t [min]

S1 01/01/2015 01/01/2018 1096 1096 0 60

R1 01/01/2015 01/01/2018 1096 1096 0 60

S2 01/01/2015 01/01/2018 1096 1096 0 60

R2 01/01/2015 01/01/2018 1096 1077 19 60

S3 27/03/2007 26/06/2017 3744 3744 0 60

R3 01/04/2009 26/06/2017 3008 3008 0 60

S4 01/12/2006 23/03/2018 4131 4131 0 60

R4 01/12/2006 23/03/2018 4131 4131 0 60

S5 11/01/2008 18/07/2017 3476 3476 0 60

R5 01/07/2007 18/07/2017 3671 3671 0 60

S6 01/12/2006 23/03/2018 4131 4131 0 60

R6 01/12/2006 23/03/2018 4131 4131 0 60

S7 01/01/2013 31/12/2013 365 365 0 5

R7 01/01/2013 31/12/2013 365 365 0 5

S8 01/01/2016 31/12/2016 366 366 0 5

R8 01/01/2016 31/12/2016 366 366 0 5

S9 20/08/2018 18/08/2019 364 364 0 5

R9 20/08/2018 18/08/2019 364 364 0 5

S10 30/08/2018 30/08/2019 365 365 0 5

R10 30/08/2018 30/08/2019 365 365 0 5

S11 30/08/2018 30/08/2019 365 365 0 5

R11 30/08/2018 30/08/2019 365 365 0 5

S12 01/01/2010 01/01/2011 365 365 0 15

R12 01/01/2010 01/01/2011 365 365 0 15

S13 01/01/2010 01/01/2011 365 365 0 15

R13 01/01/2010 01/01/2011 365 365 0 15

S14 01/01/2010 01/01/2011 365 365 0 15

R14 01/01/2010 01/01/2011 365 365 0 15

S15 01/01/2010 01/01/2011 365 365 0 15

R15 01/01/2010 01/01/2011 365 365 0 15

S16 01/01/2011 01/01/2012 365 365 0 15

R16 01/01/2011 01/01/2012 365 365 0 15

S17 01/01/2011 01/01/2012 365 365 0 15

R17 01/01/2011 01/01/2012 365 365 0 15

S18 01/01/2011 09/05/2011 128 128 0 15

R18 01/01/2011 09/05/2011 128 128 0 15

S19 01/01/2011 01/01/2012 365 365 0 15

R19 01/01/2011 01/01/2012 365 365 0 15 * N. mes. point = number of the measured point for the temperature data




21

Table 1.5: Characteristics of the measured points for the collected temperature history data regarding the steel pipe in the solar DH network in Chemnitz, Germany (4GDH).

Temperature history data Category N. mes.

point* Direction DN [mm]

OD [mm] ts [mm] H [m]

S20 supply 200 219.1 4.5 0.8-1.2 Main pipe

R20 return 200 219.1 4.5 0.8-1.2

S21 supply 250 273.0 5.0 0.8-1.2 Distribution pipe

R21 return 250 273.0 5.0 0.8-1.2

SL1 level 1

SL2 level 2

SL3 level 3 Heat storage

SL4 level 4

S22 supply 80 88.9 3.2 0.8-1.2 Solar field 1

R22 return 80 88.9 3.2 0.8-1.2

S23 supply 80 88.9 3.2 0.8-1.2 Solar field 2

R23 return 80 88.9 3.2 0.8-1.2

S24 supply 25 33.7 2.3 0.8-1.2

Solar DH (SolFW Project)

House connection R24 return 25 33.7 2.3 0.8-1.2


Table 1.6: Characteristics of the collected temperature history data regarding the steel pipe in the solar DH network in Chemnitz, Germany (4GDH).

N. mes. point* Start date Finish date Number of days

start-finish Number of

days recorded Number of

days missing

Measuring interval ∆t

[min]

S20 01/01/2018 31/12/2018 365 365 0 1

R20 01/01/2018 31/12/2018 365 365 0 1

S21 01/01/2018 31/12/2018 365 365 0 1

R21 01/01/2018 31/12/2018 365 365 0 1

SL1 01/01/2018 31/12/2018 365 365 0 1

SL2 01/01/2018 31/12/2018 365 365 0 1

SL3 01/01/2018 31/12/2018 365 365 0 1

SL4 01/01/2018 31/12/2018 365 365 0 1

S22 01/01/2018 31/12/2018 365 365 0 1

R22 01/01/2018 31/12/2018 365 365 0 1

S23 01/01/2018 31/12/2018 365 365 0 1

R23 01/01/2018 31/12/2018 365 365 0 1

S24 01/01/2018 31/12/2018 365 365 0 5

R24 01/01/2018 31/12/2018 365 365 0 5 * N. mes. point = number of the measured point for the temperature data




22

Figure 1.6: Schematic representation of the supply station at the solar DH system in Chemnitz (Shrestha et al., 2018).

Table 1.7 and Table 1.8 summarize the evaluated fatigue damage for the collected

temperature history data, from conventional and 4th generation DH networks,

respectively, by linearly extrapolating the results for a lifetime of 30 years and 50 years.

For comparison purposes, the tables indicate also the allowable number of full

equivalent cycles N0, recommended in EN13941, depending on the pipe category.




23

Table 1.7: Results of the evaluated equivalent full temperature cycles N0, for all temperature history data from conventional DH pipes, considering two different values of the reference temperature ∆Tref, for a lifetime of 30 and 50 years, by linear extrapolation.


N0(∆Tref = Tmax - 10°C) N0(∆Tref = 110°C) N0 (criteria EN 13941) N. mes. point*

Tmax (°C)

Tmean (°C) 30 years 50 years 30 years 50 years 30 years 50 years

S1 119.1 95.3 6.73 11.21 6.51 10.84 1000-2500 1700-4200

R1 84.4 39.7 6.42 10.70 1.35 2.25 1000-2500 1700-4200

S2 117.9 97.9 2.05 3.42 1.90 3.17 1000-2500 1700-4200

R2 71.3 45.2 4.64 7.74 0.45 0.75 1000-2500 1700-4200

S3 115.8 61.1 47.08 78.47 40.27 67.12 100-250 170-420

R3 99.4 45.7 22.03 36.72 9.59 15.99 100-250 170-420

S4 114.3 86.8 35.05 58.42 28.37 47.28 100-250 170-420

R4 127.4 33.1 11.28 18.80 14.63 24.38 100-250 170-420

S5 110.4 88.7 68.81 114.68 47.75 79.58 100-250 170-420

R5 75.6 24.3 19.63 32.71 2.49 4.14 100-250 170-420

S6 115.8 61.9 45.13 75.22 38.60 64.34 100-250 170-420

R6 127.4 33.1 11.28 18.80 14.63 24.38 100-250 170-420

S7 125.7 101.6 84.90 141.50 103.92 173.20 100-250 170-420

R7 105.4 60.6 60.55 100.92 34.26 57.09 100-250 170-420

S8 122.0 101.6 12.24 20.40 13.15 21.92 100-250 170-420

R8 105.6 57.2 86.03 143.38 49.08 81.80 100-250 170-420

S9 115.9 98.3 12.58 20.96 10.82 18.03 1000-2500 1700-4200

R9 55.1 38.3 1223.22 2038.70 34.56 57.61 1000-2500 1700-4200

S10 118.5 92.4 4.66 7.77 4.41 7.35 1000-2500 1700-4200

R10 62.8 45.8 297.93 496.56 15.82 26.36 1000-2500 1700-4200

S11 112.6 90.7 32.41 54.02 24.53 40.88 1000-2500 1700-4200

R11 60.2 38.7 1521.94 2536.56 66.01 110.02 1000-2500 1700-4200

S12 120.8 97.1 4.18 6.97 4.30 7.17 100-250 170-420

R12 80.0 61.3 2.26 3.76 0.37 0.62 100-250 170-420

S13 122.1 96.5 1.33 2.22 1.44 2.39 100-250 170-420

R13 73.5 59.1 0.34 0.56 0.04 0.06 100-250 170-420

S14 119.4 92.9 19.31 32.19 18.89 31.49 100-250 170-420

R14 83.1 60.5 14.31 23.85 2.79 4.65 100-250 170-420

S15 122.1 96.6 1.26 2.10 1.36 2.26 100-250 170-420

R15 68.5 58.5 0.50 0.84 0.04 0.07 100-250 170-420

S16 111.4 95.7 6.15 10.25 4.44 7.40 100-250 170-420

R16 80.0 60.1 3.15 5.24 0.52 0.86 100-250 170-420

S17 120.3 94.6 4.41 7.35 4.46 7.43 100-250 170-420

R17 65.9 58.4 1.94 3.24 0.13 0.22 100-250 170-420

S18 111.4 93.6 27.24 45.39 19.67 32.78 100-250 170-420

R18 83.0 64.2 45.96 76.60 8.91 14.86 100-250 170-420

S19 120.6 94.7 3.49 5.82 3.57 5.95 100-250 170-420

R19 68.2 57.7 0.62 1.04 0.05 0.08 100-250 170-420




24

Table 1.8: Results of the evaluated equivalent full temperature cycles N0, for all temperature history data from 4GDH pipes, considering two different values of the reference temperature ∆Tref, for a lifetime of 30 and 50 years, by linear extrapolation.


1.4 Results and discussion

The number of full temperature cycles N0 for the temperature data collected in Norway

at the Vika heat plant in supply, in 2013 (S7), exceed the lower limit recommended by

EN 13941 for transmission pipelines, referring to a service life of 30 years and 50 years

(Table 1.7). For the rest of collected temperature data on conventional DH networks,

the calculated number of full temperature cycles N0 is below the standard limits.

On the other hand, for the temperature data gathered from the supply pipes in the two

solar fields of the 4GDH network in Chemnitz (S22, S23), the number of full

temperature cycles N0 exceeds the standard limits for the transmission and distribution

pipelines (Table 1.8). This elevated thermal loading fluctuation, occurring in a limited

portion of the network, is associated with the typical day-night solar thermal cycles.

Clearly, such volatility is drastically reduced below the standard limit, in the main

heating circuit, because of the controlling strategy adopted by the DH company.

Among 4GDH pipelines, the house connection return pipe (R24) presented the largest

number of fluctuations, due to the consumers operation, however below the standard

limits. Moreover, the number of full temperature cycles in the distribution pipes

N0(∆Tref = Tmax - 10°C) N0(∆Tref = 110°C) N0 (criteria EN 13941) N. mes. point*

Tmax (°C)

Tmean (°C) 30 years 50 years 30 years 50 years 30 years 50 years

S20 146.9 134.3 9.91 16.51 23.76 39.61 100-250 170-420

R20 104.7 59.091 10.97 18.29 6.03 10.05 100-250 170-420

S21 88.46 72.043 5.99 9.98 1.55 2.58 250-500 420-840

R21 63.7 55.374 2.47 4.12 0.14 0.23 250-500 420-840

SL1 65.68 44.166 394.83 658.05 25.92 43.20 - -

SL2 62.74 45.827 184.25 307.09 9.74 16.23 - -

SL3 86.34 51.367 102.01 170.02 23.66 39.44 - -

SL4 93.52 56.45 120.09 200.16 39.91 66.52 -

S22 127.54 41.362 643.01 1071.69 838.30 1397.16 - -

R22 76 38.488 852.80 1421.33 110.52 184.20 - -

S23 94.26 39.811 1923.84 3206.40 662.34 1103.91 - -

R23 64.46 37.344 1786.71 2977.84 107.35 178.91 - -

S24 82.4 70 340.69 567.82 63.93 106.56 1000-2500 1700-4200

R24 68.7 41.17 1426.31 2377.18 115.66 192.77 1000-2500 1700-4200




25

(S21/R21) is significantly lower than in the rest of the 4GDH system. Evidently, the

thermal fluctuations in the 4GDH transmission and house connection pipes are greater

in supply (S20) and return (R24), respectively (Table 1.8).

To investigate the influence of the length of the data measuring interval ∆t, the number

of full temperature cycles N0 has been calculated for a service life of 30 years,

assuming a smaller measuring interval (∆t), when possible: 2 min, 4 min, 5 min, 15 min,

30 min, 45 min and 60 min. Figure 1.7 presents the variation of the number of full

temperature cycles N0, corresponding to a reference temperature ∆Tref = 110°C, and a

lifetime of 30 years, as a function of the sampling interval ∆t, for the temperature data

from conventional DH pipes in Norway and Germany. Similarly, Figure 1.8 shows the

variation of N0 with ∆t, for the 4GDH temperature data collected in Germany.

Generally, the number of full temperature cycles N0 decreases for greater values of the

measuring interval ∆t. This behavior depends on the measured data, and is stronger for

the temperature measurements S7 and S18, where the number of temperature cycles

N0 drops more than 70%, if measured every 60 min (Figure 1.7). Clearly, the return

house connection pipes exhibited a greater variation of the number of full temperature

cycles N0 with the sampling frequency ∆t, compared to the corresponding supply pipes

(Figure 1.7(b); Figure 1.8), due to the consumers operation.

Therefore, a large measuring time interval (∆t = 60min), can lead to an underestimation

of the number of full temperature cycles N0, and associated fatigue damage, depending

on the location in the network and pipe operating conditions. This is consistent with the

observations of Randløv et al. (1996), suggesting that a more frequent sampling is

necessary for low cycle fatigue analysis.

In conclusion, 4GDH pipelines are susceptible to greater thermal fluctuation in a limited

portion of the network, in the solar thermal circuit, associated with the typical day-night

solar thermal cycles. This elevated volatility drops drastically before entering the main

heating circuit, due to controlling measures adopted by DH companies. Moreover, other

4GDH systems with more plannable heat sources, like waste, biomass, geothermal, are

expected to have a lower temperature fluctuation, due to the absence of any localized

volatility as in the solar thermal circuit, and the controlling strategy of the DH operator.

Therefore, the lifetime of 4GDH pipelines is expected to increase due to the lower

operating temperature, and the low impact of thermal loading volatility in the network,

compared to conventional DH.




26

a)

0

20

40

60

80

100

120

0 5 10 15 20 25 30 35 40 45 50 55 60


Num

ber o

f ful

l tem

pera

ture

cyc

les

N0

S7

R7

S8

R8

b)

0

10

20

30

40

50

60

70

0 5 10 15 20 25 30 35 40 45 50 55 60

Measuring interval ∆t N

umbe

r of f

ull t

empe

ratu

re c

ycle

s N

0

S9

R9S10R10S11R11

c)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

0 5 10 15 20 25 30 35 40 45 50 55 60


Num

ber o

f ful

l tem

pera

ture

cyc

les

N0

S12

R12

S16

R16

d)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

0 5 10 15 20 25 30 35 40 45 50 55 60


Num

ber o

f ful

l tem

pera

ture

cyc

les

N0

S13

R13

S17

R17

e)

0

2

4

6

8

10

12

14

16

18

20

0 5 10 15 20 25 30 35 40 45 50 55 60


Num

ber o

f ful

l tem

pera

ture

cyc

les

N0

S14

R14

S18

R18

f)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

0 5 10 15 20 25 30 35 40 45 50 55 60


Num

ber o

f ful

l tem

pera

ture

cyc

les

N0

S15

R15

S19

R19

Figure 1.7: Number of equivalent full temperature cycles N0, for a reference temperature ∆Tref = 110°C, and a lifetime of 30 years, as a function of the measuring interval ∆t, for the collected temperature data from conventional DH pipelines in Norway and Germany: a) S7, R7, S8, R8; b) S9, R9, S10, R10, S11, R11; c) S12, R12, S16, R16; d) S13, R13, S17, R17; e) S14, R14, S18, R18; f) S15, R15, S19, R19.




27

0

20

40

60

80

100

120

0 5 10 15 20 25 30 35 40 45 50 55 60


Num

ber o

f ful

l tem

pera

ture

cyc

les

N0

S20

R20

S21

R21

S24

R24

Figure 1.8: Number of equivalent full temperature cycles N0, for a reference temperature ∆Tref = 110°C, and a lifetime of 30 years, as a function of the measuring interval ∆t, for the collected temperature data from 4GDH pipelines: a) S20, R20, S21, R21, S22, R22, S24, R24.




28

2 Investigation of fatigue theories and shear stren gth

experience

This chapter focuses on the influences of future mechanical load spectra on the

operational lifetime of steel service pipes. First, an overview on fatigue and damage

accumulation theories for steel is reported, followed by the different evaluation criteria.

Then, preliminary quantifications on fatigue resistances are performed, laying the

foundation for further analysis within this work package. Finally, impact parameters on

the shear strength of naturally aged pipes are described in order to identify the main

parameters for the compilation of shear strength data.

2.1 Comparison of fatigue theories for steel

Fatigue damage accumulation theories predict the effects of cyclic mechanical loads on

material components. Herein, the considered mechanical loads are quasi-static,

induced due to slowly changing temperatures in the DH system (thermally induced

mechanical load cycles). On the other hand, static loads (due to overburden heights)

and dynamic loads (mainly due to changing operational pressures) are not considered.

The application of fatigue theories allows predicting the technical lifetime of the

structural components. Based on past mechanical load cycles, the remaining lifetime

might be approximated as well.

Fatigue theories (linear or non-linear) assume that any mechanical load cycle causes a

certain damage in the structural components (Gudehus and Zenner, 1995; Reinhardt,

2010). The “Woehler-curves” (Wöhler-curves) relate the applied mechanical loads

(stresses) σimax to the number of mechanical load cycles Nimax to failure:

( )maxmaxmax iii Nσσ ∆=∆ (2.1)

Regarding the Woehler-curve, the correlation of Δσimax and Nimax may be described as

follows:

1. Short term tensile strength, involving a low number of load cycles Nimax and

highest individual loads bearable Δσmax(Nmin),

2. Fatigue strength: increasing number of load cycles Nimax, while individual loads

bearable Δσimax = Δσimax(Nimax) decrease (slope of decrease: k),




29

3. Endurance strength: Infinite number of load cycles Nimax; no damage caused by

individual loads occurring below the endurance strength Δσend(Nend), (Figure 2.1)

The damage D caused by each individual mechanical load Δσi(t) depends on the

fatigue theory itself. Thus, damage D occurring might be calculated by relating

individual number of mechanical load cycles ni(Δσi(t)) and the maximum number

mechanical load cycles Nimax(Δσi(t)):

( )maxii NnDD = , with ( )( )tnn iii σ∆= , and ( )( )tNN iii σ∆= maxmax (2.2)

This section describes different fatigue (damage accumulation) theories focussing on

ductile materials (such as steel). This is particularly important, because the application

of these theories to DH has not been updated since 1999 and most service pipes of DH

systems, as well as many relevant components of DH systems are made of steel.

Linear methods and theories (most commonly used for approximating the mechanical

ageing of DH media pipes) are compared to more complex (non-linear) theories

available today. Finally, criteria for the assessment of these theories are reported,

considering their impact in asset management and network design.

Figure 2.1: Woehler-curve of a ductile component, e. g. steel; a) Palmgren-Miner modified; b) Palmgren-Miner elementary.

2.1.1 State of the art – linear fatigue theories fo r ductile materials

Linear fatigue theories for ductile materials represent the simplest approach for the

calculation of fatigue. Linear theories directly relate the damage D to the ratio of




30

individual number of mechanical load cycles ni and maximum number mechanical load

cycles Nimax of an individual load (causing mechanical stress) σi(t):

maxii NnD Σ= (2.3)

The original linear fatigue theory for technical components bases on Palmgren

(Palmgren, 1924). Three decades later, Miner republished the concept (Miner, 1945).

Linear fatigue theories base on several assumptions:

1. Loads occurring are sinusoidal,

2. Failure occurs due to the total amount of work absorbed within the component/

specimen,

3. Work hardening is neglected (the energy absorbed during each load cycle stays

constant),

4. Failure at D = 1 is defined by crack initiation.

However, the original Miner rule does not consider any load occurring below the

endurance strength Δσend. Therefore, modifications of linear fatigue theories were

developed, considering the impact of load cycles below Δσend on the fatigue of the

component:

1. Palmgren-Miner elementary: neglecting the endurance strength Δσend of the

component, the section of fatigue strength is prolonged with the same slope k.

Thus, the influence of load cycles below Δσend on the fatigue of the component

might be considered.

2. Palmgren-Miner modified: considering the mechanisms behind crack initiation,

the section of fatigue strength is prolonged with a minor slope k* = 2k-1

(Haibach, 2006).

Summarizing, linear fatigue theories (Palmgren, 1924; Miner, 1945) directly relate

individual numbers of mechanical load cycles ni(Δσi(t)) and maximum numbers

mechanical load cycles Nimax(σi(t)). This is a straightforward approach for the

mathematical description of ageing due to stresses σi(t). However, linear fatigue

theories are state of the art in predicting damages of DH piping systems in Germany

(AGFW, 2007). This is mainly due to the simple structure of the theory and calculations,

as well as the easy handling of sequences for Δσi(t). On the other hand, influences of




31

sequential effects (high loads with initial damages of the material) are neglected,

whereas uncertainties of linear fatigue theories are quite relevant (Pöting, 2003). This is

mainly due to missing data on the variability of Nimax at the same stress Δσi(Nimax).

2.1.2 Non-linear fatigue theories for ductile mater ials

Fatigue damage is a highly complex and non-linear process. Thus, a linear description

seems to be inadequate for its description and non-linear descriptions were developed

for highly stressed components of ductile materials (e. g. steel). Thus, the development

of fatigue and damage D depends on additional material parameters. Herein, several

theories describe fatigue of ductile materials, based on:

1. several individual material parameters, that have to be measured within specific

test series, (Kujawaski and Ellyin, 1984; Leonatris, 1995; Linn and Scholz, 2013;

Miller and Zachariah, 1977; Nikbin, 2013; Schütz et al., 1983; Bernard-Connolly

et al., 1983),

2. material parameter χi that might be defined on the basis of the Woehler-curve,

(Haibach, 2006; Haibach, 1970; Subramanyan, 1976; Hashin and Laird, 1980;

Manson and Halford, 1981).

The latter theories (Bernard-Connolly et al., 1983; Haibach, 2006; Haibach, 1970;

Subramanyan, 1976; Hashin and Laird, 1980) are the main focus of this report, as no

test specimen are available for specific test series, which are not planned within this

research project.

Regarding the latter theories, fatigue and damage D occurring might be calculated by

correlating individual number of mechanical load cycles ni and maximum number

mechanical load cycles Nimax as well as the material parameter χi, whereas the material

parameter χi is defined by two-level endurance tests. Thus, fatigue may be calculated

for multi-level mechanical loads (Kujawaski and Ellyin, 1984):

1maxmax2

2

max2

2

max1

1

1

3

2

2

1

=

+

++

+

=

−

m

m

N

n

N

n

N

n

N

nD

m

m

χχ

χχ

χχ

K (2.4)




32

Thus, the simplest formulation of this equation for two-level mechanical loads may be

derived as well:

+

=

+

=

=

max2

2

max1

1

max2

2

max1

1

max1

12

11

N

n

N

n

N

n

N

n

N

nD

χχχχ

(2.5)

Based on the multi-level formulation, the definition of the material parameter χi differs

from theory to theory. Regarding the theories in focus of this research project, the

material parameter χi is defined by individual stresses occurring due to mechanical load

cycles σi(t) (Subramanyan, 1976) or by individual maximum number of mechanical load

cycles Nimax (Hashin and Laird, 1980; Manson and Halford, 1981).

2.1.2.1 Theories based on stress parameters

According to Subramanyan (1976), the material parameter χi may be defined by the

individual stress occurring at any mechanical load cycle σi(t) and the bearable stress of

the endurance strength of the material component σend. Hence, there is no

experimental effort for the definition of the material parameter χi:

endii σσ

χ∆−∆

= 1 (2.6)

and the formulation for two-level mechanical loads becomes:

+

=

∆−∆∆−∆

max2

2

max1

11

2

N

n

N

nD

end

end

σσσσ

(2.7)

Summarizing, Subramanyan (1976) directly relates individual numbers of mechanical

load cycles ni(Δσi(t)) and maximum numbers mechanical load cycles Nimax(Δσi(t)). In

addition, stress levels of previous load cycles and the stress Δσend of the endurance

strength are considered. Thus, the mathematical description of fatigue is directly related

to stresses occurring. This is a straightforward approach for the mathematical

description of ageing due to stresses Δσi(t). Non-linear fatigue theories based on

stresses are beyond state of the art in predicting damages of DH piping systems. This

is mainly due to the complex structure of non-linear theories and calculations.




33

2.1.2.2 Theories based on the number of mechanical load cycles

According to Hashin and Laird (1980), Manson and Halford (1981), the material

parameter χi may be defined by the maximum number of mechanical load cycles Nimax.

However, Hashin and Laird (1980) additionally considers the bearable number of

mechanical load cycles to cause failure at endurance strength Nend = Nmax(Δσend),

whereas the approach of Manson and Halford (1981) depends on a constant empirical

material parameter p. In both cases, there is no experimental effort for the definition of

the material parameter χi and p.

2.1.2.2.1 Theories based on endurance strength

According to Hashin and Laird (1980), the material parameter χi depends on the

number of mechanical load cycles to cause failure at endurance strength Nend, and the

maximum number of mechanical load cycles Nimax:

=

end

i

i

N

Nlog

1χ (2.8)

and the formulation for two-level mechanical loads becomes:

+

=

2

2log

log

1

11

2

N

n

N

nD end

end

N

N

N

N

(2.9)

Summarizing, Hashin and Laird (1980) directly relates individual numbers of

mechanical load cycles ni(Δσi(t)) and maximum numbers mechanical load cycles

Ni(Δσi(t)). In addition, the maximum number of previous mechanical load cycles Ni, and

the number of load cycles causing failure at endurance strength Nend(Δσend) are

considered. As thermally induced stresses are relevant for fatigue of components, this

approach seems to be not as transparent as previous approaches based on the relation

of developed stresses.

2.1.2.2.2 Theories based on empirical material para meters

According to Manson and Halford (1981), the material parameter χi depends on the

maximum number of mechanical load cycles Ni, and an additional empirical material

parameter p:




34

( )pii N=χ (2.10)

Based on empirical determinations, the additional material parameter p becomes 0.4.

Thus, the formulation for two-level mechanical loads becomes:

12

2

1

1

4.0

2

1

=

+

=

N

n

N

nD

N

n

(2.11)

Summarizing, Manson and Halford (1981) directly relates individual numbers of

mechanical load cycles ni(Δσi(t)) and maximum numbers mechanical load cycles

Ni(Δσi(t)). In addition, maximum number of previous mechanical load cycles Ni and an

empirical (and constant) material parameter (p) are considered. Again, this approach is

not as transparent as previous approaches basing on the relation of stresses occurring,

as thermally induced stresses are relevant for fatigue of components. Furthermore the

variability of the empirical material parameter p is not clarified. However, the individual

number of mechanical load cycles may be determined more easily from operational

data of DH systems than thermally induced stresses within DH systems.

Furthermore, this non-linear fatigue theory is beyond the state of the art in predicting

damages of DH piping systems. This is mainly due to the complex structure of this

theory. On the other hand, the influence of sequential effects (high loads with initial

damages of the material) is considered, whereas the handling of sequence effects is

rather complex, as each change in stress amplitude must be considered within an

individual term in the formulation. Finally, the uncertainties of this non-linear fatigue

theory are potentially minimal (Pöting, 2003). However, the latter must be clarified

within the first calculations on fatigue resistance, as shown in the following paragraph.

2.1.3 Summary and evaluation of different theories of fatigue accumulation

A summary on different theories for fatigue and damage accumulation is given in

Table 2.1. Proposed analytic evaluation criteria for the different theories are:

(i) transparency of mathematical/ physical approach, (ii) level of sophistication (in

comparison to state of the art in DH practice), (iii) usability, (iv) consideration of

sequential effects, and (v) relative accuracy in comparison to other theories (according

to literature survey). However, these criteria must be complemented according to the

results of first calculations and will finally be evaluated in the following paragraphs.




35

Table 2.1: Summary on analytic evaluation criteria for the different theories on fatigue and damage accumulation.

Theory

Basis: -Transparency of approach-

Level of Sophist.

Usability Sequential effects

Relative Accuracy,

(Pöting, 2003)

Linear Miner (1945)

Basis: no. of load cycles ni

-HIGH-

State of the art -LOW-

Easy structure

-HIGH-

Not Considered

-NO-

-LOW-

Non-linear A Subramanyan

(1976)

Basis: additional mat. Parameter χi(Δσi; Δσend)

-HIGH-

Beyond State of the art -HIGH-

complex structure

-LOW-

Considered

-YES-

-MEDIUM-

Non-linear B Hashin and

Laird (1980)

Basis: additional mat. Parameter χi(ni(Δσi); Nend)

-MEDIUM-


complex structure

-LOW-

Considered

-YES-

-MEDIUM-

Non-linear C Manson (1981)

Basis: additional mat. Parameters

(empirical) χi(Ni(Δσi) p) -MEDIUM-


Relatively complex structure

-MEDIUM-

Considered

-YES-

-BEST-

2.2 Estimating fatigue resistances for future load conditions

Fatigue and damage resistance according to linear and non-linear fatigue theories is

quantified illustratively within this chapter. For this purpose, a mechanical load

spectrum is utilized and modified, in order to evaluate the results obtained from

different theories on damage accumulation. Thus, fatigues occurring due to linear and

non-linear theories can be calculated, regarding:

1. The detailed load spectrum: no agglomeration of identical load cycles,

2. Sequential effects: relevant irregularities in the distribution of load cycles leading

to major differences for the damages D calculated regarding different load

scenarios:




36

a. precise mechanical load sequence representing in-situ data,

b. best-case scenario (load sequence: low-high),

c. worst-case scenario (load sequence: high-low).

3. Quantity of mechanical loads: loads occurring should be realistic, e. g. according

to AGFW (2007),

4. Typical mechanical load cycles of DH networks.

Finally, due to the special mathematical structure of non-linear theories, another major

issue must be considered regarding the material parameter χi = χi (Δσi; Δσend) or

χi = χi (Ni(Δσi)).

5. Relative characteristic of mechanical load cycle ΔΣi and ΔNi: the difference

between two consecutive mechanical load cycles Δσi - Δσi+1 and the previous

load cycle Δσi is of major importance for the extent of χi. Big gaps between two

consecutive mechanical loads will lead to an overestimation of χi (due to χi << 1),

and unrealistically high damages. Therefore, the absolute value of χi (according

to Subramanyan, 1976; Hashin and Laird, 1980; Manson and Halford, 1981)

must be restricted.

The impact of this last aspect might be regarded comparing the results on the damages

calculated for the ill- and well-conditioned load spectra. The minimum of χi is well below

0.2 for the ill-conditioned mechanical load spectrum, while being well above 0.7 for the

well-conditioned mechanical load spectrum (worst-case scenario).

2.2.1 Definition of illustrative mechanical load sp ectrum

In order to quantify fatigue due to a specific mechanical load spectrum, a Woehler-

curve has to be defined within a first step. Besides the definition of a Woehler-curve on

the basis of an experimental test series (which is not part of this research project),

these may be defined synthetically (Gudehus and Zenner, 1995; Hück et al., 1983), as

well as according to given standards and directives.

In accordance to the state of the art and practice in Germany (AGFW, 2007), a typical

Woehler-curve for the fatigue strength Δσimax = Δσimax(Nimax) of a media pipe is defined.

However, AGFW (2007) does not define any boundaries for Δσimax, such as short term

tensile strength Δσmax or endurance strength Δσend. However, these definitions are




37

necessary for the use of non-linear theories on damage accumulation. Figure 2.2

illustrates the Woehler-curve for a welded distribution pipeline made of P235GH

(1.0345), according to AGFW (2007). This Woehler-curve is supplemented by

considerations and calculations according to Hück et al. (1983).

The short term tensile strength, based on the tensile strength Δσmax of a typical media

pipe, made of P235GH (1.0345) Δσmax, may be defined by:

2max 400mm

N=∆σ (2.12)

where Δσmax defined above is validated by the definition of a Wohler-curve according to

Hück et al. (1983).

The fatigue strength Δσimax(Nmin), based on AGFW (2007), may be defined for a welded

distribution pipeline, made of P235GH (1.0345), by:

( ) 25,0

2max 67,65000 −⋅⋅=∆ ii Nmm

Nσ (2.13)

which leads to:

( ) ( ) 664,3664,367,65000400 maxmin25,0

22max =∆⇒⋅⋅==∆ − σσ Nmm

N

mm

N (2.14)

The endurance strength, based on Hück et al. (1983), the endurance strength

Δσend(Nend) may be defined for a welded distribution pipeline made of P235GH (1.0345)

by:

( ) ( ) 000,000,76067,65000 max2

25,0

2=∆⇒≈⋅⋅=∆ − σσ endendend N

mm

NN

mm

N (2.15)

Summarizing, relevant amplitudes for stresses occurring Δσi are in the range of

60 N/mm² < Δσi < 400 N/mm². Based on this Woehler-curve, mechanical load spectra

may be defined. For illustrative purposes, these load spectra must consider easy

applicability, as well as the impact of sequential effects (asymmetric mechanical load

sequence). Therefore, three different load spectra are regarded:

1. Precise mechanical load sequence representing in-situ data,

2. Best-case scenario, represented by descending mechanical loads (low-high),




38

3. Worst-case scenario, represented by ascending mechanical loads (high-low).

Figure 2.2: Woehler-curve of a welded distribution line; P235GH (1.0345) (AGFW, 2007; Hück et al., 1983).

2.2.1.1 Ill-conditioned load spectrum

The ill-conditioned mechanical load spectrum, disregarding homogeneity of loads, is

given in Figure 2.3. The load spectrum reflects typical amplitudes for stresses Δσi

within media pipes of DH systems. Based on this mechanical load spectrum, a

mechanical load sequence is given, as indicated in Table 2.2 (minimum amplitudes for

stress, 100 N/mm² = Δσmin > Δσend). Thus, fatigue and damage occurring may be

approximated and evaluated for different linear and non-linear theories. The

unfavourable relative characteristic of the mechanical load cycles is given in Table 2.2,

as well as with χi > 0.16 (Manson and Halford, 1981).




39

Figure 2.3: Illustrative example of an ill-conditioned mechanical load sequence of distribution pipeline, showing precise mechanical load sequence (above), as well as resulting best- and worst-case scenarios.




40

Table 2.2: Mechanical load sequences of ill-conditioned mechanical load amplitude and material parameters χi for different load scenarios.

Precise mechanical sequence

Δσi [N/mm²]

ni [-] Occurrence

Ni [-]

χi [-] (Subramanya

n, 1976)

χi [-] (Hashin,

Laird, 1980)

χi [-] (Manson,

Halford, 1981)

300 1 1h < t < 3h Ca. 11,560

0.165 0.314 0.172

100 1 4h < t < 6h Ca. 950,000

1.00 1.00 1.00

100 1 6h < t < 8h Ca. 950,000

7.33 3.49 7.42

350 1 1h < t < 9h Ca. 6,300

n.a.n. n.a.n. n.a.n.

Best-case scenario (low-high)

Δσi [N/mm²]

ni [-] Occurrence

Ni [-]

χi [-] (Subramany

an, 1976)

χi [-] (Hashin,

Laird, 1980)

χi [-] (Manson,

Halford, 1981)

100 2 s. above Ca. 950,000

6.06 3.19 5.80

300 1 s. above Ca. 11,560

1.21 1.10 1.28

350 1 s. above Ca. 6,300


Worst-case scenario (high-low)

Δσi [N/mm²]

ni [-] Occurrence

Ni [-]

χi [-] (Subramany

an, 1976)

χi [-] (Hashin,

Laird, 1980)

χi [-] (Manson,

Halford, 1981)

350 1 s. above Ca. 6,300

0.827 0.912 0.781

300 1 s. above Ca. 11,560

0.165 0.314 0.172

100 2 s. above Ca. 950,000





41

2.2.1.2 Well-conditioned load spectrum

The well-conditioned mechanical load spectrum regarding homogeneity of loads is

given in Figure 2.4. The load spectrum reflects typical amplitudes for stresses Δσi

within media pipes of DH systems. Based on this mechanical load spectrum, a

mechanical load sequence is given, as indicated in Table 2.3 (minimum amplitudes for

stress, 100N/mm² = Δσmin > Δσend). Thus, fatigue and accumulated damage may be

approximated and evaluated for different linear and non-linear theories. The favourable

relative characteristic of mechanical load cycles is also given in Table 2.3, with χi > 0.74

(Manson and Halford, 1981).

Figure 2.4: Illustrative example of an well-conditioned mechanical load sequence of distribution line precise mechanical load sequence (above), as well as resulting best- and worst-case scenarios.




42

Table 2.3: Mechanical load sequences of well-conditioned mechanical load amplitude and material parameters χi, for different load scenarios.

Precise mechanical sequence

Δσi [N/mm²]

ni [-] Occurrence

Ni

[-]

χi [-] (Subramanyan,

1976)

χi [-] (Hashin,

Laird, 1980)

χi [-] (Manson,

Halford, 1981)

300 1 1h < t < 3h Ca. 11,560

0.791 0.866 0.747

250 1 4h < t < 6h Ca. 23,650

1.00 1.00 1.00

250 1 6h < t < 8h Ca. 23,650

1.53 1.237 1.713

350 1 1h < t < 9h Ca. 6,300


Best-case scenario (low-high)

Δσi [N/mm²]

ni [-] Occurrence Ni [-]


1976)

χi [-] (Hashin,

Laird, 1980)

χi [-] (Manson,

Halford, 1981)

250 2 s. above Ca. 23,650

1.26 1.13 1.34

300 1 s. above Ca. 11,560

1.21 1.10 1.28

350 1 s. above Ca. 6,300


Worst-case scenario (high-low)

Δσi [N/mm²]

ni [-] Occurrence

Ni [-]


1976)

χi [-] (Hashin,

Laird, 1980)

χi [-] (Manson,

Halford, 1981)

350 1 s. above Ca. 6,300

0.827 0.912 0.781

300 1 s. above Ca. 11,560

0.791 0.886 0.747

250 2 s. above Ca.

23,650 n.a.n. n.a.n. n.a.n.




43

2.2.2 Quantification of fatigue resistances

This section quantifies the impact of different fatigue theories on the consumed lifetime,

as well as the deviation between these theories, while considering the impact of

sequential effects. For this purpose, fatigue occurring due the different load scenarios

are compared (precise mechanical load sequence, best-case scenario, and worst-case

scenario, as shown in Figure 2.3 and Figure 2.4).

2.2.2.1 Results for ill-conditioned load spectrum

Table 2.4 reports the damage D occurring, based on an ill-conditioned load spectrum,

for different linear (Palmgren, 1924; Miner, 1945) and non-linear theories

(Subramanyan, 1976; Hashin and Laird, 1980; Manson and Halford, 1981).

Table 2.4: Damages occurring due to the ill-conditioned mechanical load sequence in Figure 2.3, for different theories of damage accumulation.

Theory Precise sequence Best-case scenario Worst-case scenario

D = D(ni; Ni(σi)) Linear Miner (1945) D = 0.165%

D = D(ni; Ni(σi);χi(σi; σend)) Non-linear A Subramanyan

(1976) D = 0.119% D = 0.119 % D = 40.32 %

D = D(ni(σi); Nend; χi(ni(σi); Nend)) Non-linear B Hashin; Laird

(1980) D = 0.135 % D = 0.135 % D = 15.30 %

D = D(ni; Ni(σi); χi(Ni(σi); p)) Non-linear C Manson (1981) D = 0.114 % D = 0.114 % D = 40.57 %

2.2.2.2 Results for well-conditioned load spectrum

Table 2.5 reports the damages D occurring, based on an well-conditioned load

spectrum, for different linear (Palmgren, 1924; Miner, 1945) and non-linear theories

(Subramanyan, 1976; Hashin and Laird, 1980; Manson and Halford, 1981).




44

Table 2.5: Damages occurring due to the well-conditioned mechanical load sequence in Figure 4 for different theories for damage accumulation.

Theory Precise sequence Best-case scenario Worst-case scenario

D = D(ni; Ni(σi)) Linear Miner (1945) D = 0.221 %

D = D(ni; Ni(σi);χi(σi; σend)) Non-linear A Subramanyan

(1976) D = 0.123 % D = 0.121 % D = 1.34 %

D = D(ni(σi); Nend; χi(ni(σi); Nend)) Non-linear B Hashin; Laird

(1980) D = 0.150 % D = 0.146 % D = 0.554 %

D = D(ni; Ni(σi); χi(Ni(σi); p)) Non-linear C Manson (1981) D = 0.116 % D = 0.115 % D = 2.06 %

2.2.3 Summary on the quantification of fatigue and interpretation of results

Results for the ill- and well-conditioned load spectrum are discussed for linear and non-

linear theories. Herein, the dependency of the results on the highest load cycles within

the load spectrum is analyzed. For this purpose, the damage calculation considers the

impact of the highest mechanical load cycles on the overall damage D due to:

1. The singular load cycle of 350N/mm² (D350),

2. The singular load cycle of 300N/mm² (D300),

3. Both highest load cycles (D350&300), and the remaining damage that occurs due to

the lowest load cycles D250 = D - D350&300 (D from Table 2.5).




45

2.2.3.1 Overall results

Based on the results of Table 2.4 and Table 2.5 for the ill- and well-conditioned load

spectrum, the damages D calculated depend on the load scenario, and load spectrum:

1. Precise mechanical load scenario:

Damages D calculated are in a narrow range for all theories and spectra (ill-,

well-conditioned) considered. Comparing different theories, deviations for D are

higher for the well-conditioned load spectrum. D is in a realistic range for all

theories.

2. Best-case scenario:

Damages D calculated are in a narrow range for all theories and spectra (ill-,

well-conditioned) considered. Comparing different theories, deviations for D are

higher for the well-conditioned load spectrum. D is in a realistic range for all

theories. Regarding all load spectra, sequential effects have a minor impact on

D. The latter is slightly below the damage values for the precise mechanical load

scenario.

3. Worst-case scenario:

Damages D calculated are significantly higher for all non-linear theories, and in

comparison to other load scenarios. Comparing different theories, deviations for

D are in the same range for all load spectra. D is realistic for the well-conditioned

load spectrum, and out of any realistic range for the ill-conditioned load

spectrum. Regarding the ill-conditioned load spectrum, D strongly depends on

sequential effects by a factor superior to 100, whereas this effect is diminished

for the well-conditioned load scenario (by factor inferior to 15). D is higher for the

ill-conditioned load spectrum than for the well-conditioned load spectrum.

2.2.3.2 Impact of highest load cycles on overall damage D

Following considerations are limited to the well-conditioned load spectrum, as results of

the ill-conditioned load spectrum are questionable (due to the relative characteristic of

load occurring):

1. Despite of the lower loads, damages D calculated for the ill-conditioned

mechanical load spectrum are higher than for the well-conditioned load

spectrum.




46

2. Damages D calculated for the ill-conditioned load spectrum are out of any

realistic range.

3. Damages D calculated for the ill-conditioned load spectrum strongly depend on

the lowest loads due to sequential effects, which is in direct contradiction to any

physical considerations.

The impact of the highest mechanical load cycles (350N/mm² and 300N/mm², as well

as both loads in combination) on the overall damage D calculated is given in Table 2.6.

Table 2.6: Damages occurring due to singular load cycles (D350 & D300) and both

highest load cycles (D350&D300) for the well-conditioned load spectrum.

Theory Precise sequence

Best-case scenario

Worst-case scenario

D = D(ni; Ni(σi))

D350 = 0.107 %

D300 = 0.058 %

Linear Miner

(Palmgren, 1924; Miner, 1945)

D350&300 = 0.163 % → D250 = 0.058

D = D(ni; Ni(σi);χi(σi; σend))

D350 ≈ 0.107 % D350 = 0.107 %%

D300 ≈ 0.058 % D300 = 0.058 %

Non-linear A Subramanyan

(Subramanyan, 1976)

D350&300 ≈ 0.119 % → D250 = 0.004 %

D350&300 = 0.456 % → D250 = 0.884 %

D = D(ni(σi); Nend; χi(ni(σi); Nend))

D350 ≈ 0.107 % D350 = 0. 107 %

D300 ≈ 0.058 % D300 = 0.058 %

Non-linear B Hashin; Laird (Hashin and Laird, 1980)

D350&300 ≈ 0.135 % → D250 = 0.015 %

D350&300 = 0.252 % → D250 = 0.302 %

D = D(ni; Ni(σi); χi(Ni(σi); p))

D350 ≈ 0.107 % D350 = 0.107 %

D300 ≈ 0.058 % D300 = 0.058 %

Non-linear C Manson

(Manson and Halford, 1981)

D350&300 ≈ 0.114 % → D250 = 0.002 %

D350&300 = 0.534 % → D250 = 1.526 %




47

Based on these results for the well-conditioned load spectrum, the damage D

calculated depends on the load scenario and theory considered:

1. Precise mechanical load scenario:

(i) Damages D350 and D300 are identical for all theories,

(ii) D350&300 is highest for the linear theory,

(iii) Considering all theories, D350&300 are in a quite narrow range for all theories

(deviation < 45% between (Palmgren, 1924; Miner, 1945) and (Manson and Halford,

1981)),

(iv) Whereas non-linear effects result in diminished damages D350&300 (compare D350&300

of (Palmgren, 1924; Miner, 1945) to D350&300 of (Subramanyan, 1976; Hashin and Laird,

1980; Manson and Halford, 1981)).

2. Best-case scenario:


(ii) D350&300 is highest for the linear theory. Considering all theories, D350&300 are in a

quite narrow range for all theories (deviation < 45% between (Palmgren, 1924; Miner,

1945) and (Manson and Halford, 1981)),

(iii) Whereas non-linear effects result in diminished damages D350&300 (compare

D350&300 of (Palmgren, 1924; Miner, 1945) to D350&300 of (Subramanyan, 1976; Hashin

and Laird, 1980; Manson and Halford, 1981)),

(iv) Considering non-linear theories, D350&300 deviates insignificantly between the best-

case scenario, and the precise mechanical load scenario (deviations < 2% for

(Subramanyan, 1976; Hashin and Laird, 1980; Manson and Halford, 1981)).

3. Worst-case scenario:


(ii) D350&300 is higher for non-linear theories and highest for the linear theory according

to (Manson and Halford, 1981),

(iii) Considering non-linear theories, D350&300 is in a broader range (deviations up to

about 120% between (Subramanyan, 1976) and (Manson and Halford, 1981)),

(iv) Non-linear effects result in enhanced damages D350&300 (compare D350&300 of

(Palmgren, 1924; Miner, 1945) to D350&300 of (Subramanyan, 1976; Hashin and Laird,

1980; Manson and Halford, 1981), while D350 + D300 < D350&300, for all non-linear

theories),




48

(v) Considering non-linear theories, D350&300 deviate significantly between the worst-

case scenario and the precise mechanical load scenario (deviations up to ca. 370% for

(Manson and Halford, 1981)).

2.2.4 Interpretation of results and evaluation of u sability – critical aspects

The damage D occurring due to different load sequences (ill- and well- conditioned),

and scenarios (precise mechanical load sequence, as well as best- and worst-case

scenario for the same load sequence) has been examined.

1. Regarding best-case scenarios, the impact of sequential effects on the damage

D calculated is of minor significance (minor impact of sequential effects). This

has been confirmed by previous examinations on more complex load spectra at

FFI.

2. Regarding best-case scenarios, and precise mechanical load sequences, the

impact of high loads on damages D calculated, is disproportionately high. Thus,

the damage D calculated within the illustrative example depends on high loads

by more than 90%. This impact is of the same magnitude as within linear

theories.

3. Regarding the worst-case scenarios, the impact of sequential effects on the

damage D calculated is of major significance (major impact of sequential

effects). This also has been confirmed by previous examinations on more

complex load spectra at FFI.

4. Regarding the worst-case scenarios, the impact of low loads on damages D

calculated, is disproportionately high. Thus, the damage D calculated within the

illustrative example depends on low loads by more than 50% (up to 75%). This

impact seems to be realistic, comparing it to the impact of low loads within linear

theories.

Summarizing, non-linear theories seem to be generally suitable for the description of

mechanical ageing of media pipes within DH systems. Thus, these theories may deliver

more realistic results for damages occurring due to mechanical loads. On the other

hand, some critical aspects concerning the use of non-linear theories, the impact of

sequential effects, and the transferability of non-linear theories to DH systems have

been identified:




49

1. Critical aspect I: implementation of operational data for non-linear theories.

Linear and non-linear theories on damage accumulation deliver realistic results for

the damage prediction. However, special attention must be given to the conditioning

(esp. relative characteristic) of the loads occurring. Bigger gaps between following

load cycles result in unrealistically high damage D, as shown in the worst-case

scenario, for the ill-conditioned load spectrum. However, as load cycles in-situ can

not be conditioned according to this mathematical stipulation, this might be

problematic in implementing operational data for non-linear theories, applying to

DH-networks.

2. Critical aspect II: Unrealistic impact of sequential effects.

The impact of favorable and unfavorable sequential effects is considered by all non-

linear theories. Due to these effects, the damage D, calculated due to the lowest

mechanical loads, increases significantly for every load scenario. Thus, the damage

occurring due to low-load cycles is 20 to 750 higher (Subramanyan, 1976; Hashin

and Laird, 1980), comparing the results for D250 in Table 2.6.

3. Critical aspect III: Transferability of non-linear theories.

The transferability of non-linear theories on media pipes of DH-systems must be

discussed, as non-linear theories have been developed for highly-stressed

components, e. g. Bernard-Connolly et al. (1983), typically based on two-level

endurance tests, whereas media pipes in DH systems undergo limited multi-level

stresses.

Finally, regarding literature and obtained results, the presumed better relative accuracy

of Manson and Halford (1981), according to Pöting (2003), cannot be verified (as

evident in critical aspect II). Therefore, in future steps, the results from all non-linear

theories (Subramanyan, 1976; Hashin and Laird, 1980; Manson and Halford, 1981)

should be considered, and compared to those of linear theories (Palmgren, 1924; Miner,

1945) in order to compare, and validate the obtained results.

2.3 Compilation of shear strength data from natural ly aged pipes

Varying mechanical and thermal loads have a negative effect on the lifetime and

usability of any component within technical systems. Regarding DH systems,

mechanical and thermal loads influence the ageing of media pipes, thermal insulations

and casing. This section focuses on the shear strength of pre-insulated pipe systems,




50

as this parameter is of major importance for pipe stability, and reliability of supply on a

long-term perspective. First, the axial shear strength data from naturally aged pipes

examined at FFI are compiled and analysed. Herein, the parameters influencing the

axial shear strength of naturally aged pre-insulated piping systems are identified and

described. Secondly, referring to the test results of the artificially aged pipes at FFI, the

impact parameters on the evolution of the axial shear strength of the thermal insulation,

are determined.

2.3.1 Naturally aged pipes

The FFI has conducted studies on the composite properties of naturally aged

preinsulated bonded DH pipe. The 16 examined pipes were exposed after different

operating time from six different places.

First, the axial shear strength of the pipes in naturally aged condition was determined

according to DIN EN 253 5.4 (DIN EN 253, 2009. The axial length of the test specimen

is equal to 2.5 times the polyurethane insulation thickness, but at least 200 mm. The

tests were carried out on a system with a 100 kN load cell (accuracy class 0.1). The

force was applied centrally, in the vertical axis direction, to the service pipe of the test

specimen, at a speed of 5 mm/min, while the jacket casing likewise rested centrically

on the abutment. The axial displacement of the service pipe during the force application

was monitored with an inductive position sensor (accuracy class 0.2). The test

temperature was 23±2°C.

The recording of the measured results during the test took place by means of electronic

data processing. The amount of the axial shear strength was calculated according to

the equation below, considering the dead weight of the service pipe in the axial force

Fax:

πτ

⋅⋅=

s

axax DL

F (2.16)

where

τax axial shear strength, in MPa; Fax axial force, in N; L length of specimen, in mm; Ds outside diameter of the service pipe, in mm




51

All available important data of the 16 pipes, as well as the measured axial shear

strength, and the foam density in naturally aged condition are summarized in Table 2.7.

On this basis, the following analysis was carried out to determine the relationship

between the axial shear strength and the various and possible influencing parameters.

Table 2.7: Overview of the 16 pipe samples.

1-1 1-2 2-1 2-2 3-1 3-2 4-1 4-2

excavation date 06.2006 11.2007 12.2007 10.2007

installation date 1992 12.1984 1986 1997

operating time (year) 15,5 23 22 11

DN steel medium pipe (-) 65 150 150 250

sample length (mm) 140 250 250 400

overlap height (m) 0,95 0,95 1,1 1,0

design temperatur (°C) 130 130 130 130

design pressure (bar) 16 25 25 16

supply pipe (x) X X X X

return pipe (x) X X X X

axial shear strength at

room temperature (MPa) 0,172 0,253 0,225 0,274 0,213 0,184 0,110 0,204

foam density (kg/m³) 63,1 77,5 99,9 98,5 59,1 62,5 75,7 64,8

5-1 5-2 5-3 5-4 6-1 6-2 6-3 6-4

excavation date 12.2009 06.2012

installation date 1985 2003

operating time (year) 25 10

DN steel medium pipe (-) 150 150

sample length (mm) 250 250

overlap height (m) 0,5 1,2

design temperatur (°C) 120 130

design pressure (bar) 25 25

supply pipe (x) X X X X

return pipe (x) X X X X

axial shear strength at

room temperature (MPa) 0,120 0,147 0,336 0,297 0,185 0,232 0,299 0,255

foam density (kg/m³) 81,2 103,3 70,6 87,9 78,7 64,3 76,8 65,6

S1 S2 S3 S4

S5 S6

Figure 2.5 shows the measured axial shear strength in naturally aged condition,

depending on the type of pipe (supply or return). With one exception, the supply line

has lower values than the return line. On average, the axial shear strength of the supply

line is 0.176 MPa, while that of the return line is 0.263 MPa. This difference shows that

thermal loading is an important factor influencing the service life of the pipeline. For




52

comparison, the minimum requirement for axial shear strength according to DIN

EN 253 for the pipeline in unaged condition (0.12 MPa at test temperature 23±2°C) was

also indicated. Of the 16 pipes, two supply pipes (S4-1 after 11 operating years, S5-1

after 25 operating years) are below or equal to the limit value.

Figure 2.5: The axial shear strength versus the pipe type.

Figure 2.6: The axial shear strength versus the pipe size.

Figure 2.6 represents the axial shear strength as a function of the pipe size. Clearly, 12

pipes of the 16 test samples have a nominal diameter of 150 mm, which is a typical

nominal size of most built-in district heating pipelines. The measured values are

relatively widely scattered between 0.12 MPa and 0.34 MPa. Despite the lack of

sample size for smaller and larger dimensions, the thin pipe has the greater residual




53

axial shear strength values than the thick pipe (Figure 2.6). Similar results were also

reported in (Meigen and Schuricht, 2004; Schuricht, 2004).

Figure 2.7 represents the measured axial shear strengths as a function of the operating

time. Evidently, the supply pipe exhibits a lower residual axial shear strength than the

return pipe. Considering a potential line for the supply and return data, the two lines are

almost horizontal and parallel. Thus, in this case, there seems to be no correlation

between the residual axial shear strength and the operating time.

Figure 2.7: The axial shear strength versus the operating time.

In addition to the axial shear strength, the foam density was determined according to

DIN EN 253. Figure 2.8 shows the measured axial shear strength versus the measured

foam density. The foam density of the investigated pipes was very different, but all

meet the requirements of DIN EN 253 (the minimum requirement is 55 kg/m³). A

relationship between the residual axial shear strength and the foam density could not

be directly deduced.




54

Figure 2.8: The axial shear strength versus the foam density.

All specimens were tested until the foam failed and cracked. Table 2.8 summarizes the

positions of the fracture in the axial shear strength test. All of the samples are produced

with the discontinuous processing method, while most of the fracture occurs in the first

cell layers near the steel-service-pipe. Only in the case of sample 6, the break occurred

both in proximity of the service pipe, and in the polyurethane insulation foam (Table

2.8).




55

Table 2.8: Manufacturing process, and the break-position of the 16 pipe samples.

Pipe Manufacturing process Break

S 1-1 Disconti PUR/St












S 6-1 Disconti PUR/St & PUR/PUR




PUR/St: Break in the first cell layers near the steel-medium-pipe

PUR/PUR: Break in the polyurthane foam insulation

2.3.2 Artificially aged pipes

To estimate the remaining service life of the exposed pipes, the 16 pipes at the FFI

were subjected to the accelerated thermal aging, according to DIN EN 253, 5.4.3.

The service pipe was heated during the artificial aging at a temperature of 160°C,

during which the casing was maintained at a room temperature. After 600 h (25 days),

1200 h (50days), 1800 h (75 days) aging, one test specimen was cut from the pipeline,

and the axial shear strength was determined again at room temperature (23 ± 2°C).

This allowed to determine the evolution of axial shear strength as a function of the

aging time, until reaching the critical shear strength.

The measured axial shear strength after artificial aging, for the pipe specimens are

plotted in Figure 2.9 (for each pipe), and in Figure 2.10 (for all 16 pipes). The evolution

of the shear strength is very individual. However, the average bond strength was

greatly reduced after aging for 600 hours, while achieving the standard limit (DIN EN

253) after 1200 hours of aging.




56

Figure 2.9: The measured axial shear strength of the artifically aged pipes versus the ageing time.




57

Figure 2.10: The measured axial shear strength of all artifically aged pipes versus the ageing time.

2.3.3 Summary

Despite the lack of data of the operating temperature history, and the axial shear

strength of the pipe in unaged condition, the enclosed investigation showed a

significant influence of the thermal load on the axial shear strength, as also noted in

(AGFW, 2011; Meigen and Schuricht, 2004; Schuricht, 2004).

In addition to the thermal load, other parameters, including age, pipe size, and foam

density were analyzed. Despite the small number of samples, the results showed a

large scattering. Therefore, it is very difficult to derive a direct relationship between the

residual shear strength and the operating time, as well as the foam density.

From the test result, it is strongly recommended to keep a documentation of the new

pipe well before built-in. Moreover, as much data as possible should be collected during

operation (Herbst, 2015). On the basis of this data, it would possible to determine the

specifications for a thermal aging test procedure in the future, and derive the long term

temperature resistance of preinsulated bonded pipe. This would lead to more accurate

forecasts of the status change in district heating networks, and produce optimized plans

for maintenance and refurbishment measures.




58

3 Investigation of thermal ageing in combination wi th cyclic

mechanical loads

3.1 Background

Mechano-chemical degradation of polymers is well-known, but poorly understood. It

comprises of all aspects of stress-induced scissions of chain molecules (Kausch, 1986;

Terselius et al., 1986). In the presence of oxygen, the radicals formed react

immediately with oxygen, followed by rearrangement reaction which make the break

permanent. All polymers are strongly anisotropic at the molecular level (1-10 nm),

where the material properties vary with the different crystallographic orientations.

Generally, two failure mechanisms can occur: chain slippage and chain scission. Many

parameters, beside the stress level and loading time, affect these mechanisms, such as

degree of chain orientation, presence of entanglements and / or cross-links (Andrews,

1969). The kinetic theory of polymer fraction, the effect of motion, and physical

properties of molecules on the macroscopic behaviour have been studied during five

decades. The effect of deformation and rupture of molecular chains, crystals and

morphological structures on the strength of the polymeric materials in certain

applications have been investigated (Kausch, 1986).

Thermal degradation, and additional mechanical stress have a synergy effect on

molecular rearrangements, which may cause disentanglements and slips of chain

segments to local reorientations and formations of voids. Three principal mechanisms

may contribute to fatigue failure: thermal softening, excessive creep or flow, and the

initiation and propagation of fatigue cracks (Kausch, 1986). Moreover, fatigue cracks

also depend on stress levels, strain amplitudes, deformations, frequency, ambient and

internal temperatures (Andrews, 1969).

The consequence of chain scissions, reduction of molecular weight, and radical

formations in polymeric material results in accelerated degradation by e.g. oxidative

degradation, and in some cases by cross-linking (Casale et al., 1975; Lauer, 1975).

These parameters intensify by the ageing of the polymeric materials during their service

life. Time and temperature are crucial parameters in environmental degradation for

polyurethane in an application such as DH pipes.

The estimation of the lifetime of DH pipes is commonly based on accelerated thermal

ageing, regardless of other influencing factors. The objective of this chapter is to




59

investigate the ageing of DH pipes subjected to both cyclic mechanical loads and

elevated temperatures, by focusing on polyurethane degradation.

3.2 Choice of objects and conditions

The analysis was performed with the following choices and conditions.

Object: the investigations were carried out using straight DH-pipes (DN 50/160 mm),

which are usually employed for 3GDH, and composed of a steel pipe as a service pipe,

rigid polyurethane foam as insulation, and a high density polyethylene pipe as a casing.

The DH pipes used for the experiments were produced by Powerpipe Systems AB

using a discontinuous processing method. These new samples were used in order to

have the same history for the tested pipe with and without load, as well as for the pipes

aged at different temperatures.

Mechanical load: a varying axial load was applied to simulate the shear occurring in the

expansion zone of a pipe in the ground. The maximum shear stress occurring at the

interface of the service pipe and the foam was 31 kPa, and the time period of the cycle

was 1 hour.

Conditions: The ambient temperature was 23 ± 2°C, and internal temperatures in the

service pipe were 130, and 140 ± 2 ⁰C, respectively.

3.3 Selection of mechanical loading

In the sliding zones, the pipe assemblies are exposed to high temperature and

mechanical loading, due to varying operating temperature and thermal expansion. In

these zones, the axial forces vary along the pipe due to friction and sliding. The soil

friction causes axial shear stresses in the pipe assembly, reaching a maximum in the

polyurethane (PUR) insulation, at the interface with the service pipe. Here, the PUR

insulation also degrades faster, given the higher temperature. The failure mode

investigated is the loss of adhesion between the PUR insulation and the steel service

pipe. This could cause thermal expansion of the steel service pipe, leading to fatigue

failure at critical locations like joints or weld defects. Hence, the end of life of a pipe

segment is due to that failure mode. The shear stresses only depend on the friction

force per unit length of pipe, which in turn depends on the friction coefficient, and the

soil pressure on the pipe. It is assumed that the pipe is buried above the ground water

level, so that the ground water pressure does not act on the casing.




60

In the experiments, pipes of dimension DN 50/160 mm were chosen, where DN 50

refers to the service pipe, and 160 mm to the casing. The reasons for this choice are

that it has been used previously in two research projects (Yarahmadi et al., 2017a;

2017b), it is commonly used, and it is manageable in the laboratory. The chosen length

of the pipes was 3.4 m. Table 3.1 presents the input parameters for calculating a

reasonable magnitude of the axial load in the experiments. The calculations follow the

equations given in the standard EN 13941 (2019). Different soil covers are used in the

participating countries Korea, Germany and Sweden. The maximum applied soil cover

in Korean and Germany is about 1.5 m and in Sweden the soil cover is usually 0.6 m.

In the calculations the soil cover 1.2 m was chosen. The friction coefficient is usually

about 0.4, but the maximum according to standard is 0.6, which was chosen in the

present analysis. These choices will give a relatively high value on the friction force.

Table 3.1: Input data for calculation of axial force in experiments.

Parameter Symbol Value Unit Friction coefficient µ 0.6

Soil pressure coefficient K0 0,5

Weight density of soil γ 20 kN/m3

Density of water ρw 1000 kg/m

3

Density of steel ρs 7850 kg/m

3

Density of polyethylene ρpe

960 kg/m3

Density of polyurethane ρpur

60 kg/m3

Cover HC 1.2 m

Length of pipe in experiment 3.4 m Axial force F 19 kN

The pipe with the chosen dimension may be used for a house connection. In

EN 13941 (2019), the estimated number of full thermal cycles with the range 110°C is

1000 during a service life of 30 years. The house connection is subjected to a spectrum

of different thermal cycle ranges. The temperature range influences the maximum pipe

axial force and the length of the expansion zone, i.e., the length of deformed pipe

during the cycle. Here, a simplified case is treated, and a representative temperature

range is assumed to be half the range of the full cycle. The fatigue curve of the welded

service pipe can be written:




61

b

S

kN

= (3.1)

where, N is the number of cycles until failure at the stress range S. The shape of the

fatigue curve is given by the parameters k and b. According to EN 13941 (2019), the

exponent is equal to b = 4. Hence, the corresponding number of cycles with half the

range during the service life of 30 years is:

( ) 16000551101000 40 ==N (3.2)

For the experiments, the chosen axial load range is 20 kN, while the time period of the

load cycle is one hour. This means that the desired number of load cycles of the

experiments can be reached during less than two years.

3.4 Experiments

Thermal ageing at relative high temperatures is a common method to estimate the

technical lifetime of DH pipes. According to EN 253, temperatures around 160 and

170°C are suitable for accelerated thermal ageing. However, in a previous project

(Yarahmadi et al., 2017a; 2017b), it was shown that it is important to choose the correct

ageing temperature. Too high temperature activates other degradation mechanisms

which are not relevant for the district heating application.

In the previous project (Yarahmadi and Sällström, 2015), DH pipes were aged at 130,

150, and 170°C, while the mechanical adhesion between the steel pipe and the PUR

foam was studied by testing and measuring the shear strength. The results suggested

a different behaviour for ageing temperatures equal to 150°C and higher, compared to

130°C. Figure 3.1 shows that these results can not be used to determine the activation

energy Ea in the Arrhenius relationship:

−⋅=RT

EAk aexp (3.3)

The reason is the different behaviour of the shear strength of the pipe aged at 130°C,

compared to the pipes aged at higher temperatures.




62

In the current project, five DH pipes with dimension DN50/160 were prepared for both

studying thermal ageing at elevated temperatures, and thermal ageing in combination

with mechanical axial loads. One pipe was kept at room temperature as a reference.

Four pipes were connected to the electrical installation for thermal ageing, and two of

them were also connected to the axial loading equipment during thermal ageing, as

shown in Figure 3.2. The piston acts on the service pipe, and the cylinder is connected

with bars to several axial positions to the casing. The selected ageing temperatures are

130 and 140°C, based on the results from the previous project (Yarahmadi et al., 2017a;

2017b).

Two electrical cylinders were programmed to apply a cyclic axial load of range 20 kN,

as shown in Figure 3.3.

All pipes were tested for mechanical adhesive strength, and some of the obtained PUR

samples were analysed using Fourier transform infrared (FTIR) technique.

Figure 3.1: Mechanical adhesive strength results expressed in percentage of the initial break torque (Yarahmadi et al., 2017b).




63

Figure 3.2: Schematic electrical and mechanical installation for testing of DH pipes.

Figure 3.3: Schematic axial load cycle.

3.4.1 Mechanical testing

The adhesive strength was measured as shear strength that was determined by

applying a torque to an uncovered polyurethane cylindrical plug (drill core), attached to

the service pipe, as shown in Figure 3.4.

The fracture occurs between the service pipe and the polyurethane foam (adhesion), or

in the foam (cohesion) close to the service pipe, when a cylindrical specimen is twisted

off, as the torque is measured.

The shear strength is defined as the ultimate shear stress τu occurring at the

circumference of the plug. It is calculated by use of:

3

16d

Mu π

τ = (3.4)




64

where M is the applied maximum torque, and d is the diameter of the plug.

Figure 3.4: Sketch of mechanical testing.

3.4.2 Fourier Transform Infrared spectroscopy

Changes in the PUR foam’s chemical structure because of ageing can be identified by

FTIR spectroscopy analyses. Some reactions between polyol, NCO, and the additives

are not completed during the PUR manufacturing process. Thus, the reactions can take

place during the early phase of application, leading to property changes of the PUR

foam. An important characteristic of PUR foam is the so-called NCO index, which is a

measure of the amount of NCO used, compared to the stoichiometric amount required.

Foams with a very high NCO index (large excess of NCO) have a large proportion of

the trimetric cyclic isocyanurate structure, which increases the thermal stability of the

polymer.

This section describes the effect of thermomechanical exposure on chemical structure

of PUR in pre-insulated DH pipe, analyzed using the FTIR spectroscopic method.

Some PUR plugs from the mechanical tested samples were chosen for analysis of their

chemical structure. In all PURs, the repeating unit is the urethane linkage produced

from the reaction of an isocyanate (–N=C=O) with an alcohol (–OH). The urethane

group (–NH–CO–O–) is the weak link in PUR material, regarding degradation process.

In this investigation, degradation of the urethane group was used as an indicator for

changes in the chemical structure of PUR. Thermo-oxidative stability of PUR depends

on its structure, especially the chemical structure of the polyol. The intensity of the




65

methylene diphenyl diisocyanate (MDI) aromatic ring deformation (aromatic ν(C=C)

vibration) at 1595 cm–1 was used as the internal reference during usage of Fourier

transform infrared spectroscopy (FTIR) in attenuated total reflection (ATR) mode.

3.5 Results

The DH pipes have been aged according to the description in the previous chapter, and

the mechanical adhesive strength was evaluated using the RISE plug method, after

different thermal and mechanical ageing intervals. Figure 3.5 shows the installation of

the DH pipes in the test chamber, and Table 3.2 summarizes the test information.

Figure 3.5: Electrical and mechanical test installation.

Table 3.2: Test information.

Pipe name Mechanical ageing by Cyclic load (kN)

Thermal ageing ( °C)

Reference 0 23 DHP130 0 130

DHP130 load 0-20 130 DHP140 0 140

DHP140 load 0-20 140




66

The electrical cylinders were intended to follow the top curve (blue curve in Figure 3.6).

However, no compensation for the relaxation of the polyurethane was considered,

resulting in a decrease of the load (middle and bottom curves for the pipes exposed to

130 and 140ºC, respectively, in Figure 3.6) during the interval of 28 min. Instead of

controlling the force after the desired maximum was reached, the displacement was

kept constant by applying a brake to the piston of the loading cylinder. The reason for

this was to minimize the wear of the loading cylinder.

Figure 3.6: Axial load cycle between 0 and 20 kN with a total cycle time of 58 min.

3.5.1 Mechanical adhesive strength

The testing periods were chosen to represent significant events observed in the

previous project (Yarahmadi et al., 2017a; 2017b) at similar temperatures, and are

presented in Table 3.3. The number of cycles, and the ageing time differ, since the

thermal ageing has been running more or less continuously, but there have been

interruptions of the mechanical loading.




67

Table 3.3: Test time for both temperatures.

DHP130 DHP140 Ageing time (h) # Load cycles Testing date Ageing time (h) # Load cycles Testing date

720 637 2018-07-27 529 565 2018-07-19

1320 1106 2018-08-21 1008 992 2018-08-09

3600 2550 2018-12-10 2136 2042 2018-09-25

5064 4000 2019-02-11 2976 2850 2018-11-01

7176 5536 2019-05-17 4800 4350 2019-01-17

8112 6536 2019-06-28 6072 5614 2019-03-18

8088 7114 2019-06-12

The results obtained from the mechanical tests are presented in Figure 3.7, Figure 3.8,

Figure 3.9, and Figure 3.10.

Figure 3.7: Mechanical adhesive strength from all four DH pipes aged at 130 and 140°C with and without loads.




68

Figure 3.8: Mechanical adhesive strength from DH pipes aged at 130 and 140°C with load.

Figure 3.9: Mechanical adhesive strength from DH pipes aged at 140°C with/without load.




69

Figure 3.10: Mechanical adhesive strength from DH pipes aged at 130°C with/without load.

The experimental results confirmed the mechano-chemical effect, where a faster

deterioration of the mechanical adhesive strength was obtained by combining thermal

and mechanical ageing, using axial loading and elevated temperature simultaneously.

3.5.2 Fourier-transform infrared spectroscopy

Some PUR plugs from the mechanical tests were chosen for analysis of their chemical

structure. The purpose was to study the effect of synergistic degradation mechanisms

by thermal and mechanical ageing on the chemical structure of the PUR material. Two

slices from each selected PUR plug were studied. One slice was taken near to the

contact surface between PUR and the steel service pipe. Another slice was taken 20

mm above this contact surface, as shown in Figure 3.11.

Figure 3.12 shows a FTIR spectrum from a PUR sample. The analysis focuses on the

following peaks:

• C-H in methyl at 2975 cm-1

• Unreacted NCO at 2277 cm-1

• C=O in the urethane group at 1712 cm-1 and N – H at 1512 cm-1

• Aromatic rings C=C at 1595 cm-1




70

• Isocyanurate rings at 1411 cm-1

(a) (b)

Figure 3.11: PUR plugs from mechanical tests (a), and PUR slices for FTIR test (b).

Figure 3.12: FTIR spectrum of a PUR sample.

For a correct comparison, the absorbance values of the relevant peaks were

normalized using the peak at 1595 cm-1 corresponding to the aromatic ring, regarded

as the internal reference. The normalized results are presented in Figure 3.13 and

Figure 3.14. Differences between the carbonyl peaks at 1712 cm-1 from samples close

to the steel pipe (2 mm from the steel pipe), aged at 130°C, loaded, after 150 and 211




71

days (Figure 13a), and corresponding pipe aged at 130°C, unloaded, (Figure 13c) are

obvious. Similar differences are measured using pipes after ageing at 140°C (Figures

14a and 14c). The PUR degradation is also observed in the changes in peak intensity

at 1512 cm-1 (Figures 3.13 and 3.14). The changes increased with increasing ageing

time. The FTIR analyses strongly indicate that the combined effect of cyclic mechanical

loading, and thermal ageing accelerates the rate of chemical degradation of PUR foam,

reducing its shear strength.

(a) (b)

(c) (d)

Figure 3.13: FTIR analysis of the DH pipes aged at 130 °C with and without load.




72

(a) (b)

(c) (d)

Figure 3.14: FTIR analysis of the DH pipes aged at 140°C, with and without load.

The results from the shear strength measurements confirmed the results from previous

investigations with thermal ageing at 130°C, showing after the initial part of ageing, that

the adhesive strength remains unchanged for a very long period (plateau phase). This

investigation has also confirmed that thermal ageing at 140°C exhibits the same type of

ageing behaviour, but at a higher rate of deterioration. In the pipes exposed to a

combination of thermal ageing and axial loads, the first part of the ageing process

observed in thermal ageing is missing. The adhesive strength decreases until a plateau

is reached at the level of about 44% of the original adhesive strength, which is

significantly lower compared to thermal ageing. The plateau phase is also reached

roughly after half the time of the corresponding thermal ageing, due to mechano-

chemical processes. The FTIR analyses revealed that this effect originates from the

chemical degradation of PUR, and is not only a result of fatigue.




73

3.6 Interpretation of results and evaluation of usa bility

The aim of this chapter was, to understand the effect of simultaneity of load and

thermal ageing on the adhesion strength between steel pipe and PUR insulation in a

DH-pipe. The measurements have been done using the RISE plug method, and the

FTIR spectroscopy. Both measurements confirm an increase of the degradation

process with combination of load and thermal ageing, for both pipes aged at 130 and

140°C. Clearly, the lower the applied temperature, the slower the process of material

ageing.

To perform such study, some assumption and calculation were needed. The estimation

of the relevant load acting on service pipe, as a result of the axial movements caused

by changes in temperature, and the estimated number of load cycles occurring in the

entire service life of a DH pipe, was calculated before set up of the experiment. The

RISE plug method, and the FTIR are good complementary methods for evaluating the

synergic effect of mechanical load, and thermal ageing on the deterioration of

properties for loaded pipe, in comparison to unloaded pipes.




74

4 Field tests

The purpose of this workpackage is to perform the field study of naturally aged DH

pipes, in order to compare the mechanical and chemical effects between high and low

temperature. Therefore, a number of test specimens of naturally aged pipes were

acquired from the DH sites in South Korea to analyze the operating temperature, and

evaluate the shear strength.

On-site supply and return pipes were tested to analyze the effects of high and low

temperatures. The temperature level of supply and return pipes in South Korea is about

100~120°C, and 40~60°C, respectively. The temperature variation in return pipes can

be assumed analogous to that in 4GDH, with relatively more thermal fluctuation,

compared to the current supply temperature.

4.1 Field selection and data acquisition

4.1.1 Selecting and test preparation of naturally a ged DH pipes

The naturally aged DH pipes were gathered from four DH branches of KDHC in South

Korea for shear strength tests. The minimum length of test pipes is 1000 mm, to obtain

at least three specimens (SPMs) for axial shear test, and one SPM for spare and/or gas

analysis, etc. Figure 4.1 shows an example of sampling location, while the method to

cut the test SPMs from each sampling pipe is shown in Figure 4.2. Figure 4.3 shows a

view of acquiring the pipe samples in the field.

The collected pipe samples were sealed on the field as shown in Figure 4.4, and

transported immediately to the test site. In order to perform the shear strength test, the

pipe samples were cut to 200 mm length, as shown in Figure 2.5. The cut specimens

were wrapped with aluminum foil to minimize the property changes before the test, as

shown in Figure 2.6.

Table 4.1 summarizes the characteristics of the sampling pipes, including the sampling

branch and location, dimension, age, installation time, as well as the operating

temperature in supply and return.




75

Figure 4.1: Example of sampling location for field test.

Figure 4.2: Test specimen cutting.




76

Figure 4.3: Pipe sample acquisition.

Figure 4.4: Acquired samples: (left) Daegu branch, (right) Goyang branch.




77

Figure 4.5: Sample cutting.

Figure 4.6: Prepared test samples.




78

Table 4.1: Dimension, ageing time and sample number of naturally aged pipes.

Dimension Branch and

location Carrier [mm]

Casing [mm]

Installation year

Sampling and test year Aged year

Type (Supply / Return)

SPM No

Daegu 65 140 1997 2018 21 R #01

S #02

S #03

R #04 Goyang 80 160 1995 2018 23

R #05

S #06

S #07

R #08 Suwon-1 125 225 2001 2019 18

R #09

S #10

S #11

S #12

R #13

Suwon-2 125 225 1998 2019 21

R #14

S #15

S #16

S #17

R #18

R #19

Suwon-3 100 200 1998 2019 21

R #20

S #21

S #22

R #23 Jungang-1 100 200 1987 2019 32

R #24

S #25

S #26

S #27

R #28

R #29

Jungang-2 80 160 1987 2019 32

R #30

S #31

S #32

S #33

R #34

R #35

Jungang-3 80 160 1987 2019 32

R #36




79

4.1.2 Measuring the shear strength

Figure 4.7 shows the pipe specimen before the test, and Figure 4.8 shows the test

device, and set-up for the axial shear strength test. The test was carried out in

accordance with EN253.

Figure 4.7: Test specimen before the test.

Figure 4.8: Shear strength test set-up.




80

4.2 Results

4.2.1 Shear strength of naturally aged DH pipes

Figure 4.9 shows the tested pipe specimens. The speed of stroke was 5 mm/min and

the axial force was recorded. Figure 4.10 to 4.17 show the load-stroke curve obtained

by the shear strength test at each sampling location.

SPM #01 SPM #02 SPM #03 SPM #04

SPM #05 SPM #06 SPM #07 SPM #08

SPM #09 SPM #10 SPM #11 SPM #12

Figure 4.9: Test specimens after the test.




81

SPM #13 SPM #14 SPM #15 SPM #16

SPM #17 SPM #18 SPM #19 SPM #20

SPM #21 SPM #22 SPM #23 SPM #24

Figure 4.9: Test specimens after the test (contd.).




82

SPM #25 SPM #26 SPM #27 SPM #28

SPM #29 SPM #30 SPM #31 SPM #32

SPM #33 SPM #34 SPM #35 SPM #36

Figure 4.9: Test specimens after the test (contd.).




83

Figure 4.10: Shear strength curves / Daegu.

Figure 4.11: Shear strength curves / Goyang.




84

Figure 4.12: Shear strength curves / Suwon-1.





85


Figure 4.15: Shear strength curves / Jungang-1.




86






87

According to the standard EN 253, the shear strength is calculated from the following

formula:

πτ

⋅⋅=

s

axax DL

F (4.1)

where,

τax axial shear strength, in MPa;

Fax axial force, in N;

L length of specimen, in mm;

Ds outside diameter of the service pipe, in mm

The calculated shear strength of the SPMs are summarized in Table 4.2.

Figure 4.18 shows the shear strength of 36 naturally aged DH pipes by ageing year.

The shear strength of the supply and return pipes is widely distributed in the range of

0.13 to 0.46MPa. At first glance, it does not seem to follow any special trend,

depending on the ageing year. However, the linear trend line, assuming the initial shear

strength as 0.4MPa, shows that the shear strength drop rate of the supply pipes is

faster than the return pipes. In this case, the expected lifetime for reaching the

minimum required shear strength of 0.12MPa, according to EN 253, was 45.9 years for

the supply pipes, and 140 years for the return pipes.

Moreover, despite the same ageing time, the decrease in shear strength is dependent

on the temperature history.




88

Table 4.2: Calculation of shear strength.

SPM No.

Type (Supply / Return)

Max. axial load [kgf]

Max. axial load [N]

SPM length [mm]

Outside diameter of service pipe

[mm]

Axial shear strength

[kPa]

#01 R 1239 12152 200 76.3 253

#02 S 2090 20503 200 89.1 366

#03 S 2361 23162 200 89.1 414

#04 R 2674 26232 200 89.1 469

#05 R 2671 26203 200 89.1 468

#06 S 2222 21798 200 139.8 248

#07 S 2098 20581 200 139.8 234

#08 R 2241 21979 200 139.8 250

#09 R 2467 24201 200 139.8 276

#10 S 1164 11419 200 139.8 130

#11 S 1200 11767 200 139.8 134

#12 S 1376 13494 200 139.8 154

#13 R 1403 13759 200 139.8 157

#14 R 1443 14151 200 139.8 161

#15 S 1269 12449 200 114.3 173

#16 S 1504 14749 200 114.3 205

#17 S 1544 15147 200 114.3 211

#18 R 2805 27517 200 114.3 383

#19 R 2569 25197 200 114.3 351

#20 R 2864 28096 200 114.3 391

#21 S 900 8829 200 114.3 123

#22 S 858 8412 200 114.3 117

#23 R 1125 11031 200 114.3 154

#24 R 1098 10766 200 114.3 150

#25 S 1619 15877 200 89.1 284

#26 S 1856 18207 200 89.1 325

#27 S 2434 23873 200 89.1 426

#28 R 2512 24638 200 89.1 440

#29 R 2471 24236 200 89.1 433

#30 R 2598 25486 200 89.1 455

#31 S 1107 10860 200 89.1 194

#32 S 1197 11738 200 89.1 210

#33 S 1330 13047 200 89.1 233

#34 R 2523 24746 200 89.1 442

#35 R 2336 22916 200 89.1 409

#36 R 2649 25987 200 89.1 464




89

Figure 4.18: Axial shear strength - All.

Figure 4.19 shows only the shear strength of the supply pipes. SPMs #10 to 12 and

#15 to 17 have the same ageing years of 21, but the measured shear strength varies

between 0.13 to 0.15MPa, and 0.17 to 0.21MPa, respectively. This trend can be more

clearly distinguished in #21 to 22 and #25 to 27, with the same 32 aged years. The

return pipes have the same tendency, as shown in Figure 4.20.




90

Figure 4.19: Axial shear strength – supply pipes.

Figure 4.20: Axial shear strength – return pipes.

The operating temperature of tested SPMs was analyzed to explain the cause of these

trend. Figure 4.21 to 4.27 show the temperature histories of tested SPMs over the last




91

3 years. The temperature histories of Daegu (Figure 4.21) and Goyang (Figure 4.22)

branches were also used in the fatigue analysis in workpackage 1 (chapter 1).

Figure 4.24 and Figure 4.25 represent the temperature history of SPM #10 to 14, and

SPM #15 to 20, respectively. In the case of “Suwon-2 (Figure 4.24)”, the heating site is

a government office building, showing very large daily temperature changes. High

demand heating, and hot water supply is concentrated only during daytime, and supply

is cut off at night and during the holidays. It is typical of intermittent (on and off)

operation, due to the nature of government offices. On the other hand, “Suwon-3

(Figure 4.25)” shows a typical pattern of heat supply in apartment.

The same trend can be found in the temperature history “Jungang-1 (Figure 4.26)” of

the SPMs #21 to 24 and “Jungang-2 (Figure 4.27)” of the SPMs #25 to 30. The return

temperature of “Jungang-1” occurs at a greater fluctuation than “Jungang-2”, which

may be associated with the decrease in shear strength.

In conclusion, the analysis of naturally aged pipes from DH sites in South Korea

showed that the shear strength of the DH pipes is related not only to operating

temperature itself, but also to the extent of temperature fluctuation.

The results demonstrate the validity of the new test method performed in workpackage

3 (chapter 3), considering the effect of temperature and axial load at the same time. It

also presents important implications to consider when determining the lifetime of DH

pipes in 4GDH operating condition, associated with large changes in supply

temperature.

Figure 4.21: Operating temperature – Daegu.




92

Figure 4.22: Operating temperature – Goyang.

Figure 4.23: Operating temperature – Suwon-1.




93

Figure 4.24: Operating temperature – Suwon-2

Figure 4.25: Operating temperature – Suwon-3.




94

Figure 4.26: Operating temperature – Jungang-1.

Figure 4.27: Operating temperature – Jungang-2 and Jungang-3.




95

4.2.2 FTIR analysis of naturally aged DH pipes

Two parts of naturally aged pipe, provided by KDHC, have been evaluated at RISE,

using the Piopsy Method (a combination of RISE plug method and FTIR analysis).

These two pieces for FTIR test were obtained from same pipe gathered from Suwon-2

location (SPMs #10 to #14) for shear strength test (Table 4.1). Herein one piece was

from a supply pipe, and the other one from a return pipe, as shown in Figure 4.28.

Figure 4.28: Two naturally aged pipe pieces: one from a supply pipe (FTIR SPL-S) and another from a return pipe (FTIR SPL-R).

Three plug tests were carried out on each piece of pipe. The obtained results are

summarized in Table 4.3. The values obtained by the plug method showed results

almost similar to the axial shear strength test. The relative shear strength between the

supply and return pipes is equal to σsup /σret = 0.78.




96

Table 4.3: Results from the plug tests.

Return Supply

Test #1 1.77 1.5

Test #2 1.97 1.45

Test #3 1.71 1.32

Average 1.82 1.42

St. dev. 0.14 0.09

The chemical structure of the obtained plugs was analysed using the FTIR-ATR

method. Two slices of approximately 2 mm were cut from each plug. One slice from the

contact surface between PUR and steel service pipe, and the other slice 20 mm above

this point. Three measurements were performed on each slice. The absorption values

were normalized using the peak of aromatic ring as an internal reference. The

absorption indexes of some relevant peaks are shown in Figure 4.29. Peaks 1712 and

1512 shows higher degradation of the contact surface at the supply pipe.

Figure 4.29. Normalized absorption indexes of some relevant peaks (S= supply and R= Return).

The result from FTIR indicate significant changes for the supply pipe near the steel pipe,

in comparison to the return pipe. Moreover, the results of FTIR analysis of naturally

aged DH pipes are similar to those of artificial ageing at 130~140°C with cyclic loads,

performed in workpackage 3 (chapter 3). This proves that the new accelerated ageing

techniques suggested in this study represent well the natural ageing conditions.




97

5 Consequences for network design and asset managem ent

strategy

The purpose of this workpackage is to examine the consequences of the results

obtained within the present research project for improving the current network design.

5.1 Analyze consequences and impacts of future load s on the service pipe

Considering the lower impact of operating temperature, and thermal loading fluctuation

in the network, the lifetime of pre-insulated bonded single pipes used in 4GDH is

expected to increase, in comparison to 3GDH pipelines, with the same design

configuration. The latter are typically designed for 30 years, although many pipelines in

operation are even older (Weidlich and Schuchardt, 2017). Consequently, 4GDH

pipelines would manifest a slower material degradation, and potentially lead to the

implementation of new pipe materials with enhanced thermo-mechanical properties,

economically and environmentally more beneficial.

This conclusion can be transferred to other DH networks. However, the findings in this

study are based on a limited number of data sets, while several other network set-ups,

and operational modes exist. Presumably, DH networks with power to heat devices,

fast unloading big storages, and deviating customer behaviour could manifest different

load characteristics.

One important lesson learned is related to the data logging process. The sensitivity

analysis performed in this study showed that the measuring time interval in the

temperature data should be sufficiently small, to accurately estimate the number of full

temperature cycles, and associated fatigue damage, depending on the particular

operating conditions of the DH pipes.

5.2 Consequences and impacts of future loads on the adhesion

between service pipe and insulation

The analysis of the shear strength data from naturally aged pipes demonstrated that

thermal loading has a significant influence on the pipe axial shear strength. Moreover,

the observed axial shear strength for a thin pipe was greater than for a thick pipe.

However, detailed information on the operating temperature history and initial pipe




98

material data are necessary, for obtaining a direct relationship between the residual

shear strength and the operating time, as well as the foam density.

The implemented laboratory test set-up allowed to investigate accelerated ageing of

DH pipes, considering the combined effect of thermo-oxidative degradation and cyclic

mechanical stresses. While changes of the adhesive strength in pipes exposed only to

thermal ageing follow the same pattern as in previous investigations, changes in

adhesive strength in pipes, exposed to the combined mechanical and thermal ageing,

exhibit partly a different behaviour. The adhesive strength decreases until a plateau is

reached at a level of about 44% of the original adhesive strength, which is significantly

lower compared with thermal ageing. The plateau is reached after about 200 days at

130ºC, and after about 100 days at 140ºC, which roughly corresponds to half the

thermal ageing time without mechanical stresses.

Clearly, the accelerated ageing tests demonstrated that combined effect of mechanical

loading and thermal ageing does not only cause mechanical fatigue, but it also

accelerates the rate of chemical degradation of the PUR foam.

Furthermore, in the naturally aged pipes, the rate of the shear strength drop in the

supply pipes is faster than the return pipes, due to the higher operating temperature. In

addition to the ageing time, the shear strength of the naturally aged DH pipes depends

on the temperature history, requiring proper data logging.

5.3 Recommendations concerning network design and a sset management of 4th generation DH systems

Asset management for 4GDH is not common today. This kind of infrastructure is young

compared to conventional DH, or to other infrastructure (as for instance sewers, where

predictive maintenance is daily business). Therefore, the first important

recommendation for utilities with 4GDH networks is to start data gathering, based on

asset management, as soon as possible. Temperature history and failures should be

documented, with highest accuracy possible. Specifically, the frequency of the

measured temperature data should be sufficiently small (e.g. 5 min), to accurately

estimate the number of full temperature cycles, and associated fatigue damage of the

steel service pipe, depending on the particular operating conditions of the DH pipes.

These data should be stored in a reliable way. In addition, it is recommended to

document the starting point of the most important properties of the pipe before




99

installation. At least, the shear strength, the compression strength, and the thermal

conductivity should be determined according to EN 253. Although this standard is valid

only for 3GDH pipes, the adopted methods are transferable to different types of DH

pipes. For low and very low temperatures some deviations have to be taken into

account, considering the latest standards in this field (for instance prEN 17414 and

prEN 17415 for district cooling).

The lower operating temperature in 4GDH would increase the lifetime of preinsulated

district heating pipes, designed according to EN 253. This would create new

opportunities for new pipe material, and deviations from EN 253, which is expected to

realize economic potentials for 4GDH. This development perspective challenges

existing ageing models, and the current asset management strategies. Therefore, it is

recommended to create a material and load database for each district heating network,

taking into account the pipe materials with initial properties, trench conditions, and load

history. This would lay the foundation for a good predictive maintenance, and a

reduction of economic risks for replacement and repair.

Concluding remarks

The aim of this research project is to determine the lifetime of 4th generation DH

heating networks, developing a new approach, that takes into account the increased

cyclic mechanical and thermal loads, as well the decreased thermal ageing.

The fatigue analysis of the steel pipe, performed considering the collected temperature

data from conventional and 4th generation DH pipelines, showed that the latter are

subjected to greater thermal fluctuation in the limited region of the solar thermal circuit.

The fatigue demand drops drastically before entering the main heating circuit, due to

controlling measures adopted by DH companies. Therefore, the lifetime of 4GDH

pipelines is expected to increase due to the lower operating temperature, and the low

impact of thermal loading volatility in the network, compared to conventional DH.

Moreover, a large measuring time interval in the temperature data, can lead to an

underestimation of the number of full temperature cycles, and associated fatigue

damage, depending on the particular operating conditions of the DH pipes. This

indicates that a more frequent sampling is necessary, while performing low cycle

fatigue analysis, requiring proper data logging.




100

The experimental investigation of the adhesion strength of DH pipes showed a faster

deterioration of the mechanical adhesion strength, when combining thermal ageing and

axial loading simultaneously. Clearly, the most severe conditions are at the interface

between the steel pipe and the foam material, undergoing larger strains and greater

chemical changes, triggered by the mechanical load. Interestingly, the FTIR analyses

indicated that the observed higher rate of deterioration originates from the chemical

degradation, and is not only a result of fatigue.

The analysis of the naturally aged DH pipelines showed that, in addition to the ageing

time, the shear strength of DH pipes depends on the temperature history, decreasing

with the level of operating temperature and amount of fluctuation.

The obtained results permit to gain a better understanding of the performance of

traditional and 4GDH pipelines in operation, that need to be suitably considered in the

engineering design standards of DH networks, contributing to a more sustainable and

energy efficient infrastructure.

Acknowledgments

The authors would like to acknowledge Prof. Thorsten Urbaneck from the Department

of Mechanical Engineering at the Chemnitz University of Technology, and Mr. Thomas

Göschel from inetz GmbH, for providing helpful guidance and detailed information on

the collected temperature data within the recent German research project "Solar district

heating for the Brühl district in Chemnitz – accompanying research (SolFW)". Thanks is

extended to Mr. Stefan Hay from AGFW GmbH, for the helpful support in gathering

4GDH temperature data. Thanks are extended to Enercity Netz GmbH for providing the

DH network data, and the test samples of DH pipes, as well as the colleagues at FFI for

all the support in performing the tests. Thanks are extended to Power Pipe AB for the

valuable discussion and manufacturing of DH pipes, as well as to the colleagues at

Pipe Centre at RISE for all the support and help to set up the experimental part.

Moreover, the authors would like to acknowledge Mr. Eun Sick Kang from the

Pipeteckorea Co. Ltd. for the cooperation in the axial shear strength test of naturally

aged pipes in Korea. Finally, thanks are extended to the members of the IEA DHC

Expert Group for their useful input and guidance during this research project, and in

reviewing the final report.




101

Bibliography

AGFW-Arbeitsblatt FW 401 – Teil 10 (2007). Verlegung und Statik von

Kunststoffmantelrohren (KMR) für Fernwärmenetze – statische Auslegung; Grundlagen

der Spannungsermittlung. Hrsg. v. AGFW Arbeitsgemeinschaft für Wärme und

Heizkraftwirtschaft e.V. beim VDEW e.V., Frankfurt a. M.

Andrews, E.H. (1969) Fatigue in polymers, Testing of Polymers, Vol. IV, W. Brown, ed,

New York: Interscience, 237.

ASME B31.1 (2016) Power piping, American society of mechanical engineers.

ASME B31.3 (2016) Process piping, American society of mechanical engineers.

ASTM Standard E 1049, 1985 (2011). Standard Practices for Cycle Counting in Fatigue

Analysis. West Conshohocken, PA: ASTM International, 2011.

Bernard-Connolly, M., Bui-Quoc, T., Biron, A. (1983). Multilevel strain controlled fatigue

on a type 304 stainless steel. Journal of Engineering Materials and Technology, 105(3),

188-194.

Bleck, W., Dahl, W., Nonn, A., Amlung, L., Feldmann, M., Schäfer, D., Eichler, B.

(2009). Numerical and experimental analyses of damage behaviour of steel moment

connection. Engineering Fracture Mechanics, 76(10), 1531-1547.

Casale, A., Porter, R.S., Johnson, J.F. (1975) Rubber Chem. and Techn. 44/2, 534-577.

Christensen, R., Hansen K.E., Neergaard L.B., Randlov P., Olsson N. (1999). Fatigue

Analysis of District Heating Systems, IEA District Heating and Cooling, Programme of

Research, Development and Demonstration on District Heating and Cooling.

Dowling, N. E. (2013). Mechanical Behaviour of Materials. Engineering Methods for

Deformation, Fracture, and Fatigue. Fourth Edition. Pearson.

Downing, S., Galliart, D., Berenyi, T. (1976). A Neuber's rule fatigue analysis procedure

for use with a mobile computer. SAE Transactions, 1252-1261.

Downing, S.D., Socie, D.F. (1982). Simple rainflow counting algorithm. International

Journal of Fatigue. 1. pp. 31-40.

EN 13480-3 (2017) Metallic industrial piping – Part 3: design and calculation, European

committee for standardization (CEN).

EN 13941 (2019) Design and installation of preinsulated bonded pipe systems for

district heating.




102

EN 253 (2019) District heating pipes - Bonded single pipe systems for directly buried

hot water networks - Factory made pipe assembly of steel service pipe, polyurethane

thermal insulation and a casing of polyethylene.

prEN 17414 (2019) District cooling pipes - Factory made flexible pipe systems - Part 1:

Classification, general requirements and test methods; Part 2: Bonded system with

plastic service pipes; requirements and test methods; Part 3: Non bonded system with

plastic service pipes; requirements and test methods.

prEN 17415 (2019) District cooling pipes - Bonded single pipe systems for directly

buried cold water networks - Part 1: Factory made pipe assembly of steel or plastic

service pipe, polyurethane thermal insulation and a casing of polyethylene.

Fernandes, A. A., de Jesus, A. M., Jorge, R. N. (2018). Monotonic and Ultra-Low-Cycle

Fatigue Behaviour of Pipeline Steels: Experimental and Numerical Approaches.

Springer.

Frederiksen S., Werner S. (2013). District heating and cooling. Sweden:

Studentlitteratur, 697.

Gudehus, H.,Zenner, H. (1995). Leitfaden für eine Betriebsfestigkeitsrechnung. Verlag

Stahleisen mbH.

Haibach, E. (2006). Betriebsfestigkeit: Verfahren und Daten zur Bauteilberechnung.

Springer-Verlag.

Haibach, E. (1970). Modifizierte lineare Schadensakkumulations-hypothese zur

Berücksichtigung des Dauerfestigkeitsabfalls mit fortschreitender Schädigung.

Laboratorium für Betriebsfestigkeit.

Hashin, Z., Laird, C. (1979). Cumulative damage under two level cycling: some

theoretical predictions and test data. Fatigue & Fracture of Engineering Materials &

Structures, 2(4), 345-350.

Hück, M., Thrainer, L., Schütz, W. (1983). Berechnung von Wöhlerlinien für Bauteile

aus Stahl, Stahlguß und Grauguß: synthetische Wöhlerlinien. Stahleisen.

ISO 12110-2 (2013). Metallic materials - Fatigue testing - Variable amplitude fatigue

testing - Part 2: Cycle counting and related data reduction methods.

Kanvinde, A. M., Fell, B. V., Deierlein, G. G. (2007). Physics-based continuum models

by Abaqus to simulate fracture and ultra low cycle fatigue in steel structures. Structural

Engineering Research Frontiers, 249(33), 14.




103

Kausch, H.H. (1986) Polymer fracture, 2nd ed., Springer, Heidelberg. New York.

Lauer, W. (1975) Kautschuk + Gummi, Kunstoffe 28/9, 536-613.

Leonatris, G. (1995). Ein Konzept zur Lebensdauervorhersage, Dissertation,

Universität-Gesamthochschule Kassel.

Linn, S., Scholz, A. (2013). Creep-fatigue lifetime assessment with phenomenological

and constitutive material laws. Procedia Engineering, 55, 607-611.

Manson, S. S., Halford, G. R. (1981). Practical implementation of the double linear

damage rule and damage curve approach for treating cumulative fatigue damage.

International journal of fracture, 17(2), 169-192.

Markl, A. R. C. (1955). Piping-flexibility analysis. Trans. ASME, 77(2), 12743.

Markl, A.R.C. (1952) Fatigue testing of piping components, Trans. ASME, 1952, pp.

287-303

Mathworks. (2018). Matlab Documentation.

https://ch.mathworks.com/help/signal/ref/rainflow.html#d120e139322

Matsuishi, M., Endo, T. (1968). Fatigue of metals subjected to varying stress, Japan

society of Mechanical Engineers, Fukuoka, Japan.

Miner, M. A. (1945). Cumulative fatigue damage. Journal of applied mechanics, 12(3),

A159-A164.

Miller, K. J., Zachariah, K. P. (1977). Cumulative damage laws for fatigue crack

initiation and stage I propagation. The Journal of Strain Analysis for Engineering Design,

12(4), 262-270.

Nikbin, K. (2013). Creep/fatigue crack growth testing, modelling and component life

assessment of welds. Procedia Engineering, 55, 380-393.

Okamura, H., Sakai, S., Susuki, I. (1979). Cumulative fatigue damage under random

loads. Fatigue and Fracture of Engineering Materials and Structures, 1(4), 409-419.

Palmgren, A. (1924). Die Lebensdauer von Kugellagern, VDI-Zeitschrift, 58, 339-341.

Penderos, M. (1996). Thermal Cycling of Directly Buried District Heating Networks:

Application of Cumulative Damage Theory to Some Field Cases.

Pöting, S. (2003). Lebensdauerabschätzung im High-cycle-fatigue-Bereich.

Papierflieger.




104

Randløv, R., Hansen, K. E., Penderos, M. (1996). Temperature Variations in

Preinsulated DH Pipes Low Cycle Fatigue. IEA District Heating and Cooling,

Programme of Research, Development and Demonstration on District Heating and

Cooling.

Reinhardt, H. W., Reinhardt, H. W. (2010). Ingenieurbaustoffe. Berlin: Ernst & Sohn.

Rice R. C. (1997). SAE fatigue design handbook, 3rd Edition.

Shrestha, N. L., Urbaneck, T., Oppelt, T., Platzer, B., Göschel, T., Uhlig, U., & Frey, H.

(2017). Implementation of large solar thermal system into district heating network in

Chemnitz (Germany). In International Solar Energy Society (ed.): ISES Solar World

Conference (pp. 322-332).

Subramanyan, S. (1976). A cumulative damage rule based on the knee point of the SN

curve. Journal of Engineering Materials and Technology, 98(4), 316-321.

Terselius, B., Gedde, U. W., Jansson, J.F. (1986) Mechano-chemical Phenomena in

Polymers- Failure of Plastics edited by Brostow/Corneliussen, Hanser Publisher.

Weidlich, I., Schuchardt, G. K. (2017). New Approach for Asset Management in District

Heating (DH) Networks. Energy Procedia, 113, 22-27.

Wetzel, R. M. (1971). A method of fatigue damage analysis. PhD Thesis, Department

of Civil Engineering, University of Waterloo, Ontario, Canada.

Yarahmadi, N., Sällström, J.H. (2015) Improved maintenance strategies for district

heating pipe-lines, IEA DHC/CHP Annex10.

Yarahmadi, N., Vega, A., Jakubowicz, I. (2017). Life time for district heating pipe:

Phase 1. Stockholm: Energiforsk AB.

Yarahmadi, N., Vega, A., Jakubowicz, I. (2017). Livslängd för fjärrvärmerör: Phase 2.

Life time for district heating pipe: Energiforsk AB.




105

Appendix A: fatigue analysis results of the tempera ture data

This section reports in detail the rainflow cycle matrix, as well as the number of

equivalent full temperature cycles N0 corresponding to each temperature history data

analyzed in workpackage 1 (chapter 1).

Figure A-1. Histogram of the cycle counts as a function of temperature mean and range, for the Daegu branch supply pipe (measuring period: 3 years, from 01/01/2015 to 01/01/2018).

Table A-1. Results of the equivalent full temperature cycles N0 for the Daegu branch supply pipe (measuring period: 3 years, from 01/01/2015 to 01/01/2018).

Daegu supply pipe (S1) N0 N0 (30 years) N 0 (50 years) Tmax Tmean ∆Tref = Tmax - 10°C 0.67 6.73 11.21

∆Tref = 110°C 0.65 6.50 10.84 119.1°C 95.3°C




106

Figure A-2. Histogram of the cycle counts as a function of temperature range, for the Daegu branch return pipe (measuring period: 3 years, from 01/01/2015 to 01/01/2018).

Table A-2. Results of the evaluated full temperature cycles N0 for the Daegu branch return pipe (measuring period: 3 years, from 01/01/2015 to 01/01/2018).

Daegu return pipe (R1) N 0 N0 (30 years) N 0 (50 years) Tmax Tmean ∆Tref = Tmax - 10°C 0.64 6.42 10.70

∆Tref = 110°C 0.13 1.35 2.25 84.4°C 39.7°C




107

Figure A-3. Histogram of the cycle counts as a function of temperature range, for the Goyang branch supply pipe (measuring period: 3 years, from 01/01/2015 to 01/01/2018).

Table A-3. Results of the evaluated full temperature cycles N0 for the Goyang branch supply pipe (measuring period: 3 years, from 01/01/2015 to 01/01/2018).

Goyang supply pipe (S2) N 0 N0 (30 years) N 0 (50 years) Tmax Tmean ∆Tref = Tmax - 10°C 0.21 2.05 3.42

∆Tref = 110°C 0.19 1.90 3.17 117.9°C 97.9°C




108

Figure A-4. Histogram of the cycle counts as a function of temperature range, for the Goyang branch return pipe (measuring period: 3 years, from 01/01/2015 to 01/01/2018).

Table A-4. Results of the evaluated full temperature cycles N0 for the Goyang branch return pipe (measuring period: 3 years, from 01/01/2015 to 01/01/2018).

Goyang return pipe (R2) N0 N0 (30 years) N 0 (50 years) Tmax Tmean ∆Tref = Tmax - 10°C 0.46 4.64 7.74

∆Tref = 110°C 0.04 0.45 0.75 71.3°C 45.2°C




109

Figure A-5. Histogram of the cycle counts as a function of temperature range, for the Göteborg-Danska supply pipe (measuring period: 10 years, 2 months, 30 days (3744 days), from 27/03/2007 to 26/06/2017).

Table A-5. Results of the evaluated full temperature cycles N0 for the Göteborg-Danska supply pipe (measuring period: 10 years, 2 months, 30 days (3744 days)).

Göteborg-Danska supply pipe (S3) N0 N0 (30 years) N 0 (50 years) Tmax Tmean

∆Tref = Tmax - 10°C 16.09 47.08 78.47 ∆Tref = 110°C 13.76 40.27 67.12

115.8°C 61.1°C




110

Figure A-6. Histogram of the cycle counts as a function of temperature range, for the Göteborg Danska return pipe (measuring period: 8 years, 2 months, 25 days (3008 days), from 01/04/2009 to 26/06/2017).

Table A-6. Results of the evaluated full temperature cycles N0 for the Göteborg-Danska return pipe (measuring period: 8 years, 2 months, 25 days (3008 days)).

Göteborg-Danska return pipe (R3) N0 N0 (30 years) N 0 (50 years) Tmax Tmean

∆Tref = Tmax - 10°C 6.05 22.03 36.72 ∆Tref = 110°C 2.63 9.59 15.99

99.4°C 45.7°C




111

Figure A-7. Histogram of the cycle counts as a function of temperature range, for the Göteborg-Hisingsbron supply pipe (measuring period: 11 years, 3 months, 23 days (4131 days)).

Table A-7. Results of the evaluated full temperature cycles N0 for the Göteborg-Hisingsbron supply pipe (measuring period: 11 years, 3 months, 23 days, (4131 days)).

Göteborg- Hisingsbron supply pipe (S4) N0 N0 (30 years) N 0 (50 years) Tmax Tmean

∆Tref = Tmax - 10°C 13.21 35.05 58.42 ∆Tref = 110°C 10.69 28.37 47.28

114.3°C 86.8°C




112

Figure A-8. Histogram of the cycle counts as a function of temperature range, for the Göteborg-Hisingsbron return pipe (measuring period: 11 years, 3 months, 23 days (4131 days)).

Table A-8. Results of the evaluated full temperature cycles N0 for the Göteborg-Hisingsbron return pipe (measuring period: 11 years, 3 months, 23 days (4131 days)).

Göteborg- Hisingsbron return pipe (R4) N0 N0 (30 years) N 0 (50 years) Tmax Tmean

∆Tref = Tmax - 10°C 4.25 11.28 18.80 ∆Tref = 110°C 5.51 14.63 24.38

127.4°C 33.1°C




113

Figure A-9. Histogram of the cycle counts as a function of temperature range, for the Göteborg-Marieholm supply pipe (measuring period: 9 years, 6 months, 7 days (3476 days)).

Table A-9. Results of the evaluated full temperature cycles N0 for the Göteborg-Marieholm supply pipe (measuring period: 9 years, 6 months, 7 days, (3476 days)).

Göteborg-Marieholm supply pipe (S5) N0 N0 (30 years) N 0 (50 years) Tmax Tmean

∆Tref = Tmax - 10°C 21.83 68.81 114.68 ∆Tref = 110°C 15.15 47.75 79.58

110.4°C 88.7°C




114

Figure A-10. Histogram of the cycle counts as a function of temperature range, for the Göteborg-Marieholm return pipe (measuring period: 11 years, 3 months, 23 days (4131 days)).

Table A-10. Results of the evaluated full temperature cycles N0 for the Göteborg-Hisingsbron return pipe (measuring period: 11 years, 3 months, 23 days, (4131 days)).

Göteborg-Marieholm return pipe (R5) N0 N0 (30 years) N 0 (50 years) Tmax Tmean

∆Tref = Tmax - 10°C 6.57 19.63 32.71 ∆Tref = 110°C 0.83 2.49 4.14

75.6°C 24.3°C




115

Figure A-11. Histogram of the cycle counts as a function of temperature range, for the Göteborg-Falutorget supply pipe (measuring period: 11 years, 3 months, 23 days (4131 days)).

Table A-11. Results of the evaluated full temperature cycles N0 for the Göteborg-Falutorget supply pipe (measuring period: 11 years, 3 months, 23 days, (4131 days)).

Göteborg- Falutorget supply pipe (S6) N0 N0 (30 years) N 0 (50 years) Tmax Tmean

∆Tref = Tmax - 10°C 17.01 45.13 75.22 ∆Tref = 110°C 14.55 38.60 64.34

115.8°C 61.9°C




116

Figure A-12. Histogram of the cycle counts as a function of temperature range, for the Göteborg-Falutorget return pipe (measuring period: 11 years, 3 months, 23 days (4131 days)).

Table A-12. Results of the evaluated full temperature cycles N0 for the Göteborg-Falutorget return pipe (measuring period: 11 years, 3 months, 23 days, (4131 days)).

Göteborg- Falutorget return pipe (R6) N0 N0 (30 years) N 0 (50 years) Tmax Tmean

∆Tref = Tmax - 10°C 4.25 11.28 18.80 ∆Tref = 110°C 5.51 14.63 24.38

127.4°C 33.1°C




117

Figure A-13. Histogram of the cycle counts as a function of temperature range, for the Oslo Vika 2013 supply pipe (measuring period: 1 year (365 days), from 01/01/2013 to 31/12/2013).

Table A-13. Results of the evaluated full temperature cycles N0 for the Oslo Vika 2013 supply pipe (measuring period: 1 year (365 days)).

Oslo Vika 2013 supply pipe (S7) N0 N0 (30 years) N 0 (50 years) Tmax Tmean

∆Tref = Tmax - 10°C 2.83 84.90 141.50 ∆Tref = 110°C 3.46 103.92 173.20

125.7°C 101.6°C




118

Figure A-14. Histogram of the cycle counts as a function of temperature range, for the Oslo Vika 2013 return pipe (measuring period: 1 year (365 days), from 01/01/2013 to 31/12/2013)).

Table A-14. Results of the evaluated full temperature cycles N0 for the Oslo Vika 2013 return pipe (measuring period: 1 year (360 days)).

Oslo Vika 2013 return pipe (R7) N0 N0 (30 years) N 0 (50 years) Tmax Tmean

∆Tref = Tmax - 10°C 2.02 60.55 100.92 ∆Tref = 110°C 1.14 34.26 57.09

105.4°C 60.6°C




119

Figure A-15. Histogram of the cycle counts as a function of temperature range, for the Oslo Vika 2016 supply pipe (measuring period: 1 year (365 days), from 01/01/2013 to 31/12/2013)).

Table A-15. Results of the evaluated full temperature cycles N0 for the Oslo Vika 2016 supply pipe (measuring period: 1 year (360 days)).

Oslo Vika 2016 supply pipe (S8) N0 N0 (30 years) N 0 (50 years) Tmax Tmean

∆Tref = Tmax - 10°C 0.41 12.24 20.40 ∆Tref = 110°C 0.44 13.15 21.92

122.0°C 101.6°C




120

Figure A-16. Histogram of the cycle counts as a function of temperature range, for the Oslo Vika 2016 return pipe (measuring period: 1 year (365 days), from 01/01/2016 to 31/12/2016)).

Table A-16. Results of the evaluated full temperature cycles N0 for the Oslo Vika 2016 return pipe (measuring period: 1 year (360 days)).

Oslo Vika 2016 return pipe (R8) N0 N0 (30 years) N 0 (50 years) Tmax Tmean

∆Tref = Tmax - 10°C 2.87 86.03 143.38 ∆Tref = 110°C 1.64 49.08 81.80

105.6°C 57.2°C




121

Figure A-17. Histogram of the cycle counts as a function of temperature range, for the Soerengkaia 153 supply pipe (measuring period: 1 year (364 days), from 20/08/2018 to 18/08/2019)).

Table A-17. Results of the evaluated full temperature cycles N0 for the Soerengkaia 153 supply pipe (measuring period: 1 year (364 days)).

Soerengkaia 153 supply pipe (S9) N0 N0 (30 years) N 0 (50 years) Tmax Tmean

∆Tref = Tmax - 10°C 0.42 12.58 20.96 ∆Tref = 110°C 0.36 10.82 18.03

115.9°C 98.3°C




122

Figure A-18. Histogram of the cycle counts as a function of temperature range, for the Soerengkaia 153 return pipe (measuring period: 1 year (365 days), from 20/08/2018 to 18/08/2019)).

Table A-18. Results of the evaluated full temperature cycles N0 for the Soerengkaia 153 return pipe (measuring period: 1 year (364 days)).

Soerengkaia 153 return pipe (R9) N0 N0 (30 years) N 0 (50 years) Tmax Tmean

∆Tref = Tmax - 10°C 40.63 1223.22 2038.70 ∆Tref = 110°C 1.15 34.56 57.61

55.1°C 38.3°C




123

Figure A-19. Histogram of the cycle counts as a function of temperature range, for the Brobekkveiien 80 supply pipe (measuring period: 1 year (365 days), from 30/08/2018 to 30/08/2019)).

Table A-19. Results of the evaluated full temperature cycles N0 for the Brobekkveiien 80 supply pipe (measuring period: 1 year (365 days)).

Brobekkveiien 80 supply pipe (S10) N0 N0 (30 years) N 0 (50 years) Tmax Tmean

∆Tref = Tmax - 10°C 0.16 4.66 7.77 ∆Tref = 110°C 0.15 4.41 7.35

118.5°C 92.4°C




124

Figure A-20. Histogram of the cycle counts as a function of temperature range, for the Brobekkveiien 80 return pipe (measuring period: 1 year (365 days), from 30/08/2018 to 30/08/2019)).

Table A-20. Results of the evaluated full temperature cycles N0 for the Brobekkveiien 80 return pipe (measuring period: 1 year (365 days)).

Brobekkveiien 80 return pipe (R10) N0 N0 (30 years) N 0 (50 years) Tmax Tmean

∆Tref = Tmax - 10°C 9.92 297.93 496.56 ∆Tref = 110°C 0.53 15.82 26.36

62.8°C 45.8°C




125

Figure A-21. Histogram of the cycle counts as a function of temperature range, for the Skoeyen terasse 4 supply pipe (measuring period: 1 year (365 days), from 30/08/2018 to 30/08/2019)).

Table A-21. Results of the evaluated full temperature cycles N0 for the Skoeyen terasse 4 supply pipe (measuring period: 1 year (365 days)).

Skoeyen terasse 4 supply pipe (S11) N0 N0 (30 years) N 0 (50 years) Tmax Tmean

∆Tref = Tmax - 10°C 1.08 32.41 54.02 ∆Tref = 110°C 0.82 24.53 40.88

112.6°C 90.7°C




126

Figure A-22. Histogram of the cycle counts as a function of temperature range, for the Skoeyen terasse 4 return pipe (measuring period: 1 year (365 days), from 30/08/2018 to 30/08/2019)).

Table A-22. Results of the evaluated full temperature cycles N0 for the Skoeyen terasse 4 return pipe (measuring period: 1 year (365 days)).

Skoeyen terasse 4 return pipe (R11) N0 N0 (30 years) N 0 (50 years) Tmax Tmean

∆Tref = Tmax - 10°C 50.70 1521.94 2536.56 ∆Tref = 110°C 2.20 66.01 110.02

60.2°C 38.7°C




127

Figure A-17. Histogram of the cycle counts as a function of temperature range, for the Hannover CoCa 2010 supply pipe (measuring period: 1 year (365 days), from 01/01/2010 to 01/01/2011).

Table A-17. Results of the evaluated full temperature cycles N0 for the CoCa 2010 supply pipe (measuring period: 1 year (365 days), from 01/01/2010 to 01/01/2011).

CoCa 2010 supply pipe (S12) N 0 N0 (30 years) N 0 (50 years) T max Tmean ∆Tref = Tmax - 10°C 0.14 4.18 6.97

∆Tref = 110°C 0.14 4.30 7.17 120.8°C 97.1°C




128

Figure A-18. Histogram of the cycle counts as a function of temperature range, for the Hannover CoCa 2010 return pipe (measuring period: 1 year (365 days), from 01/01/2010 to 01/01/2011).

Table A-18. Results of the evaluated full temperature cycles N0 for the CoCa 2010 return pipe (measuring period: 1 year (365 days), from 01/01/2010 to 01/01/2011).

CoCa 2010 return pipe (R12) N0 N0 (30 years) N 0 (50 years) T max Tmean ∆Tref = Tmax - 10°C 0.08 2.26 3.76

∆Tref = 110°C 0.01 0.37 0.62 80.0°C 61.3°C




129

Figure A-19. Histogram of the cycle counts as a function of temperature range, for the Hannover GKH 2010 supply pipe (measuring period: 1 year (365 days), from 01/01/2010 to 01/01/2011).

Table A-19. Results of the evaluated full temperature cycles N0 for the GKH 2010 supply pipe (measuring period: 1 year (365 days), from 01/01/2010 to 01/01/2011).

GKH 2010 supply pipe (S13) N0 N0 (30 years) N 0 (50 years) T max Tmean ∆Tref = Tmax - 10°C 0.04 1.33 2.22

∆Tref = 110°C 0.05 1.44 2.39 122.1°C 96.5°C




130

Figure A-20. Histogram of the cycle counts as a function of temperature range, for the Hannover GKH 2010 return pipe (measuring period: 1 year (365 days), from 01/01/2010 to 01/01/2011).

Table A-20. Results of the evaluated full temperature cycles N0 for the GKH 2010 return pipe (measuring period: 1 year (365 days), from 01/01/2010 to 01/01/2011).

GKH 2010 return pipe (R13) N 0 N0 (30 years) N 0 (50 years) T max Tmean ∆Tref = Tmax - 10°C 0.01 0.34 0.56

∆Tref = 110°C 0.001 0.04 0.06 73.5°C 59.1°C




131

Figure A-21. Histogram of the cycle counts as a function of temperature range, for the Hannover HKW 2010 supply pipe (measuring period: 1 year (365 days), from 01/01/2010 to 01/01/2011).

Table A-21. Results of the evaluated full temperature cycles N0 for the HKW 2010 supply pipe (measuring period: 1 year (365 days), from 01/01/2010 to 01/01/2011).

HKW 2010 supply pipe (S14) N 0 N0 (30 years) N 0 (50 years) T max Tmean ∆Tref = Tmax - 10°C 0.64 19.31 32.19

∆Tref = 110°C 0.63 18.89 31.49 119.4°C 92.9°C




132

Figure A-22. Histogram of the cycle counts as a function of temperature range, for the Hannover HKW 2010 return pipe (measuring period: 1 year (365 days), from 01/01/2010 to 01/01/2011).

Table A-22. Results of the evaluated full temperature cycles N0 for the HKW 2010 return pipe (measuring period: 1 year (365 days), from 01/01/2010 to 01/01/2011).

HKW 2010 return pipe (R14) N0 N0 (30 years) N0 (50 years) T max Tmean ∆Tref = Tmax - 10°C 0.48 14.31 23.85

∆Tref = 110°C 0.09 2.79 4.65 83.1°C 60.5°C




133

Figure A-23. Histogram of the cycle counts as a function of temperature range, for the Hannover KWH 2010 supply pipe (measuring period: 1 year (365 days), from 01/01/2010 to 01/01/2011).

Table A-23. Results of the evaluated full temperature cycles N0 for the KWH 2010 supply pipe (measuring period: 1 year (365 days), from 01/01/2010 to 01/01/2011).

KWH 2010 supply pipe (S15) N0 N0 (30 years) N0 (50 years) T max Tmean ∆Tref = Tmax - 10°C 0.04 1.26 2.10

∆Tref = 110°C 0.05 1.36 2.26 122.1°C 96.6°C




134

Figure A-24. Histogram of the cycle counts as a function of temperature range, for the Hannover KWH 2010 return pipe (measuring period: 1 year (365 days), from 01/01/2010 to 01/01/2011).

Table A-24. Results of the evaluated full temperature cycles N0 for the KWH 2010 return pipe (measuring period: 1 year (365 days), from 01/01/2010 to 01/01/2011).

KWH 2010 return pipe (R15) N0 N0 (30 years) N 0 (50 years) T max Tmean ∆Tref = Tmax - 10°C 0.02 0.50 0.84

∆Tref = 110°C 0.001 0.04 0.07 68.5°C 58.5°C




135

Figure A-25. Histogram of the cycle counts as a function of temperature range, for the Hannover CoCa 2011 supply pipe (measuring period: 1 year (365 days), from 01/01/2011 to 01/01/2012).

Table A-25. Results of the evaluated full temperature cycles N0 for the CoCa 2011 supply pipe (measuring period: 1 year (365 days), from 01/01/2011 to 01/01/2012).

CoCa 2011 supply pipe (S16) N 0 N0 (30 years) N 0 (50 years) T max Tmean ∆Tref = Tmax - 10°C 0.20 6.15 10.25

∆Tref = 110°C 0.15 4.44 7.40 111.4°C 95.7°C




136

Figure A-26. Histogram of the cycle counts as a function of temperature range, for the Hannover CoCa 2011 return pipe (measuring period: 1 year (365 days), from 01/01/2011 to 01/01/2012).

Table A-26. Results of the evaluated full temperature cycles N0 for the CoCa 2011 return pipe (measuring period: 1 year (365 days), from 01/01/2011 to 01/01/2012).

CoCa 2011 return pipe (R16) N0 N0 (30 years) N 0 (50 years) T max Tmean ∆Tref = Tmax - 10°C 0.10 3.15 5.24

∆Tref = 110°C 0.02 0.52 0.86 80.0°C 60.1°C




137

Figure A-27. Histogram of the cycle counts as a function of temperature range, for the Hannover GKH 2011 supply pipe (measuring period: 1 year (365 days), from 01/01/2011 to 01/01/2012).

Table A-27. Results of the evaluated full temperature cycles N0 for the GKH 2011 supply pipe (measuring period: 1 year (365 days), from 01/01/2011 to 01/01/2012).

GKH 2011 supply pipe (S17) N 0 N0 (30 years) N 0 (50 years) T max Tmean ∆Tref = Tmax - 10°C 0.15 4.41 7.35

∆Tref = 110°C 0.15 4.46 7.43 120.3°C 94.6°C




138

Figure A-28. Histogram of the cycle counts as a function of temperature range, for the Hannover GKH 2011 return pipe (measuring period: 1 year (365 days), from 01/01/2011 to 01/01/2012).

Table A-28. Results of the evaluated full temperature cycles N0 for the GKH 2011 return pipe (measuring period: 1 year (365 days), from 01/01/2011 to 01/01/2012).

GKH 2011 return pipe (R17) N 0 N0 (30 years) N 0 (50 years) T max Tmean ∆Tref = Tmax - 10°C 0.06 1.94 3.24

∆Tref = 110°C 0.004 0.13 0.22 65.9°C 58.4°C




139

Figure A-29. Histogram of the cycle counts as a function of temperature range, for the Hannover HKW 2011 supply pipe (measuring period: 1 year (128 days), from 01/01/2011 to 09/05/2011).

Table A-29. Results of the evaluated full temperature cycles N0 for the HKW 2011 supply pipe (measuring period: 1 year (128 days), from 01/01/2011 to 09/05/2011).

HKW 2011 supply pipe (S18) N 0 N0 (30 years) N 0 (50 years) T max Tmean ∆Tref = Tmax - 10°C 0.32 27.24 45.39

∆Tref = 110°C 0.23 19.67 32.78 111.4°C 93.6°C




140

Figure A-30. Histogram of the cycle counts as a function of temperature range, for the Hannover HKW 2011 return pipe (measuring period: 1 year (365 days), from 01/01/2011 to 09/05/2011).

Table A-30. Results of the evaluated full temperature cycles N0 for the HKW 2011 return pipe (measuring period: 1 year (128 days), from 01/01/2011 to 09/05/2011).

HKW 2011 return pipe (R18) N0 N0 (30 years) N 0 (50 years) T max Tmean ∆Tref = Tmax - 10°C 0.54 45.96 76.60

∆Tref = 110°C 0.10 8.91 14.86 83.0°C 64.2°C




141

Figure A-31. Histogram of the cycle counts as a function of temperature range, for the Hannover KWH 2011 supply pipe (measuring period: 1 year (365 days), from 01/01/2011 to 01/01/2012).

Table A-31. Results of the evaluated full temperature cycles N0 for the KWH 2011 supply pipe (measuring period: 1 year (365 days), from 01/01/2011 to 01/01/2012).

KWH 2011 supply pipe (S19) N0 N0 (30 years) N 0 (50 years) T max Tmean ∆Tref = Tmax - 10°C 0.12 3.49 5.82

∆Tref = 110°C 0.12 3.57 5.95 120.6°C 94.7°C




142

Figure A-32. Histogram of the cycle counts as a function of temperature range, for the Hannover KWH 2011 return pipe (measuring period: 1 year (365 days), from 01/01/2011 to 01/01/2012).

Table A-32. Results of the evaluated full temperature cycles N0 for the KWH 2011 return pipe (measuring period: 1 year (365 days), from 01/01/2011 to 01/01/2012).

KWH 2011 return pipe (R19) N0 N0 (30 years) N 0 (50 years) T max Tmean ∆Tref = Tmax - 10°C 0.02 0.62 1.04

∆Tref = 110°C 0.002 0.05 0.08 68.2°C 57.7°C




143

Figure A-33. Histogram of the cycle counts as a function of temperature range, for the solar thermal DH main network supply pipe (measuring period: 365 days, from 1/01/2018 to 31/12/2018, ∆t = 1min).

Table A-33. Results of the evaluated full temperature cycles N0 for the solar thermal DH main network supply pipe (measuring period: 365 days ).

Main network supply pipe (S20) N0 N0 (30 years) N 0 (50 years) Tmax Tmean

∆Tref = Tmax - 10°C 0.330 9.91 16.51 ∆Tref = 110°C 0.792 23.76 39.61

146.9°C 134.3°C




144

Figure A-34. Histogram of the cycle counts as a function of temperature range, for the solar thermal DH main network return pipe (measuring period: 365 days, from 1/01/2018 to 31/12/2018, ∆t = 1min).

Table A-34. Results of the evaluated full temperature cycles N0 for the solar thermal DH main network return pipe (measuring period: 365 days ).

Main network return pipe (R20) N0 N0 (30 years) N 0 (50 years) Tmax Tmean

∆Tref = Tmax - 10°C 0.366 10.97 18.29 ∆Tref = 110°C 0.201 6.03 10.05

104.7°C 59.1°C




145

Figure A-35. Histogram of the cycle counts as a function of temperature range, for the solar thermal DH secondary network supply pipe (measuring period: 365 days, from 1/01/2018 to 31/12/2018, ∆t = 1min).

Table A-35. Results of the evaluated full temperature cycles N0 for the solar thermal DH secondary network supply pipe (measuring period: 365 days ).

Secondary network supply pipe (S21) N0 N0 (30 years) N 0 (50 years) Tmax Tmean

∆Tref = Tmax - 10°C 0.199 5.99 9.98 ∆Tref = 110°C 0.052 1.55 2.58

88.5°C 72.0°C




146

Figure A-36. Histogram of the cycle counts as a function of temperature range, for the solar thermal DH secondary network return pipe (measuring period: 365 days, from 1/01/2018 to 31/12/2018, ∆t = 1min).

Table A-36. Results of the evaluated full temperature cycles N0 for the solar thermal DH secondary network return pipe (measuring period: 365 days ).

Secondary network return pipe (R21) N0 N0 (30 years) N 0 (50 years) Tmax Tmean

∆Tref = Tmax - 10°C 0.082 2.47 4.12 ∆Tref = 110°C 0.005 0.14 0.23

63.7°C 55.4°C




147

Figure A-37. Histogram of the cycle counts as a function of temperature range, for the heat storage temperature level 1 (measuring period: 365 days, from 1/01/2018 to 31/12/2018, ∆t = 1min).

Table A-37. Results of the evaluated full temperature cycles N0 for the heat storage temperature level 1 (measuring period: 365 days ).

Heat storage temperature level 1 (SL1) N0 N0 (30 years) N 0 (50 years) T max Tmean

∆Tref = Tmax - 10°C 13.152 394.83 658.05 ∆Tref = 110°C 0.863 25.92 43.20

65.7°C 44.2°C




148


Table A-38. Results of the evaluated full temperature cycles N0 for the heat storage temperature level 2 (measuring period: 365 days ).


∆Tref = Tmax - 10°C 6.138 184.25 307.09 ∆Tref = 110°C 0.324 9.74 16.23

62.7°C 45.8°C




149


Table A-39. Results of the evaluated full temperature cycles N0 for the heat storage temperature level 3 (measuring period: 365 days).


∆Tref = Tmax - 10°C 3.398 102.01 170.02 ∆Tref = 110°C 0.788 23.66 39.44

86.3°C 51.4°C




150


Table A-40. Results of the evaluated full temperature cycles N0 for the heat storage temperature level 4 (measuring period: 365 days).


∆Tref = Tmax - 10°C 4.000 120.09 200.16 ∆Tref = 110°C 1.330 39.91 66.52

93.5°C 56.5°C




151

Figure A-41. Histogram of the cycle counts as a function of temperature range, for the solar thermal field 1 supply pipe (measuring period: 365 days, from 1/01/2018 to 31/12/2018, ∆t = 1min).

Table A-41. Results of the evaluated full temperature cycles N0 for the solar thermal field 1 supply pipe (measuring period: 365 days).

solar thermal field 1 supply pipe (S22) N0 N0 (30 years) N 0 (50 years) Tmax Tmean

∆Tref = Tmax - 10°C 21.419 643.01 1071.69 ∆Tref = 110°C 27.924 838.30 1397.16

127.5°C 41.4°C




152

Figure A-42. Histogram of the cycle counts as a function of temperature range, for the solar thermal field 1 return pipe (measuring period: 365 days, from 1/01/2018 to 31/12/2018, ∆t = 1min).

Table A-42. Results of the evaluated full temperature cycles N0 for the solar thermal field 1 return pipe (measuring period: 365 days).

solar thermal field 1 return pipe (R22) N0 N0 (30 years) N 0 (50 years) Tmax Tmean

∆Tref = Tmax - 10°C 28.407 852.80 1421.33 ∆Tref = 110°C 3.682 110.52 184.20

76.0°C 38.5°C




153

Figure A-43. Histogram of the cycle counts as a function of temperature range, for the solar thermal field 2 supply pipe (measuring period: 365 days, from 1/01/2018 to 31/12/2018, ∆t = 1min).

Table A-43. Results of the evaluated full temperature cycles N0 for the solar thermal field 2 supply pipe (measuring period: 365 days ).

solar thermal field 2 supply pipe (S23) N0 N0 (30 years) N 0 (50 years) Tmax Tmean

∆Tref = Tmax - 10°C 64.084 1923.84 3206.40 ∆Tref = 110°C 22.063 662.34 1103.91

94.3°C 39.8°C




154

Figure A-44. Histogram of the cycle counts as a function of temperature range, for the solar thermal field 2 return pipe (measuring period: 365 days, from 1/01/2018 to 31/12/2018, ∆t = 1min).

Table A-44. Results of the evaluated full temperature cycles N0 for the solar thermal field 2 return pipe (measuring period: 365 days ).

solar thermal field 2 return pipe (R23) N0 N0 (30 years) N 0 (50 years) Tmax Tmean

∆Tref = Tmax - 10°C 59.516 1786.71 2977.84 ∆Tref = 110°C 3.576 107.35 178.91

64.5°C 37.3°C




155

Figure A-45. Histogram of the cycle counts as a function of temperature range, for the solar thermal DH house connection supply pipe (measuring period: 360 days, from 06/12/2018 to 02/12/2019, ∆t = 5min).

Table A-45. Results of the evaluated full temperature cycles N0 for the solar thermal DH house connection supply pipe (measuring period: 360 days ).

House connection supply pipe (S24) N0 N0 (30 years) N 0 (50 years) Tmax Tmean

∆Tref = Tmax - 10°C 11.206 340.69 567.82 ∆Tref = 110°C 2.103 63.93 106.56

82.4°C 70.0°C




156

Figure A-46. Histogram of the cycle counts as a function of temperature range, for the solar thermal DH house connection return pipe (measuring period: 360 days, from 06/12/2018 to 02/12/2019, ∆t = 5min).

Table A-46. Results of the evaluated full temperature cycles N0 for the solar thermal DH house connection return pipe (measuring period: 360 days ).

House connection return pipe (R24) N0 N0 (30 years) N 0 (50 years) Tmax Tmean

∆Tref = Tmax - 10°C 46.914 1426.31 2377.18 ∆Tref = 110°C 3.804 115.66 192.77

68.7°C 41.2°C

annex xii final report effects of loads on asset ... · 3. critical aspect iii: transferability of...

Documents