SIST-TP CEN/TR 1295-2:2005
(Main)Structural design of buried pipelines under various conditions of loading - Part 2: Summary of nationally established methods of design
Structural design of buried pipelines under various conditions of loading - Part 2: Summary of nationally established methods of design
In addition to EN 1295-1, this Technical Report gives additional guidance when compared with EN 1295-1 on the application of the nationally established methods of design declared by and used in CEN member countries at the time of preparation of this document (see informative Annex A).
This Technical Report is an important source of design expertise, but it cannot include all possible special cases, in which extensions or restrictions to the basic design methods may apply.
Since in practice precise details of types of soil and installation conditions are not always available at the design stage, the choice of design assumptions is left to the judgement of the engineer. In this connection the document can only provide general indications and advice.
Statische Berechnung von erdverlegten Rohrleitungen unter verschiedenen Belastungsbedingungen - Teil 2: Zusammenstellung national eingeführter Berechnungsverfahren
Calcul de résistance mécanique des canalisations enterrées sous diverses conditions de charge - Partie 2: Résumé des méthodes nationales de dimensionnement
En complément à l'EN 1295-1 et par rapport à cette dernière, le présent Rapport technique donne des lignes directrices supplémentaires pour l'application des méthodes de calcul reconnues au plan national, déclarées et utilisées dans les États membres du CEN au moment de la préparation du présent document (voir l'Annexe A informative).
Le présent Rapport technique est une source importante d'expertise sur le calcul de la résistance mécanique, mais il ne peut inclure tous les cas spéciaux possibles, pour lesquels des extensions ou des restrictions des méthodes de calcul de base peuvent s'appliquer.
Puisque dans la pratique des détails précis sur les types de sols et sur les conditions de pose ne sont pas toujours connus au stade du projet, le choix des hypothèses du projet est laissé à l'appréciation de l'ingénieur. De ce fait, le document peut seulement donner des indications et des conseils généraux.
Projektiranje vkopanih cevovodov pri različnih pogojih obtežb – 2. del: Pregled nacionalnih metod projektiranja
General Information
Standards Content (Sample)
SLOVENSKI STANDARD
01-december-2005
3URMHNWLUDQMHYNRSDQLKFHYRYRGRYSULUD]OLþQLKSRJRMLKREWHåE±GHO 3UHJOHG
QDFLRQDOQLKPHWRGSURMHNWLUDQMD
Structural design of buried pipelines under various conditions of loading - Part 2:
Summary of nationally established methods of design
Statische Berechnung von erdverlegten Rohrleitungen unter verschiedenen
Belastungsbedingungen - Teil 2: Zusammenstellung national eingeführter
Berechnungsverfahren
Calcul de résistance mécanique des canalisations enterrées sous diverses conditions de
charge - Partie 2: Résumé des méthodes nationales de dimensionnement
Ta slovenski standard je istoveten z: CEN/TR 1295-2:2005
ICS:
23.040.01 Deli cevovodov in cevovodi Pipeline components and
na splošno pipelines in general
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
TECHNICAL REPORT
CEN/TR 1295-2
RAPPORT TECHNIQUE
TECHNISCHER BERICHT
August 2005
ICS 23.040.01
English Version
Structural design of buried pipelines under various conditions of
loading - Part 2: Summary of nationally established methods of
design
Calcul de résistance mécanique des canalisations Statische Berechnung von erdverlegten Rohrleitungen
enterrées sous diverses conditions de charge - Partie 2: unter verschiedenen Belastungsbedingungen - Teil 2:
Résumé des méthodes nationales de dimensionnement Zusammenstellung national eingeführter
Berechnungsverfahren
This Technical Report was approved by CEN on 28 February 2005. It has been drawn up by the Technical Committee CEN/TC 165.
CEN members are the national standards bodies of Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France,
Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia,
Slovenia, Spain, Sweden, Switzerland and United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
Management Centre: rue de Stassart, 36 B-1050 Brussels
© 2005 CEN All rights of exploitation in any form and by any means reserved Ref. No. CEN/TR 1295-2:2005: E
worldwide for CEN national Members.
Contents
Foreword .4
Introduction.5
1 Scope.6
2 Normative references.6
3 Terms and definitions.6
4 Additional details about established methods .6
Annex A (informative) Summary of Methods of different countries.7
A.1 Austria.7
A.1.1 General remarks.7
A.1.2 Differences between "option 1" and ÖNORM B 5012.7
A.1.3 Principles.8
A.2 Belgium.9
A.2.1 General.9
A.2.2 Flowchart.9
A.2.3 Design, equations, tables and charts, symbols and abbreviations .9
A.3 Denmark.21
A.3.1 General.21
A.3.2 Charges.24
A.3.3 Safety.26
A.3.4 Partial safety factors.27
A.3.5 Calculations.27
A.4 France.29
A.4.1 Scope.29
A.4.2 Original features of the method .29
A.4.3 Description.29
A.4.4 Example of calculation.37
A.5 Germany.39
A.5.1 Introduction.39
A.5.2 Types of soil.39
A.5.3 Live loads.40
A.5.4 Effects of the installation on the structural calculation .44
A.5.5 Loading.44
A.5.6 Load distribution.45
A.5.7 Pressure distribution at pipe circumference .50
A.5.8 Sectional forces, stresses, strains, deformations.51
A.5.9 Dimensioning.52
A.6 Netherlands.56
A.6.1 General.56
A.6.2 Earth load.56
A.6.3 Evenly distributed surface load .57
A.6.4 Traffic loads.57
A.6.5 Heavy transport.57
A.6.6 Loads form external and internal water pressure .58
A.6.7 Thermal loading.58
A.6.8 Moments and normal forces .59
A.6.9 Calculation model for a concrete pipe .62
A.6.10 Recommended design values.69
A.7 Norway.73
A.7.1 Types of loads.73
A.7.2 Soil loads.73
A.7.3 Self weight of pipe.73
A.7.4 Weight of water.74
A.7.5 Traffic load.74
A.7.6 Load distribution and bedding reaction.74
A.7.7 Safety analysis.74
A.7.8 Structural design.74
A.8 Sweden.75
A.8.1 Design of buried plastic pipes .75
A.8.2 Calculation method for rigid pipes .83
A.9 United Kingdom.86
A.9.1 General description.86
A.9.2 Calculation procedures.86
A.9.3 Rigid pipes.87
A.9.4 Semi-rigid pipes.90
A.9.5 Flexible pipes.93
Bibliography.110
Foreword
This Technical Report (CEN/TR 1295-2:2005) has been prepared by Technical Committee CEN/TC 165
“Wastewater engineering”, the secretariat of which is held by DIN.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights.
CEN [and/or CENELEC] shall not be held responsible for identifying any or all such patent rights.
This Technical Report was prepared by a Joint Working Group (JWG 1) of Technical Committees TC 164, Water
supply, the secretariat of which is held by AFNOR, and TC 165, Waste water engineering, the secretariat of which
is held by DIN.
This Technical Report is intended for use in conjunction with the series of product standards covering pipes of
various materials for the water industry.
This Technical Report includes an Informative Annex A in which are included additional details about the nationally
established methods of design declared, submitted by and used in member countries, and collated by the Joint
Working Group.
Introduction
The structural design of buried pipelines constitutes a wide ranging and complex field of engineering, which has
been the subject of extensive study and research, in many countries over a period of very many years.
Whilst many common features exist between the design methods which have been developed and established in
the various member countries of CEN, there are also differences reflecting such matters as geological and climatic
variations, as well as different installation and working practices.
In view of these differences, and of the time required to develop a common design method which would fully reflect
the various considerations identified in particular national methods, a two stage approach has been adopted for the
development of this document.
In accordance with this two stage approach, the Joint Working Group, at its initial meeting, resolved "first to
produce a document giving guidance on the application of nationally established methods of structural design of
buried pipelines under various conditions of loading, whilst working towards a common method of structural
design". This document represents the full implementation of the first part of that resolution.
1 Scope
In addition to EN 1295-1, this Technical Report gives additional guidance when compared with EN 1295-1 on the
application of the nationally established methods of design declared by and used in CEN member countries at the
time of preparation of this document (see informative Annex A).
This Technical Report is an important source of design expertise, but it cannot include all possible special cases, in
which extensions or restrictions to the basic design methods may apply.
Since in practice precise details of types of soil and installation conditions are not always available at the design
stage, the choice of design assumptions is left to the judgement of the engineer. In this connection the document
can only provide general indications and advice.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated references,
only the edition cited applies. For undated references, the latest edition of the referenced document (including any
amendments) applies.
EN 1295-1, Structural design of buried pipelines under various conditions of loading — Part 1: General
requirements
3 Terms and definitions
For the purposes of this document, the terms and definitions given in EN 1295-1 apply.
4 Additional details about established methods
Annex A gives for several countries details about the established methods of design declared, submitted by and
used in member countries.
Annex A
(informative)
Summary of Methods of different countries
A.1 Austria
A.1.1 General remarks
The Austrian Standard Őnorm B 5012:2005 is based on the "option 1" contained in CEN/TR 1295-3.
This "option 1" had been prepared by the TG1 of the CEN/TC164-165/JWG1 as a result of thorough study of the
subject and long-lasting consultations carried out from 1992 onwards.
Although the design method described in "option 1" was mainly based on two recognised and well-tested "national
methods", the German ATV-DVWK-A 127 and the (former) Austrian ÖNORM B 5012-1 and – 2, some new
assumptions had to be incorporated in the re-drafted "option 1" in order to consider the most recent experience
gained in this domain.
Therafter, it was of course also necessary to prove the correctness of the newly made assumptions by means of
comprehensive field testing. This particular kind of testing was done during the period from 2000 to 2004. The tests
results obtained were already incorporated in the ÖNORM B 5012 a revision of the former parts 1 and 2 of this
standard.
Therefore the ÖNORM B 5012:2005 represents a calculation method which is based on the most recent
experience in this field, but it still complies with the calculation principles elaborated by "JWG 1" regarding the
"option 1" of CEN/TR 1295-3.
A.1.2 Differences between "option 1" and ÖNORM B 5012
The ÖNORM B 5012 differs in the following points from "option 1":
1) Two different applications of ÖNORM B 5012 enable to make
i) calculations for pipe design and
ii) back-calculations of failure situations
For the pipe design the soil moduli proposed in "option 1" (Table 4) shall be reduced by the factor 0,5, whereas for
back-calculations the unchanged soil moduli from "option 1" should be used.
The purpose for this distinction is the following:
The results of calculations for the pipe design should be close to the 95 % fractile of the scattering design values,
like deflection, stress or strain. Then the required safety or failure probability is assured by using the safety factors
proposed in ÖNORM B 5012.
However, for back-calculations of failure situations the calculation results should be as close as possible to the
mean value of the measured values.
2) Factor f is changed in ÖNORM B 5012 in comparison to "option 1" ( compare equation 23 in "option 1"
R,GW
and ÖNORM B 5012).
3) The soil pressure ratios K and K are partly changed (compare Table 11 in "option 1" and ÖNORM B
1 2
5012).
4) The recommended support angles α are partly changed (compare Table 13 in "option 1" and ÖNORM B
v
5012).
5) In ÖNORM B 5012 the horizontal bedding stiffness S and factor ζ is calculated in a clearer and easier
Bh
way than in "option 1" (compare 8.3.2 in "option 1" and ÖNORM B 5012).
6) The estimated values of relative initial ovalization δ in "option 1" are reduced in ÖNORM B 5012 by the
v,io
factor 0,5 (compare Tables 19 and 20 in "option 1" with Table 18 and 19 in ÖNORM B 5012).
nd
7) In ÖNORM B 5012 it is proposed to use the theory 2 order calculation more consequently than in "option
1" (in ÖNORM for flexible pipes with deflections greater than 1 % in comparison to 5 % in "option 1").
A.1.3 Principles
Like "option 1", the ATV-DVWK-A 127 and the ÖNORM model the calculation system of ÖNORM B 5012 is based
on the model of the embedded circular or non circular ring. The pipe-soil interaction is taken into account by the
following interpretations:
1) In vertical direction: Using the shear-stiff beam model above the pipe for the calculation of the vertical
loading due to the earth weight and uniformly distributed surcharge;
2) In horizontal direction: Using the compatibility condition of the horizontal pipe and soil movements taking
into account all loads considered in the calculation (e.g. for the calculation of the horizontal bedding
reaction pressures).
Further descriptions of details about the principles and the calculation method are stated in CEN/TR 1295-3.
A.2 Belgium
A.2.1 General
Calculation procedure of the ISO 2785: Directives for selection of asbestos-cement pipes subject to external loads
with or without internal pressure.
A.2.2 Flowchart
A.2.3 Design, equations, tables and charts, symbols and abbreviations
A.2.3.1 Symbols and abbreviations
A width of uniform surcharge of small extent, in metres;
a distance between two wheels on a single axle of a truck, in metres;
B width of trench at the crown of the pipe, in metres;
B’ distance of the spring-line of a pipe from the wall of the trench in which it is buried, in metres;
h distance between two wheels of two different axles of a truck, in metres;
c diagonal distance between two wheels of two different axles of a truck, in metres;
C.C earth-load coefficient for a trench with vertical walls;
C load coefficient for superimposed concentrated moving loads;
c
C load coefficient for uniform surcharges of small extent;
d
C load coefficient for uniform surcharges of large extent;
n
C , C , C , C coefficients of vertical deformation of pipe;
v d1 v2 v3
C , C coefficients of horizontal deformation of pipe;
h2 h3
d nominal or internal diameter of pipe, in millimetres;
D external diameter of pipe, in metres;
e base of natural logarithms;
E modulus of elasticity, in Newtons per square millimetre;
E modulus of elasticity of pipe, in Newtons per square millimetre;
p
E modulus of compression of soil, in Newtons per square millimetre;
s
E modulus of elasticity of road construction material, in Newtons per square millimetre;
t
E , E , E , E moduli of compression of soil and backfill in various zones of the trench, in Newton per square
1 2 3 4
millimetre;
H, H , H heights of earth cover of a pipe, in metres;
1 2
H equivalent height of earth cover a pipe laid under a paved road, in metres;
e
HT heavy truck;
I modulus of inertia of the wall of the pipe per unit length, in cubic millimetres;
k factor of ring-bending moment;
k , k , k , k factors of ring-bending moments due to vertical and horizontal loads, horizontal reaction pressure
v1 h1 hp w
and water-load respectively;
K , K coefficients of lateral earth pressure;
1 2
L length of uniform surcharge of small extent, in metres;
LT light truck;
m, m , m , m concentration factors of vertical earth pressure over the pipe;
0 1 m
M ultimate ring-bending moment of pipe when tested in accordance with ISO 881 or ISO 160, in
e
Kilonewton metre per metre;
M maximum ring-bending moment in the wall of a buried, Kilonewton metre per metre;
m
M the ring-bending moment that will fracture the pipe when combined with an internal hydraulic pressure
p1;
M the ultimate ring-bending moment when no internal pressure affects the pipe;
n concentration factor of lateral earth pressure on the sides of the pipe;
P intensity of distributed load, in kilonewtons per square metre;
d
P pipe projection ratio;
j
P hydraulic working pressure, in Megapascal;
w
P the internal hydraulic pressure that will fracture the pipe when combined with a ring-bending moment
M ;
P the internal hydraulic pressure that will burst a pipe which is not exposed to any external load;
P crushing load of a pipe when tested in accordance with ISO 881, in kilonewtons per 200 or 300
e
millimetre lengths of pipe;
P maximum wheel load of a truck, in kilonewtons;
v
P vertical pressure on a pipe due to moving concentrated surcharge, in kilonewtons per square metre;
vc
vertical pressure on a pipe due to moving distributed surcharge, in kilonewtons per square metre;
P
vd
q , q , q vertical earth pressure on the pipe, in kilonewtons per square metre;
v v1 v2
q total vertical pressure due to earth and moving load on the pipe, in kilonewtons per square metre;
vt
q , q , q horizontal earth pressure on the pipe, in kilonewtons per square metre;
h h1 h2
q , q , q horizontal soil reaction pressure on the pipe, in kilonewtons per square metre;
hp hp1 hp2
r mean radius of pipe, in metres;
s wall thickness of pipe, in metres;
s stiffness of pipe, in Newtons per square metre;
p
S horizontal stiffness of soil backfill in the zone of the pipe, in Newtons per square millimetre;
sh
S vertical stiffness of pipe bedding, in Newtons per square millimetre;
sv
t , t thickness of layers in a road structure, in metres;
1 2
V , V stiffness ratio;
s s1
V pipe-soil system stiffness;
ps
w, w , w unit weight of backfill soil, in kilonewtons per cubic metre;
1 2
W crushing load per unit length of pipe when tested in accordance with ISO 160, in kilonewtons per
metre;
x , x , x auxiliary parameter defined in the text;
1 2 3
α half the bedding angle of pipe;
β slope of the wall of the trench;
γ specific weight of water in kilonewtons per cubic metre;
δ deformation coefficient;
ξ correction factor;
η reduction factor of the resistance of the pipe to external load due to the action of internal pressure;
d
η reduction factor of the resistance of the pipe to internal pressure due to the action of external load;
z
ν safety factor against crushing of a pipe loaded externally without internal pressure;
d
ν safety factor against bursting of a pipe when a ring-bending moment is applied together with a internal
z
hydraulic pressure;
ρ angle of internal friction of backfill soil;
ρ‘ angle of friction between the backfill soil and the wall of the trench;
ø impact factor.
A.2.3.2 Required basic data
D, s, r, E pipe parameters ;
p
B, H trench/embankment conditions;
K , K coefficients of lateral earth pressure, out of Table A.2;
1 2
ρ angle of internal friction, out of soil investigation or Table A.1;
p projection ratio;
j
E - E - E - E soil conditions, out of soil investigation or Table A.1.
1 2 3 4
Table A.1 — Properties of soils for calculating earth-load
Group a Unit, ρ b
Types of soil Moduli of compression E at following
s
of soil
Proctor standard densities (%) achieved
weight, ω degrees
by self-consolidation compaction
kN/m
N/mm
85 90 92 95 97 100
1 Non-cohesive 20 35 2,5 6 9 16 23 40
2 Slightly cohesive 20 30 1,2 3 4 8 11 20
3 Mixed cohesive 20 25 0,8 2 3 5 8 14
4 Cohesive 20 20 0,6 1,5 2 4 6 10
a
The four types of soil are:
non-cohesive: gravel, sand;
slightly cohesive: binding non-uniform sand or gravel;
mixed cohesive: rock flour, weathered rock soils, clayey sand;
cohesive: clay, silt, loam.
b
The moduli of compression E of the soils are measured by applying the CBR (California Bearing Ratio)
s
method using a round plate of an area of 700 cm .
Table A.2 — Coefficients of lateral earth pressures
Group of soil K K
1 2
1 0,5 0,4
2 0,5 0,3
3 0,5 0,2
4 0,5 0,1
K and K shall always be considered simultaneously.
1 2
A.2.3.3 Selection of type of pipe laying
Three types of pipe laying are defined, see Figures A.1, A.2 and A.3.
key
1 Narrow trenches
2 Wide trench
3 Embankment conditions: positive projection
NOTE Type 1 covers trenches, wide trenches and positive projection embankment conditions.
Figure A.1 — Type 1 of laying
NOTE Type 2 covers negative projection conditions.
Figure A.2 — Type 2 of pipe laying
NOTE Type 3, two or more pipelines in a single trench.
Figure A.3 — Type 3 of pipe laying
A.2.3.4 Determination of the pipe soil system parameters
a) Stiffness of the pipe S
p
D − s
Ep (s)
r =
S =
p
12 r
with
b) Vertical stiffness of the bedding S
sv
E
S =
sv
P
j
Horizontal stiffness of the bedding S
c) sh
S = 0,6ξ E
sh 2
B
1,662 + 0,639 −1
D
withξ =
B B E
−1 + 1,662 − 0,361 −1
D D E
3
d) Pipe-soil fitness V (see Figure A.4)
ps
S
p
V =
ps
S
sh
The distribution of the vertical earth pressure and reaction.
a — soil bedding, V < 0,1 b — soil bedding, V > 0,1 c — concrete bedding, V < 0,1
ps ps ps
Figure A.4 — Distribution of earth pressure and reactions
For the calculation of ring-bending moments and deflections of the pipe, the vertical earth pressure is always
assumed to be rectangularly distributed over its crown, as shown in Figure A.4.
The distribution of the reaction depends on the pipe-soil system stiffness V :
ps
case 1: pipe on soil-bedding and V < 0,1, according to Figure A.4.a, i.e. vertically directed reaction,
ps
rectangularly distributed over the full width D of pipe, regardless of the actual bedding angle;
case 2: pipe on soil-bedding and V > 0,1, according to Figure A.4.b, i.e. vertically directed reaction,
ps
rectangularly distributed along the bedding angle 2 α ;
case 3: in the case of rigid bedding (for example a concrete cradle) and when V > 0,1, according to
ps
Figure A.4.c, i.e. radially directed and evenly distributed reaction along the bedding angle 2 α.
e) Deformation
C
h1
δ =
V − C
ps h
f) Deformation factors C
v
C = C + C ⋅δ
v v1 vs
C , C , C , C out of table A.3.
v h1 v3 h3
Table A.3 — Deformation factors
Factors corresponding to vertical soil pressure q
v
Bedding angle Case 1, Figure A.4.a Case 2, Figure A.4.b Case 3, Figure A.4.c
C C C C C C
2α degrees
v1 h1 v1 h1 v1 h1
60 - 0,0833 + 0,0833 - 0,1053 + 0,1026 - 0,1041 + 0,1017
90 - 0,0833 + 0,0833 - 0,0966 + 0,0956 - 0,0916 + 0,0916
120 - 0,0833 + 0,0833 -0,0893 + 0,0891 - 0,0763 + 0,0777
180 - 0,0833 + 0,0833 - 0,0833 + 0,0833 - 0,0417 + 0,0417
Factors corresponding to horizontal soil pressures q and q
h hp
Bedding angle Factors for q Factors for q
h hp
2α degrees
Cases 1 and 2 Case 3 Case 1
Figures A.4.a and b Figure A.4.c Figure A.4.a
C C C C C C
v2 h2 v2 h2 v3 h3
60 + 0,0833 - 0,0833 + 0,0827 - 0,0829 + 0,0640 - 0,0658
90 + 0,0833 - 0,0833 + 0,0798 - 0,0805 + 0,0640 - 0,0658
120 + 0,0833 - 0,0833 + 0,0721 - 0,0735 + 0,0640 - 0,0658
180 + 0,0833 - 0,0833 + 0,0417 - 0,0417 + 0,0640 - 0,0658
NOTE Factors C and C correspond to the following equations for calculating the deflection of the pipe:
v h
∆D = 2 C qr /EI
v v
and
∆D = 2 C qr /EI
h h
where
C = C or C or C ;
v v1 v2 v3
C = C or C or C ;
h h1 h2 h3
q = q or q or q
hv h hp
g) Stiffness ratio V
s
S
p
V = with lateral earth pressure q ;
s
hp
C .S
v sv
S
p
V = without lateral earth pressure q ;
s hp
C S
v1 vs
h) Concentration factor of vertical earth pressure over the pipe m
o
4K
m =
3 + K
i) Concentration factor of vertical earth pressure over the pipe m
()m −1 m ⋅V
m 0 s1
m V +
m s
1− m
m =
()m −1 V
1 s1
V +
s
1− m
0
j) Concentration factor of vertical earth pressure over the pipe m
m
H 1
m = 1+ ⋅
m
3,5 E 1 H 0,62 E 1
D
1 1
+ 2,2 + +1,6
P E()p − 0,25 D p E()p − 0,25
j 4 j j 4 j
k) Concentration factor of vertical earth pressure over the pipe m
m −1 4 − m
B B
1 1
m= ⋅ + for 1 < < 4
3 1 3 D
B
tc
m = m = C for 4 <
D
m = 1+4K tgρ
1 1
m
l) Concentration factor of lateral earth pressure on the side of the pipe n
4-m
n=
m) Earth load coefficient C
H
′
−2K tgρ
B
B
C= 1−e
2K Htgρ′
A.2.3.5 Determination of the vertical earth pressure on the pipe q
v
q = m ⋅C ⋅ w⋅ H
v
A.2.3.6 Determination of the horizontal earth pressure on the pipe Q and Q
h2 hp2
q = n ⋅K ⋅C ⋅ w⋅ H
v 2
q = δ ⋅()Q −Q
hp2 v h
A.2.3.7 Calculation of the superimposed vertical concentrated and distributed loads
concentrated load:
P = P ⋅C ⋅ µ
vc v c
where
P wheel load.
v
1 2 X 2HD 1 1 1
C = − arcsin 2H − + + ΣΙ
c
D ΠD X X X X H
X
2 3 2 3 2
1
2 2
x = 4H + D + 1
x = 4H + 1
2 3
x = 4H + D
Σ Ι = f (wheel distance, axle numbers, traffic load)
Ø = 1,5/1,4/1,2
distributed load:
P = P ⋅C ⋅ Ø
vd d d
with
A L
C = f , out of graphic
d
2H 2H
Ø = 1,2
A.2.3.8 Selection of the type of bedding
A distinction is made between three types of bedding, see Figure A.5.
Dimensions in centimetres
a) Embedment type A b) Embedment type B
NOTE Bedding types A and B correspond to case 1 or 2 of load distribution in Figures A.4.a or A.4.b, depending of the
value of the pipe system stiffness V .
ps
c) Embedment type C
Figure A.5 — Beddings
A.2.3.9 Determination of the ring bending moments
The maximum ring bending moment M in the wall of the buried pipe is calculated as follows:
m
2 3
M = ()k ⋅q + k q + k q r + k ⋅γ ⋅ r
m v vt h h hp hp w
with:
k , k , k , k the ring bending moment factors given in table A.4.
v h hp w
Table A.4 — Factor for the calculation of ring-bending moments in buried pipes
Bedding angle Cross-section Ring-bending moment factors
of pipe
2 α
k k k k
v h hp w
Case 1 of load distribution (bedding types A or B, V < 0,1)
ps
180 Crown + 0,250 - 0,250 - 0,181 + 0,172
Spring line - 0,250 + 0,250 + 0,208 - 0,196
Bottom + 0,250 - 0,250 - 0,181 + 0,220
Case 2 of load distribution (bedding types A or B, V > 0,1)
ps
60 Crown + 0,286 - 0,250 - + 0,229
Spring line - 0,293 + 0,250 - - 0,264
Bottom + 0,377 - 0,250 - + 0,420
90 Crown
+ 0,273 - 0,250 - + 0,210
Spring line - 0,279 + 0,250 - - 0,243
Bottom + 0,313 - 0,250 - + 0,321
120 Crown + 0,261 - 0,250 - + 1,190
Spring line - 0,265 + 0,250 - - 0,220
Bottom + 0,275 - 0,250 - + 0,260
Case 3 of load distribution (bedding types C, V > 0,1)
ps
90 Crown + 0,266 - 0,245 - + 0,189
Spring line - 0,271 + 0,244 - - 0,230
Bottom + 0,277 - 0,224 - + 0,262
120 Crown
+ 0,240 - 0,232 - + 0,157
Spring line - 0,240 + 0,228 - - 0,181
Bottom + 0,202 - 0,187 - + 0,145
180 Crown + 0,163 - 0,163 - + 0,035
Spring line - 0,125 + 0,125 - 0,000
Bottom + 0,087 - 0,087 - + 0,035
A.2.3.10 Calculation of the safety factor
M
e
µ =
M
m
M pw
e
ν = 1−
d
M P2
m
P ()M
2 m
ν = 1−
z
Pw M
e
where:
µ is the safety factor against crushing of a pipe loaded externally without any internal pressure;
ν is the safety factor against crushing when an internal hydraulic pressure P is applied together with a
d w
ring bending moment M ;
m
ν is the safety factor against bursting when a ring bending moment M is applied together with an
z m
internal hydraulic pressure P .
w
A.2.3.11 Are the safety factors acceptable?
The recommended minimum safety factor against crushing of non-pressure pipes is:
µ = 1,5
The recommended minimum safety factors for pressure pipes under combined loads according to the different
diameters are:
from 175 mm to 200 mm: ν = 2,5 and ν = 3,5;
d z
from 250 mm to 500 mm: ν = 2,5 and ν = 3,0;
d z
from 600 mm to 2500 mm: ν = 2,5 and ν = 2,5.
d z
NOTE When the maximum working pressure does not exceed 0,3 MPa, the two safety factors may be reduced to 2,0 each.
A.3 Denmark
A.3.1 General
The design method described below is a simplified method which can be used generally for rigid pipes. However, it
will always be acceptable to use more accurate methods if their quality is proved.
The course of the calculations in accordance with the principle using the procedures and equations described
below is illustrated on the flowchart below. In practice, routine design is usually carried out with the aid of tables of
charts based on these principles.
List of symbols
d internal diameter of pipe, m;
i
d external diameter of pipe, m;
y
F crushing test load, kN/m;
f bending tensile strength, MN/m ;
t
h depth of cover, m;
d
k factor;
l length of pipe, m;
P axle load, kN;
p railway line load, kN/m;
Q wheel load, kN;
q uniformly distributed surface load, kN/m ;
r bearing capacity, kN/m ;
t pipe wall thickness, m;
v loading per unit of area, kN/m ;
v equivalent addition of load for self-weight of pipe, kN/m ;
g
v vertical earth load, kN/m ;
j
v vertical pipe loading from uniformly distributed surface load, kN/m ;
q
v vertical pipe loading from traffic load, kN/m ;
t
v equivalent addition for water load, kN/m ;
w
γ (without index) unit weight of backfill above water table, kN/m ;
γ (with index) partial safety factor;
λ earth load coefficient (Marston coefficient);
General indices:
c concrete;
d design;
f load dependant;
k characteristic;
m material dependant;
s steel.
Figure A.6 — Flowchart for pipeline design
A.3.2 Charges
A.3.2.1 Types of loads
When designing a buried pipe the following types of loads shall be considered:
Permanent loads
earth load;
self-weight of pipe.
Variable loads
distributed surface load;
traffic loads;
loads from external and internal water pressure.
A.3.2.2 Distributed of load and bedding reaction
The vertical load is assumed uniformly distributed over a width equal to the external diameter of the pipe.
The horizontal load is assumed uniformly distributed over a width equal to:
the external diameter of the pipe when using circular pipes;
the height to the pipe from its top to its axis when using pipes with base.
The bedding reaction is assumed to be a vertical action uniformly distributed over a width equal to:
0,5 times the external diameter circular pipes laid with normal bedding;
0,7 times the external diameter of circular pipes laid with an improved bedding;
the external width of circular jacking pipes;
the width of the base when using pipes with a base.
In the longitudinal direction of the pipe the bedding reaction is assumed to be uniformly distributed. If the length of
the pipe is large in relation to its diameter due consideration shall be given as to the validity of this assumption.
NOTE If no exact evaluation is carried out the bedding reaction can be assumed uniformly distributed if the useful length is
smaller than or equal to:
1,0 m for d ≤ 0,15 m ;
i
d /0,15 m for 0,15 m< d ≤ 0,40 m ;
i i
2,7 m for d > 0,40 m.
i
A.3.2.3 Earth load
The characteristic vertical load on a pipe from the backfill is determined by:
v = λ γ h kN/m ,
j d
with the relieving effect of the lateral pressure being included in λ.
If a closer examination is not carried out and the laying conditions are not extreme, the following values for λ can
be used:
for low laying class (with no requirements for the stiffness of the sidefill): 1,62 + 0,50 h /d + 0,54 d / h ;
d y y d
for normal laying class (with the stiffness of the sidefill at least the same as the stiffness of the backfill): 1,6;
for high laying class (with the stiffness of the sidefill at least five times the stiffness of the backfill): 1,4;
for jacking pipes: 1,0;
for the upper pipe in a stepped trench: 1,62 + 0,25 h /d + 0,27 d / h ;
d y y d
for pipes supported on piles: 1,62 + 0,50 h /d + 0,54 d / h ;
d y y d
for pipes laid under water: 1,62 + 0,50 h /d + 0,54 d / h .
d y y d
The unit weight γ of the backfill may be fixed at 21 kN/m . For underwater backfill, γ may however be fixed at
11 kN/m .
A.3.2.4 Self-weight of pipes
The loading effect of the self-weight of the pipe shall be included, either as a deduction in the load bearing capacity
of the pipe or as an equivalent addition to the vertical load.
A.3.2.5 Uniformly distributed surface load
The action on a pipe from an uniformly distributed characteristic surface load q is given in kN/m and determined
by:
v = λ q.
q
A.3.2.6 Traffic load from roads
A three-axle group is assumed in which each axle load consists of two wheel loads Q with a centre-to-centre
distance of 2,0 m and an axle-to-axle distance of 1,5 m. The contact surface of the wheel load is assumed to be a
rectangle with sides of 0,2 m in the direction of travel and 0,6 m across the same.
The characteristic value of Q is assumed to be 65 kN for normal road traffic and 100 kN for heavy road traffic.
These loads include an impact factor which is independent of the earth cover.
The load v from a wheel load Q is determined - in case of depth of cover of more than some 1,3 m - in accordance
t
with Boussinesq’s theory.
NOTE With a good approximation, the traffic loading can be determined on the basis of an assumption that the distribution
of stress through the ground is 1:2. This leads to the following expression for the loading from the specific load group in kN/m :
ν = 6 ⋅Q()h + 2,6(h + 3,2)
t d d
At depths of cover h < 1,34 m the loading is changed into the action from one wheel load:
d
ν = Q()h + 0,2(h + 0,6)
t d d
which value may be reduced as a function of the pipe diameter by using the following factor:
k = 1 −()1 − 0,75 ⋅ h (10 + 3 ⋅ d − 1 d ) 18
d y y
A.3.2.7 Traffic load from railway tracks
The standard railway loading of the Danish State Railways shall be used as a basis for the calculation of the loads
from railways, i.e.:
characteristic axle load inclusive impact factor: P = 410 kN ;
evenly distributed line p = 80 kN/m.
NOTE If a stress distribution of 1:2 in the ground is assumed across the line road, the load can be determined by the
following expression:
The loading for one track in kN/m :
()( )
ν = P h + p h +2,2
t d d
The loading from two or more tracks:
for h < 2,3 m: as for one track
d
for h ≥ 2,3 m: ν =()8 ⋅ P()h + 6,4 + 2 ⋅ p(h + 6,7)
d t d d
A.3.2.8 Load from external and internal water pressure
The effect on a pipe due to its water-filled state shall usually be included, either as a deduction in the bearing
capacity of the pipe or as an equivalent addition to the vertical load.
The effect on a pipe due to an internal positive or negative pressure shall be included. A dimensioning positive
pressure shall include both the hydrostatic and the hydrodynamic pressure, as a possible surge in addition to the
wor
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