ISO/TR 10465-2:2007

Underground installation of flexible glass-reinforced pipes based on unsaturated polyester resin (GRP-UP) - Part 2: Comparison of static calculation methods

ISO/TR 10465-2:2007 presents a comparison of the ATV and AWWA methods for static calculations on underground GRP pipe installations. It is intended that this comparison will encourage the use of both procedures for GRP pipes conforming to International Standards. It is not the intent of ISO/TR 10465-2 to cover all the details of the two methods. Some aspects are, of necessity, very complex, and for a full understanding the original documents need to be studied in detail. Rather, the intention is to give a general overview and comparison of the key elements so that the user can more easily understand and appreciate the differences between the two procedures and their similarities.

Installation enterrée de canalisations flexibles renforcées de fibres de verre à base de résine polyester insaturée (GRP-UP) — Partie 2: Comparaison de méthodes de calcul statique

General Information

• Status: Published
• Publication Date: 28-Aug-2007
• ICS: 23.040.01 - Pipeline components and pipelines in general
• Technical Committee: ISO/TC 138/SC 6 - Reinforced plastics pipes and fittings for all applications
• Drafting Committee: ISO/TC 138/SC 6 - Reinforced plastics pipes and fittings for all applications
• Current Stage: 9092 - International Standard to be revised
• Start Date: 04-Apr-2025
• Completion Date: 13-Dec-2025

Relations

• Revises: ISO/TR 10465-2:1999 - Underground installation of flexible glass-reinforced thermosetting resin (GRP) pipes - Part 2: Comparison of static calculation methods
• Effective Date: 15-Apr-2008

Overview

ISO/TR 10465-2:2007 is a Technical Report that compares the two principal static calculation procedures used for the underground installation of flexible glass‑reinforced pipes based on unsaturated polyester resin (GRP‑UP). Published by ISO in 2007 (second edition), this document provides a clear, high‑level comparison of the ATV‑A 127 and AWWA M‑45 calculation methods to help users understand their similarities, differences and practical implications. It is informative in nature and does not replace the original ATV or AWWA source documents.

Key topics

The report summarizes and contrasts the main elements of static pipe design for GRP‑UP, including:

• Soil‑load distribution and how soil interacts with flexible pipes
• Initial and long‑term soil loads and their influence on pipe stresses
• Traffic loads: treatment and differences between the AWWA and ATV approaches
• Deflection: vertical deflections under various loading and installation conditions
• Circumferential bending strain: calculation approaches in both methods
• Buckling: stability assessment procedures and treatment of elastic vs. inelastic behaviour
• Internal‑pressure effects and combined loading (pressure plus external loads)
• Symbols, abbreviations and parameter definitions used by both methods

Note: ISO/TR 10465-2 offers an overview and comparison rather than exhaustive procedural detail; users should consult ATV‑A 127 and AWWA M‑45 for full calculation rules.

Practical applications

This Technical Report is useful for:

• Design engineers evaluating GRP‑UP pipelines for sewerage, drainage and non‑pressurized or low‑pressure fluid transport
• Consultants and contractors who need to interpret or compare design outputs based on different calculation systems
• Standards and compliance teams deciding which established method best fits project requirements or regional practice
• Educators and reviewers seeking a concise primer on pipe‑soil interaction, deflection, buckling and traffic load effects on GRP pipes

By clarifying differences between the ATV and AWWA methods, ISO/TR 10465‑2 helps practitioners choose and apply static calculation procedures for flexible GRP pipe installations that conform to international product standards.

Related standards

• ISO 10465‑1 - Installation procedures (Technical Specification)
• ISO 10465‑3 - Installation parameters and application limits (Technical Report)
• ATV‑A 127 - Guidelines for static calculations on drainage conduits and pipelines
• AWWA M‑45 - Fiberglass pipe design manual

Keywords: ISO/TR 10465-2:2007, GRP‑UP, glass‑reinforced pipes, underground installation, static calculation methods, ATV‑A 127, AWWA M‑45, pipe‑soil interaction, deflection, buckling, traffic loads.

Standards Content (Sample)

TECHNICAL ISO/TR
REPORT 10465-2
Second edition
2007-09-01
Underground installation of flexible
glass-reinforced pipes based
on unsaturated polyester resin
(GRP-UP) —
Part 2:
Comparison of static calculation methods
Installation enterrée de canalisations flexibles renforcées de fibres
de verre à base de résine polyester insaturée (GRP-UP) —
Partie 2: Comparaison de méthodes de calcul statique

Reference number
©
ISO 2007
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©  ISO 2007
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,
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ii © ISO 2007 – All rights reserved

Contents Page
Foreword. iv
Introduction . v
1 Scope .1
2 Normative references .1
3 Symbols and abbreviated terms .1
4 Soil-load distribution.10
5 Soil load .10
5.1 General.10
5.2 Initial loadings.10
5.3 Long-term loading .15
6 Traffic loads.15
6.1 General.15
6.2 AWWA procedure .16
6.3 ATV procedure .18
7 Deflections.20
7.1 Resulting from vertical load .20
7.2 Aspects not covered by AWWA or ATV .26
7.3 Irregularities in the installation .26
8 Circumferential bending strain.27
8.1 AWWA procedure .27
8.2 ATV procedure .27
9 Buckling.29
9.1 General.29
9.2 AWWA procedure .29
9.3 ATV procedure .31
10 Internal-pressure effects.34
10.1 General.34
10.2 Pressure strain.34
10.3 Combined loading.34
10.4 Calculations based on stress .35
Bibliography .36
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
In exceptional circumstances, when a technical committee has collected data of a different kind from that
which is normally published as an International Standard (“state of the art”, for example), it may decide by a
simple majority vote of its participating members to publish a Technical Report. A Technical Report is entirely
informative in nature and does not have to be reviewed until the data it provides are considered to be no
longer valid or useful.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO/TR 10465-2 was prepared by Technical Committee ISO/TC 138, Plastics pipes, fittings and valves for the
transport of fluids, Subcommittee SC 6, Reinforced plastics pipes and fittings for all applications.
This second edition cancels and replaces the first edition (ISO/TR 10465-2:1999), which has been technically
revised to take into account changes made to methods in base documents ATV-A 127 and AWWA M-45 (see
Introduction).
ISO 10465 consists of the following parts, under the general title Underground installation of flexible glass-
reinforced pipes based on unsaturated polyester resin (GRP-UP):
⎯ Part 1: Installation procedures [Technical Specification]
⎯ Part 2: Comparison of static calculation methods [Technical Report]
⎯ Part 3: Installation parameters and application limits [Technical Report]
iv © ISO 2007 – All rights reserved

Introduction
Work in ISO/TC 5/SC 6 (now ISO/TC 138) on writing International Standards for the use of glass-reinforced
plastics (GRP) pipes and fittings was approved at the subcommittee meeting in Oslo in 1979. An ad hoc group
was established and the responsibility for drafting various International Standards was later given to a Task
Group (now ISO/TC 138/SC 6).
At the SC 6 meeting in London in 1980, Sweden proposed that a working group be formed to develop
documents regarding a code of practice for GRP pipes. This was approved by SC 6, and Working Group 4
(WG 4) was formed for this purpose. Since 1982, many WG 4 meetings have been held which have
considered the following matters:
⎯ procedures for the underground installation of GRP pipes;
⎯ pipe/soil interaction with pipes having different stiffness values;
⎯ minimum design parameters;
⎯ overview of various static calculation methods.
During the work of WG 4, it became evident that unanimous agreement could not be reached within the
working group on the specific methods to be employed to address these issues. It was therefore agreed that
all parts of the code of practice should be made into a type 3 Technical Report, and this was the form in which
this part of ISO 10465 was first published in 1999. Since then the ISO rules dealing with the classification of
document types have been revised and this has resulted in the three parts of ISO 10465 now being published
as either a Technical Specification or a Technical Report.
ISO 10465-1, published as Technical Report in 1993 and revised as a Technical Specification in 2007,
describes procedures for the underground installation of GRP pipes. It concerns particular stiffness classes for
which performance requirements have been specified in at least one product standard, but it can also be used
as a guide for the installation of pipes of other stiffness classes.
This part of ISO 10465, published as a Technical Report in 1999 and revised in 2007, presents a comparison
of the two primary methods used internationally for static calculations on underground GRP pipe installations.
These methods are
a) the ATV method given in ATV-A 127, Guidelines for static calculations on drainage conduits and
pipelines, and
b) the AWWA method given in AWWA manual M-45, Fiberglass pipe design.
ISO 10465-3, published as a Technical Report in 2007, gives additional information, which is useful for static
calculations primarily when using an ATV-A 127 type design system in accordance with this part of
ISO 10465, on items such as:
parameters for deflection calculations;
soil parameters, strain coefficients and shape factors for flexural-strain calculations;
soil moduli and pipe stiffness for buckling calculations with regard to elastic behaviour;
parameters for rerounding and combined-loading calculations;
the influence of traffic loads;
the influence of sheeting;
safety factors.
This Technical Report is not to be regarded as an International Standard. It is proposed for provisional
application so that experience may be gained on its use in practice. Comments should be sent to the
secretariat of TC 138/SC 6.
vi © ISO 2007 – All rights reserved

TECHNICAL REPORT ISO/TR 10465-2:2007(E)

Underground installation of flexible glass-reinforced pipes
based on unsaturated polyester resin (GRP-UP) —
Part 2:
Comparison of static calculation methods
1 Scope
This part of ISO 10465 presents a comparison of the ATV and AWWA methods for static calculations on
underground GRP pipe installations. It is intended that this comparison will encourage the use of both
procedures for GRP pipes conforming to International Standards.
It is not the intent of this part of ISO 10465 to cover all the details of the two methods. Some aspects are, of
necessity, very complex, and for a full understanding the original documents need to be studied in detail.
Rather, the intention is to give a general overview and comparison of the key elements so that the user can
more easily understand and appreciate the differences between the two procedures and their similarities.
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.
ATV-A 127, Guidelines for static calculations on drainage conduits and pipelines, 3rd edition, August 2000
(German Association for Water Pollution Control)
AWWA M-45, Fiberglass pipe design manual M-45, 2005 (American Water Works Association)
3 Symbols and abbreviated terms
For the purposes of this document, the following symbols apply.
NOTE 1 This clause also contains symbols and abbreviations from ISO 10465-1 and ISO 10465-3 for completeness.
NOTE 2 Several identical symbols are used in ATV-A 127 and AWWA M-45 to represent different quantities, and
where this occurs, the origin of the symbol is given in the rightmost column.
NOTE 3 The format of the symbols listed here has been aligned as far as practicable with the ISO/IEC Directives, part
2, namely they appear in Times New Roman italic font. This format may differ slightly from the format used in ATV-A 127
and AWWA M-45.
Symbol Unit Meaning
AQL — acceptable quality level
a′ — effective relative projection
a — ageing factor (ATV)
f
a — distribution factor (AWWA)
f
B1, B2, B3, B4 — embedment conditions
b m trench width at spring-line
b′ m distance from trench wall to pipe (see Figure 1)
C — buckling scalar calibration factor
n
c , c , c , c — coefficients used to determine ζ
1 2 3 4
c — reduction factor
c — creep factor
f
cc,,c ,,c c ,,c — deformation coefficients
h,qv v,qh v,qh* h,qh h,qh* v,qv
c,,,ccc
v* v,qh* h,qh* v*
D mm mean pipe diameter
D — shape factor
f
D — shape adjustment factor
g
D — deflection lag factor
L
D % compaction (based on simple proctor)
pr
d m external pipe diameter
e
d m internal pipe diameter
i
⎡ ⎤
d m mean pipe diameter de×1000 −
( )
e
m
⎣ ⎦
d mm vertical deflection
v
d mm maximum permissible long-term deflection
vA
d mm vertical deflection at rupture
vR
dd
() % maximum permissible relative vertical deflection
vm
permissible
dd % initial vertical deflection
( )
vm
initial
(dd ) % long-term (50 year) vertical deflection
vm
dd % ultimate long-term vertical deflection
( )
vm
ult
EE,,E,E
N/m apparent flexural moduli of pipe wall
o p t,wet
E′′,,EE,E,E,E,E,E ,E N/m soil deformation moduli
12 3 4 s s s,σ 20
E N/m tensile hoop modulus
TH
e mm pipe wall thickness
e — base of natural logarithms (2,718 281 8)
F — compaction factor
2 © ISO 2007 – All rights reserved

F , F kN wheel loads
A E
FS — calculated safety factor (ATV)
FS — design factor = 2,5 (AWWA)
FS — bending safety factor
b
FS — pressure safety factor
pr
f — reduction factor for creep
f — reduction factor for ground water in pipe zone
G1, G2, G3, G4 — soil groups
HDB — extrapolated pressure strain at 50 years
H m environmental depth of cover
EVD
h m depth of cover to top of pipe
h m depth at which load from wheels interact
int
h m height of water surface above top of pipe
w
I m /m second moment of area in longitudinal direction per unit
length (of a pipe)
I — impact factor (AWWA)
f
i N/mm installation factor
f
*
K — coefficient for bedding reaction pressure
K′ — modulus of deformation
K , K — ratio of horizontal to vertical soil pressure in soil zones
1 2
1 and 2
K — ratio of horizontal to vertical soil pressures in pipe-zone
backfill, when backfill is at top of pipe (see
ISO 10465-3:2007, Annex A)
k — reduction factor to take into account the elastic-plastic
v2
soil mass law and preliminary deflections
k — bedding coefficient
x
L m load width parallel to direction of travel
L m load width perpendicular to direction of travel
LLDF — live load as a function of depth factor
M — sum of bending moments
M — multiple presence factor
p
M N/m composite constrained-soil modulus
s
M N/m value of composite constrained-soil modulus from
s1
ISO 10465-3:2007, Table A.3
M N/m composite constrained-soil modulus at 100 % SPD
s100
M N/m backfill soil constrained modulus
sb
M N/mm native soil constrained modulus
sn
mm,,m
— moment factors
qv qh qh*
N — sum of normal forces
n — number of blows
P N magnitude of wheel load
PN — nominal pressure (pipe characteristic)
P bar internal pressure
P — probability of failure
f
P MPa (N/mm) internal under-pressure
v
P N/m working pressure
w
P(X) — probability function
P bar long-term (50 year) failure pressure
p N/m soil stress resulting from traffic loads
p N/mm pressure due to prismatic soil load
E
p N/mm external water pressure
e
p N/m soil stress due to traffic load according to Boussinesq
F
p N/m soil pressure due to uniformly distributed surface load
o
p N/mm soil pressure resulting from traffic load
v
q MPa (N/mm) permissible buckling pressure
a
q MPa (N/mm) critical buckling pressure
c
q MPa (N/mm ) critical buckling pressure under sustained load
cl
q N/mm horizontal bedding reaction for pipe and contents
c*w
q , q N/mm horizontal or vertical soil pressure on pipe
h v
q N/mm horizontal bedding reaction pressure
h*
q N/mm reduced long-term horizontal soil pressure
hLT
q N/mm long-term (50 year) horizontal soil pressure
h,50
q N/mm reduced long-term vertical soil pressure
vLT
4 © ISO 2007 – All rights reserved

q N/mm long-term (50 year) vertical soil pressure
v,50
q N/mm vertical load due to pipe and contents
vwa
R — depth-of-fill correction factor
h
R — water buoyancy reduction factor
w
r — rerounding factor (AWWA)
r m mean pipe radius (AWWA)
r , r m wheel radii (ATV)
A E
r — rerounding coefficient
c
r m pipe internal radius
i
r m mean pipe radius
m
S N/mm horizontal bedding stiffness
Bh
S N/mm vertical bedding stiffness
Bv
S — long-term ring-bending strain capability of the pipe
b
S — soil support combining factor
c
S N/mm characteristic stress
k
S N/m long-term pipe stiffness
O
S N/m long-term pipe stiffness
O,50
S N/m weighted long-term pipe stiffness
o
S N/m long-term (50 year) pipe stiffness
OK
S N/m long-term (2 year) pipe stiffness
OL
SPD % standard proctor density
S N/m initial pipe stiffness
p
S N/m long-term pipe stiffness
p,50
−6
S ××810
S N/mm
p
R
−6
S N/mm S ××810
R,50 p,50
S N/mm standard deviation of strength of pipe
Res
S N/mm standard deviation of strength of pipe below ground
Res,B
S N/mm standard deviation of stress in pipe
S
S N/mm standard deviation of stress in pipe below ground
S, B
t m length of tyre footprint
l
t m width of tyre footprint
w
V — system stiffness
RB
V — stiffness ratio
S
W N/m vertical soil load on pipe
c
W N/m traffic load
L
X — safety index
y % coefficient of variation for initial tensile strength
y % coefficient of variation for tensile strength
R
z % coefficient of variation for initial ultimate deflection
α ° half the bedding angle (see Figure 2)
α — reduction factor depending upon trench proportions and
B
embedding conditions
α — value from ISO 10465-2:2007, Figure 5
Bi
α — snap-through coefficient
D
ακ, ακ , ακ — correction factor for extreme curvature of inner or outer
i e
edge
β ° half the horizontal support angle (see Figure 2)
β ° (ATV) trench wall slope angle (see Figure 1)
γ N/m bulk density of backfill material
b
γ N/m density of pipe contents
w
δ ° trench wall friction angle
δ % relative horizontal deflection
h
δ % relative vertical deflection
v
δ % negative relative vertical deflection due to traffic and
va
vacuum load
δ , δ % negative relative vertical deflection due to soil load
vc vs
δ % long-term relative vertical deflection
v50
δ % positive relative vertical deflection due to backfilling in
vio
pipe zone
δ % negative relative vertical deflection due to installation
viv
irregularities
δ % long-term negative relative vertical deflection due to soil
vs50
load
δ % negative relative vertical deflection due to weight of
vw
pipe
6 © ISO 2007 – All rights reserved

δ % relative vertical deflection due to traffic load
w
ε — bending strain caused by maximum permitted deflection
b
ε — compressive strain due to vertical load
comp
ε, ε , ε — calculated flexural strains in pipe wall
t f
ε — flexural strain due to installation irregularities
if
ε , ε — maximum permissible strain due to pressure
max R
ε — initial bending tensile strain
PK
ε — long-term bending tensile strain
PL
ε — calculated strain in pipe wall due to internal pressure
pr
ε — weighted calculated value of outer fibre strain
R
ε — total flexural strain
tot
ε — flexural strain due to total vertical load
v
ε — flexural strain due to backfilling in pipe zone
vio
ε — flexural strain due to weight of pipe
vw
ε — flexural strain due to pipe contents
w
ε — long-term maximum bending strain caused by
maximum permitted deflection
ζ — correction factor for horizontal bedding
η,,ηη,η — safety factors
tf ff
η — combined flexural safety factor
haf
η — combined tensile safety factor
hat
η — redefined safety factor for pipe to operate at PN
t,PN
ϕ ° soil internal friction angle
ϕ′ — impact factor (ATV)
ϕ — variability factor for compacted soil
s
χ — coefficient of safety
χ MN/m unit weight (density) of pipe material
P
χ N/m unit weight (density) of soil
s
χ N/m unit weight (density) of water
w
κκ,
— reduction factor for distributed load according to silo
β
theory when trench angle, β, is 90°
κκ, — reduction factor for distributed load according to silo
ooβ
theory when trench angle, β, is not 90°
λ , λ , λ , λ , λ , λ — concentration factors in soil next to pipe
B B50 P PG PG50 S
λ — maximum concentration factor
max
λ — long-term value for λ
PLT P
λ — reduction factor for soil friction with time
R
µ N/mm mean value of pipe strength (resistance)
Res
µ
N/mm mean value of strength (resistance) of pipe above
Res, A
ground
µ N/mm mean value of strength (resistance) of pipe below
Res, B
ground
µ N/mm mean value of stress in pipe below ground
S,B
v — Poisson ratio of soil
s
ρ MN/m density of pipe wall material
σ N/mm calculated compressive stress in pipe wall
c
σ — initial bending tensile stress
PK
σ — long-term bending tensile stress
PL
σ — weighted bending tensile stress
R
σ N/mm calculated tensile stress in pipe wall
t
8 © ISO 2007 – All rights reserved

Key
1 ground level 7 trench wall angle, β
2 water table 8 thickness of primary embedment
3 height of water surface above top of pipe, h 9 thickness of bedding
w
4 vertical deflection, d 10 thickness of foundation (if required)
v
5 distance from trench wall to pipe, b′ 11 pipe embedment
6 depth of cover to top of pipe, h 12 thickness of backfill
Soil moduli zones
E1 trench backfill above pipe embedment
E2 pipe embedment
E3 undisturbed native soil or in situ material to side of trench
E4 undisturbed native soil or in situ material below bottom of trench (foundation material)
NOTE 1 The AWWA M-45 design manual uses M in zone E .
sb 2
NOTE 2 The AWWA M-45 design manual uses M in zones E and E .
sn 3 4
Figure 1 — Symbols and terminology
4 Soil-load distribution
The assumed soil-load distributions used in ATV-A 127 and AWWA M-45, which are based on those made by
M.G. Spangler, are shown in Figure 2. The main difference between the two assumptions is that ATV-A 127
considers the active horizontal pressure, whereas AWWA M-45, like Spangler, assumes the value to be zero.
In ATV, the influence of active horizontal pressure is accounted for by using a value for K which is in the
range 0,1 to 0,4, when the system stiffness V is less than 1 and depending on the type of soil in the pipe
RB
zone (zone E in Figure 1).
ATV-A 127 uses horizontal (if required) and vertical deflections but AWWA M-45 only uses vertical deflection.
When, in the ATV system, the appropriate coefficients are used to calculate horizontal deflection using
Spangler’s assumption for soil-load distribution, the same deflection is obtained as with Spangler's system
provided Spangler's E′ is multiplied by 0,6.
Related to the question of soil distribution is the influence of the modulus of passive soil resistance. ATV
introduces the horizontal soil stiffness term, S , equal to 0,6 × ζ × E where ζ is the Leonhardt factor which
Bh 2
accounts for the influence of the in situ (native) soil (zone E ) and trench width (see Figure 1) and E
3 2
corresponds to Spangler’s E′.
5 Soil load
5.1 General
The calculation of soil loads needs to consider both initial and long-term loadings. Short-term loading can be
related to the initial pipe deflection, which is a property that is often used as a measure of installation quality.
Long-term loading defines the expected long-term deflection of the pipe and is therefore related to service life.
5.2 Initial loadings
5.2.1 AWWA procedure
In the AWWA procedure, the soil loading is assumed to be a soil prism in all cases. The prism has a height
equal to the depth of cover and its width is equal to the outside diameter of the pipe. The prismatic equation is
always used, and arching or silo theory is not considered.
The vertical soil load, W , is calculated using Equation (1):
c
Wh=×γ (1)
cb
where
W is the vertical soil load, in N/m ;
c
γ is the bulk density of the soil (i.e. its weight per unit volume), in N/m ;
b
h is the depth of cover, in m.

10 © ISO 2007 – All rights reserved

a)  Spangler
b)  ATV
Figure 2 — Soil stress distribution according to Spangler and ATV-A 127
5.2.2 ATV procedure
The ATV procedure for calculating soil loads is more detailed than that used by AWWA. The procedure is
based on silo theory, which assumes that frictional forces against the trench walls will lead to a reduction in
the pressure acting on the pipe due to the soil. It is assumed that these friction conditions are maintained for
the whole life of the pipe.
Trench and embankment conditions are considered as well as the angle of the trench walls and the
relationship between the horizontal and vertical soil pressures.
When the trench width is four times the pipe diameter or greater, then ATV assumes that embankment
conditions exist and consequently the soil load is a prismatic load.
The remainder of this subclause is an outline of the ATV procedure for calculating the soil load. Because of
the detailed nature of this approach, the reader is strongly recommended to read ATV-A 127 in detail very
carefully.
The vertical pressure, p , due to the prismatic soil load contains a reduction factor, κ, in Equation (2) to take
E
into account the friction effects mentioned above:
p =×κχ × h (2)
Es
Similarly, friction effects change the soil pressure, p , applied by a uniformly distributed load (UDL) acting
o
over a limited area, and this is expressed using the factor κ :
o
p′= κ × p (3)
oo o
NOTE κ Is the reduction factor for soil load. A subscript has been used above to indicate that κ is the reduction
o
factor for a UDL.
To use these reduction factors, the procedures require that:
a) E u E (for κ)
b) E < E (for κ )
o
If either of these conditions is not met or if the installation is considered to be of the embankment type, then
the factors κ and κ are taken to be equal to 1.
o
The reduction factors are derived using Equations (4) and (5):
h
⎛⎞
−×2t× K ×anδ
⎜⎟1
b
⎝⎠
1e−
κ = (4)
h
2t×× K×anδ
b
⎛⎞h
−×2t× K ×anδ
⎜⎟1
b
⎝⎠
κ = e (5)
o
where
e is the base of natural logarithms (2,718 281 8);
p is the vertical soil pressure due to the soil load, in N/m ;
E
κ is the reduction factor for silo theory;
χ is the bulk density of the soil (i.e. its weight per unit volume), in N/m ;
s
h is the depth of cover, in m;
12 © ISO 2007 – All rights reserved

κ is the silo theory reduction factor for UDL;
o
p is the soil pressure due to the UDL, in N/m ;
o
b is the trench width at spring-line, in m;
δ is the trench wall friction angle, in degrees (see Table 2);
K is the ratio of the horizontal to the vertical soil pressure in soil zone 1.
To help in other parts of the procedures, there are four classes of installation for zone 1 material above the
pipe zone (see Table 1)
Table 1 — Installation conditions
Class Description
Trench backfill compacted against undisturbed native soil in layers (without assessing
degree of compaction).
A1
These conditions also apply to sheet piles left in after installation.
Vertical timber sheeting or lightweight sheet piles or shields which are gradually removed
in stages during installation or
A2
uncompacted fill or
washing-in of the backfill (valid for soil group G1).
Vertical sheeting or shields withdrawn in one operation after all the backfill material has
A3
been put in place and compacted.
Same as A1 but degree of compaction is assessed. These conditions shall not be used
A4
with soil group G4.
For all the installation conditions detailed in Table 1, the lateral soil pressure acting on the trench walls,
expressed in terms of the vertical to horizontal soil pressure ratio, K , is assumed to be 0,5. Under these
conditions, Equations (4) and (5) reduce to Equations (4a) and (5a):
h
⎛⎞
−×tanδ
⎜⎟
b
⎝⎠
1e−
κ = (4a)
h
×tanδ
b
h
⎛⎞
−×tanδ
⎜⎟
b
⎝⎠
κ = e (5a)
o
The wall friction angle is derived from one of the equations given in Table 2, depending on the fill conditions.
Table 2 — Wall friction angle δ
Class Equation
A1 δϕ=×0,66 ′
A2 δϕ=×0,33 ′
A3 δ = 0
A4 δϕ=′
NOTE ϕ′ is the internal friction angle, in degrees, of the soil.

In the case where δ = 0 , the reduction factors κ and κ are taken to be equal to 1.
o
The other reduction factors, κ and κ , are adjusted to take into account the trench angle, as shown by
β oβ
Equations (6) and (7):
β β
⎛⎞
κκ=−1 + × (6)
β
⎜⎟
90 90
⎝⎠
β⎛⎞β
κκ=−1 + × (7)
ooβ ⎜⎟
90 90
⎝⎠
NOTE κ is the reduction factor for soil loads which takes into account the trench angle, β, and κ is the reduction
β oβ
factor for a UDL which takes into account the trench angle.
The horizontal soil pressure, q
...