ISO/TR 10465-3:1999

TECHNICAL ISO/TR
REPORT 10465-3
First edition
1999-07-15
Underground installation of flexible
glass-reinforced thermosetting resin (GRP)
pipes —
Part 3:
Installation parameters and application limits
Installation enterrée de canalisations flexibles en plastique renforcé de
fibres de verre/résine thermodurcissable (PRV) —
Partie 3: Paramètres d'installation et limites d'application
A
Reference number
ISO/TR 10465-3:1999(E)

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ISO/TR 10465-3:1999(E)
Contents
1 Scope .1
2 Normative references .1
3 Terminology .2
4 Symbols and abbreviated terms .2
5 Parameters for deflection calculations when using an ATV-A 127 type design system.7
5.1 Initial deflection.7
5.2 Long-term deflection calculated using an ATV-A 127 type design system.11
6 Soil parameters, strain coefficients and shape factors for flexural-strain calculations.12
6.1 For equations used in ATV-A 127 type design systems.12
6.2 Shape factor D .14
f
7 Influence of soil modulus and pipe stiffness on pipe-buckling calculations using ATV-A 127 type design
systems.16
7.1 Elastic buckling under internal negative pressure for depths of cover over 1 m .16
7.2 Long-term buckling under sustained external loads .17
7.3 Value of S .17
R
8 Parameters for rerounding and combined-loading calculations .17
8.1 Rerounding.17
8.2 Combined effects of internal pressure and external bending loads .17
9 Traffic loads.17
9.1 General.17
9.2 Influence on permissible initial deflection .18
9.3 Soil pressure due to traffic loads.18
10 Influence of sheeting.18
©  ISO 1999
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means, electronic
or mechanical, including photocopying and microfilm, without permission in writing from the publisher.
International Organization for Standardization
Case postale 56 • CH-1211 Genève 20 • Switzerland
Internet iso@iso.ch
Printed in Switzerland
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© ISO
ISO/TR 10465-3:1999(E)
11 Safety factors for gravity pipes and pressure pipes. 18
11.1 General . 18
11.2 Gravity pipes . 19
11.3 Pressure pipes . 20
11.4 Safety factors in buckling calculations . 22
Annex A (informative) Soil parameters . 23
Annex B (informative) Determination of concentration factors used in ATV-A 127. 32
Annex C (informative) Loading coefficients used in ATV-A 127 . 33
Annex D (informative) Horizontal bedding correction factors. 34
Annex E (informative) Selection of long-term stiffness . 36
Annex F (informative) Partly remaining soil friction used in ATV-A 127 type calculation systems . 38
Annex G (informative) Application limits for underground GRP pressure pipes . 40
Annex H (informative) Bibliography . 54
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© ISO
ISO/TR 10465-3:1999(E)
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.
The main task of ISO technical committees is to prepare International Standards, but in exceptional circumstances a
technical committee may propose the publication of a Technical Report of one of the following types:
 type 1, when the required support cannot be obtained for the publication of an International Standard, despite
repeated efforts;
 type 2, when the subject is still under technical development or where for any other reason there is the future
but not immediate possibility of an agreement on an International Standard;
 type 3, 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).
Technical Reports of types 1 and 2 are subject to review within three years of publication, to decide whether they
can be transformed into International Standards. Technical Reports of type 3 do not necessarily have to be
reviewed until the data they provide are considered to be no longer valid or useful.
ISO/TR 10465-3, which is a Technical Report of type 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.
The reasons which led to the decision to publish this document in the form of a type 2 Technical Report are
explained in the introduction.
ISO/TR 10465 consists of the following parts, under the general title Underground installation of flexible glass-
reinforced thermosetting resin (GRP) pipes:
 Part 1: Installation procedures
 Part 2: Comparison of static calculation methods
 Part 3: Installation parameters and application limits
This document 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.
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© ISO
ISO/TR 10465-3:1999(E)
Introduction
Work in ISO/TC 5/SC 6 (now ISO/TC 138) on writing 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 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, twenty-eight WG 4 meetings have been held which have considered the following
areas:
 procedures for the underground installation of GRP pipes;
 pipe/soil interaction with pipes having different stiffness values;
 minimum design features;
 an 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. Therefore WG 4 agreed that all documents should be made into a
three-part type 2 Technical Report, of which this is part 3.
Part 1 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.
Part 2 presents a comparison of the two primary methods used internationally for static calculations on underground
GRP pipe installations (ATV-A 127 and AWWA M-45).
Part 3 gives additional information, which is useful for static calculations when using an ATV-A 127 type design
system in accordance with part 2 of this Technical Report, on items such as:
 parameters for deflection calculations;
 soil parameters, strain coefficients and shape factors for flexural-strain calculations;
 soil moduli and pipe stiffnesses 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.
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TECHNICAL REPORT  © ISO ISO/TR 10465-3:1999(E)
Underground installation of flexible glass-reinforced thermosetting
resin (GRP) pipes —
Part 3:
Installation parameters and application limits
1 Scope
This part of ISO/TR 10465 gives information on parameters and application limits for the installation of GRP pipes. It
is particularly relevant when using an ATV-A 127 type design system.
Explanations of the long-term safety factors incorporated in the GRP system standards, based on simplified
probability methods, are given in annex G.
2 Normative references
The following normative documents contain provisions which, through reference in this text, constitute provisions of
this part of ISO/TR 10465. For dated references, subsequent amendments to, or revisions of, any of these
publications do not apply. However, parties to agreements based on this part of ISO/TR 10465 are encouraged to
investigate the possibility of applying the most recent editions of the normative documents indicated below. For
undated references, the latest edition of the normative document referred to applies. Members of ISO and IEC
maintain registers of currently valid International Standards.
ISO/TR 10465-1:1993, Underground installation of flexible glass-reinforced thermosetting resin (GRP) pipes —
Part 1: Installation procedures.
ISO/TR 10465-2:1999, Underground installation of flexible glass-reinforced thermosetting resin (GRP) pipes —
Part 2: Comparison of static calculation methods.
ASTM D 1586:1984, Standard test method for penetration test and split-barrel sampling of soils.
ASTM D 2166:1991, Standard test method for unconfined compressive strength of cohesive soil.
ATV-A 127, Guidelines for static calculations on drainage conduits and pipelines (December 1988).
AWWA M-45, Fiberglass pipe design manual M-45 (1997).
BS 1377 (all parts), Methods of test for soils for civil engineering purposes.
DIN 19565-1:1989, Centrifugally cast and filled polyester resin glass fibre reinforced (UP-GF) pipes and fittings for
buried drains and sewers; dimensions and technical delivery conditions.
OENORM B 4419-1:1985, Erd- und Grundbau; Untergrunderkundung durch Sondierungen; Rammsondierungen.
OENORM B 5012-1:1990, Statische Berechnung erdverlegter Rohrleitungen im Siedlungs- und Industriewasserbau;
Grundlagen.
WRc, Water Research Centre, Swindon, UK: Pipe materials selection manual — Water supply, 2nd edition, June
1995.
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© ISO
ISO/TR 10465-3:1999(E)
3 Terminology
Pipeline installation terminology can vary around the world so, where such terms are used in this part of
ISO/TR 10465, they will either be described or reference will be made to part 1 or 2, where the relevant descriptions
can be found.
4 Symbols and abbreviated terms
For the purposes of this part of ISO/TR 10465, the following symbols apply:
NOTE This clause also contains symbols and abbreviations from parts 1 and 2 for completeness.
Symbol Unit Meaning
a — Ageing factor
f
a — Distribution factor
f
B' — Support factor
b m Trench width at spring-line
b' m Distance from trench wall to pipe (see Figure 1)
c — Reduction factor
4
— Creep factor
c
f
c , c — Deformation coefficients
h v
D — Shape factor
f
D — Shape adjustment factor
g
D — Deflection lag factor
L
d m External pipe diameter
e
d mm Mean pipe diameter [(d · 1 000) – e]
m e
d mm Vertical deflection
v
d m Maximum permissible long-term deflection
vA
d mm Vertical deflection at rupture
vR
(d /d ) % Maximum permissible relative vertical deflection
v m permissible
(d /d ) % Initial vertical deflection
v m initial
(d /d ) % Long-term (50-year) vertical deflection
v m 50
(d /d ) % Ultimate long-term vertical deflection
v m ult
2
E, E , E N/m Apparent flexural moduli of pipe wall
o t,wet
2
E', E , E , E , E , E' , E' , E N/mm Soil deformation moduli
1 2 3 4 s t s
2
E N/m Tensile hoop modulus
TH
e mm Pipe wall thickness
e — Base of natural logarithms (2,718 281 8)
F — Compaction factor
F , F kN Wheel loads
A E
FS — Safety factor
FS — Bending safety factor
b
FS — Pressure safety factor
pr
HDB — Extrapolated pressure strain at 50 years
m Environmental depth of cover
H
EVD
2

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© ISO
ISO/TR 10465-3:1999(E)
Symbol Unit Meaning
h m Depth of cover to top of pipe
h m Height of water surface above top of pipe
w
4
I m /m Second moment of area in longitudinal direction per unit length (of a
pipe)
i — Initial ovalization
o
2
i N/mm Installation factor
f
K* — Coefficient for bedding reaction pressure
K , K — Ratio of horizontal to vertical soil pressure in soil zones 1 and 2
1 2
K — Ratio of horizontal to vertical soil pressure in pipe-zone backfill,
3
when backfill is at top of pipe (see annex A)
k — Bedding coefficient
x
M — Sum of bending moments
2
M N/mm Constrained-soil modulus
s
m , m , m* — Moment factors
qv qh qh
N — Sum of normal forces
n — Number of blows
10
P bar Internal pressure
PN — Nominal pressure
P(x) — Probability function
P — Probability of failure
f
2
P MPa (N/mm ) Internal underpressure
v
2
N/m Working pressure
P
W
2
p N/m External water pressure
a
2
p N/mm Pressure due to prismatic soil load
E
2
p N/m Pressure due to traffic load according to Boussinesq
F
2
p N/mm Soil pressure due to distributed load
o
2
p N/mm Soil pressure resulting from traffic load
v
2
q MPa (N/mm ) Permissible buckling pressure
a
2
q MPa (N/mm ) Critical buckling pressure
c
2
q MPa (N/mm ) Short-term critical buckling pressure
cs
2
q MPa (N/mm ) Critical buckling pressure under sustained load
cl
2
q MPa (N/mm ) Critical buckling pressure due to water
cw
2
q , q N/mm Horizontal and vertical soil pressure on pipe
h v
2
q * N/mm Horizontal bedding reaction pressure
h
2
q N/mm Long-term (50-year) horizontal soil pressure
h,50
2
q N/mm Reduced long-term horizontal soil pressure
hLT
2
q N/mm Horizontal bedding reaction for pipe and contents
c*w
2
q N/mm Long-term (50-year) vertical soil pressure
v,50
2
q N/mm Reduced long-term vertical soil pressure
vLT
2
q N/mm Vertical load due to pipe and contents
vwa
R — Water buoyancy reduction factor
w
r — Rerounding factor
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© ISO
ISO/TR 10465-3:1999(E)
Symbol Unit Meaning
r , r m Wheel radii
A E
r — Rerounding coefficient
c
2
S N/mm Horizontal bedding stiffness
Bh
2
S N/mm Vertical bedding stiffness
Bv
S — Long-term strain
b
S — Soil support combining factor
c
2
S N/mm Characteristic stress
k
2
S N/m Initial pipe stiffness
p
2
S N/m Long-term pipe stiffness
p,50
2 –6
S N/mm S ´ 8 ´ 10
R p
2 –6
S N/mm S ´ 8 ´ 10
R,50 p,50
2
s N/mm Standard deviation of strength of pipe
Res
2
s N/mm Standard deviation of strength of pipe above ground
Res,A
2
s N/mm Standard deviation of strength of pipe below ground
Res,B
2
s N/mm Standard deviation of stress in pipe
S
2
s N/mm Standard deviation of stress in pipe above ground
S,A
2
s N/mm Standard deviation of stress in pipe below ground
S,B
SPD % Standard Proctor density
V — System stiffness
RB
— Stiffness relation
V
S
2
W N/m Vertical soil load on pipe
c
2
W N/m Traffic load
L
X — Safety index
y % Coefficient of variation for tensile strength
R
y % Coefficient of variation for ultimate deflection
ult
a° (degrees) Half the bedding angle (see Figure 2)
b° (degrees) Half the horizontal support angle (see Figure 2)
c— Reduction factor applied to prismatic soil load to allow for friction
c— Reduction factor applied to prismatic soil load to allow for friction and
b
taking into account trench angle (b in ATV and w in this part of
ISO/TR 10465)
c— Reduction factor applied to a uniformly distributed load to allow for
o
friction
c— Reduction factor applied to a uniformly distributed load to allow for
ob
friction and taking into account trench angle (b in ATV but w in this
part of ISO/TR 10465)
d° (degrees) Trench wall friction angle
dmm Maximum permitted long-term installed deflection
d
d% Relative vertical deflection
v
d% Relative vertical deflection due to backfilling in pipe zone
vio
d% Relative vertical deflection due to installation irregularities
viv
d% Relative vertical deflection due to soil load
vs
d% Relative vertical deflection due to weight of pipe
vw
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© ISO
ISO/TR 10465-3:1999(E)
Symbol Unit Meaning
d% Relative vertical deflection due to traffic load
W
e— Compressive strain due to vertical load
comp
e, e, e— Calculated flexural strains in pipe wall
t f
e— Maximum permissible strain due to pressure
max
e— Calculated strain in pipe wall due to internal pressure
pr
e— Flexural strain due to total vertical load
v
e— Flexural strain due to backfilling in pipe zone
vio
e— Flexural strain due to weight of pipe
vw
e— Flexural strain due to pipe contents
W
3
gMN/m Bulk density of backfill material
b
3
gMN/m Density of pipe contents
w
h, h, h, h— Safety factors
t f ff
h— Combined flexural safety factor
haf
h— Combined tensile safety factor
hat
j° (degrees) Soil internal friction angle
k, k— Reduction factor for distributed load according to silo theory when
w
trench angle (w) is 90°
k, k— Reduction factor for distributed load according to silo theory when
o ow
trench angle (w) is not 90°
l— Concentration factor in soil next to pipe
B
l— Maximum concentration factor
max
l, l, l— Concentration factors for soil above pipe
R RG max
2
mN/mm Mean value of pipe strength (resistance)
Res
2
mN/mm Mean value of strength (resistance) of pipe above ground
Res,A
2
mN/mm Mean value of strength (resistance) of pipe below ground
Res,B
2
mN/mm Mean value of stress in pipe
S
2
mN/mm Mean value of stress in pipe above ground
S,A
2
mN/mm Mean value of stress in pipe below ground
S,B
3
rMN/m Density of pipe-wall material
3
rg/cm Density
D
2
sN/mm Calculated compressive stress in pipe wall
c
2
sN/mm Calculated tensile stress in pipe wall
t
n— Poisson's ratio for soil
s
w° (degrees) Trench wall angle (see Figure 1) (designated b in ATV-A 127)
x— Correction factor for horizontal bedding
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© ISO
ISO/TR 10465-3:1999(E)
Key
1 Ground level 5 Distance from trench wall to pipe, b'
2 Water table 6 Depth of cover to top of pipe, h
3 Height of water surface above top of pipe, h 7 Trench wall angle, w
w
4 Vertical deflection, d
v
NOTE 1 The AWWA M-45 design manual uses in zone E
E' .
b 2
NOTE 2 The AWWA M-45 design manual uses E' in zone E and E .
n 3 4
NOTE 3 E is the backfill above the pipe zone (E ) material.
1 2
NOTE 4 E is the embedment material to the side of the pipe.
2
NOTE 5 E is the in situ trench wall material.
3
NOTE 6 E is the in situ material underlying the pipe zone material (foundation material).
4
NOTE 7 In ATV-A 127, b is used for the trench wall angle instead of w.
Figure 1 — Symbols and terminology
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© ISO
ISO/TR 10465-3:1999(E)
Figure 2 — Soil distribution according to Spangler and ATV-A 127
5 Parameters for deflection calculations when using an ATV-A 127 type design system
This clause covers the soil parameters and deflection coefficients recommended for use when calculating the initial
or long-term deflection in accordance with ATV-A 127.
NOTE In the following calculations, deflections having a negative value indicate a reduction in vertical diameter.
5.1 Initial deflection
Measurement of the initial deflection shortly after installation, when the effects of traffic loads are not present, is a
very easy way of assessing the quality of the installation. The initial deflection should therefore be determined under
these loading conditions.
ATV-A 127 and the AWWA M-45 design manual do not address the effects of installation irregularities, deflection
resulting from the pipe's own weight, or the reduction in deflection due to upwards ovalization of the pipe when the
pipe zone backfill is compacted. It is recommended that, in deflection calculations, these effects be considered in
addition to the effects of soil load and superimposed loads. This recommendation is made because these effects
have been found to be significant in practice, especially for pipes having a DN greater than 2000.
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© ISO
ISO/TR 10465-3:1999(E)
5.1.1 Deflection due to vertical soil load and superimposed loads, but excluding traffic loads
d
v
The relative vertical deflection d , given byd= (% deflection when multiplied by 100), is determined using
v vs
d
m
equation (1):
NOTE This deflection has a negative value, which indicates a reduction in vertical diameter.
d 1
v
d==cc+ K * q q (1)
()·()-·[]·
vs v1 v2 v h
d S
m R
where
d is the vertical deflection of the pipe, in mm;
v
d is the mean diameter of the pipe, (d · 1 000) – e, in mm;
m e
e is the pipe wall thickness;
c
h1
K * = (2)
Vc-RB h2
c , c , c , c are deflection coefficients (see annex C);
v1 v2 h1 h2
V = S /S (3)
RB R Bh
–6 2
S = S · 8 · 10  (in N/mm ) (4)
R p
2
S is the initial pipe stiffness, in N/m ;
p
2
S = c · x · E  (in N/mm ) (5)
Bh 4 2
= 0,6 in ATV-A 127
c
4
xis a correction factor, given by:
14, 4
x= (6)
ff+-()14, 4EE
23
 
b
-1
 
dŁłe
in which f = <14, 4 (7)
 
b
1,154 + 0,444 -1
Łdłe
NOTE The correction factor x takes into account the difference in the soil moduli of the pipe embedment material
and the native soil, as well as the width of the trench. The above equations are those given in ATV-A 127 for a support
angle of 120°, but it is recommended that the equations and values given in annex D be used. Annex D covers a wider
range of support conditions than the 120° covered by equation (6). Despite appearances, the equations in annex D for
120° produce a very similar answer to that obtained using equation (6).
2
E is the modulus of the soil in the pipe zone (zone E ), in N/mm (see Figure 1);
2 2
2
E is the modulus of the native soil in zone E , in N/mm (see Figure 1);
3 3
q is the vertical pressure due to the soil loads, calculated using equation (8):
v
8

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© ISO
ISO/TR 10465-3:1999(E)
2
q = (k · g · h + k · p ) · l  (in N/mm)(8)
v b o o RG
2 2
NOTE Equation (8) uses values in MN/m and N/mm which are numerically equivalent.
h is the depth of cover, in m;
3
gis the bulk density of the backfill above the pipe, in MN/m ;
b
2
p is the soil pressure due to the distributed load at the surface, in N/mm ;
o
k and k are trench friction coefficients (see ISO/TR 10465-2 or ATV-A 127, as well as annex F of this
o
document);
q is the horizontal pressure due to soil loads, calculated using equation (9):
h
2
q = K [(k · g · h + k · p ) · l + (g · d /2)]  (in N/mm ) (9)
h 2 b o o B b e
2 2
NOTE Equation (9) uses values in MN/m and N/mm , which are numerically equivalent.
K is the ratio of the horizontal to the vertical soil pressure in soil zone 2 (see annex A);
2
lis a concentration factor (see annex B), given by:
B
 
ll--1 b 4
r R
l= · + (10)
rg
Ł3 dł3
e
NOTE Experience shows that the limits given for l for GRP pipes in ATV-A 127 are not normally reached.
RG
b is the trench width, in m;
is the outside diameter of the pipe, in m;
d
e
lis a concentration factor for the the soil above the pipe (see annex B).
R
5.1.2 Deflection due to weight of pipe
When the pipe diameter is DN 2000 or greater and the nominal stiffness of the pipe is less than SN 2000, then
account should be taken of the relative deflection resulting from the pipe's own weight, calculated using
equation (11):
1
–4
d = – 2,3 · e · r · 10 · (11)
vw
S
R
where
e is the pipe wall thickness, in mm;
3
ris the density of the pipe-wall material, in MN/m .
NOTE This deflection has a negative value, which indicates a reduction in vertical diameter.
5.1.3 Deflection due to compaction of pipe zone backfill (initial ovalization)
When the pipe zone backfill material is compacted, the horizontal soil pressure generated causes the pipe to ovalize
in the vertical direction. The magnitude of this relative vertical deflection can be calculated using equation (12):
d
e
dg=·K·(12)
vio 3 b
24·S
R
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© ISO
ISO/TR 10465-3:1999(E)
where
K is the ratio of the horizontal to the vertical soil pressure in the pipe zone backfill, when the backfill is at the
3
top of the pipe (see annex A).
NOTE This deflection has a positive value, which indicates an increase in vertical diameter.
5.1.4 Deflection resulting from installation irregularities
There are many different approaches to allow for the effect of the inevitable variation in initial deflection due to
irregularities in the installation. Most of these approaches are based on the “add on a few percent“ principle. Several
publications (see references [3], [6] and [7]) state that it is not possible to allow for the actual measured initial
deflections by traditional static calculation methods without incorporating an allowance for the influence of
installation irregularities. Such a system, however, must consider pipe stiffness, pipe diameter and soil conditions.
The calculated deflection is then used to estimate the corresponding flexural strain.
Equation (13) enables an estimate of the relative deflection due to installation irregularities to be made:
d = [c + (c · K*)] · i /S (13)
viv v1 v2 f R
NOTE This relative deflection has a negative value, which indicates a reduction in vertical diameter.
Values of i are given in Table 1.
f
Values of c and c are given in annex C.
v1 v2
Table 1 — Values of installation factor i
f
i
f
DN
2
N/mm
< 200 0,012
300 0,011
400 0,010
500 0,009
600 0,008
700 0,007
800 0,006
> 900 0,005
5.1.5 Total initial relative deflection
The estimated initial deflection is determined using equation (14):
 
d
v
= (d + d + d + d) (14)
  initial
vs vw vio viv
dŁłm
where
dis the positive relative vertical deflection caused by the backfilling in the pipe zone;
vio
dis the negative relative vertical deflection caused by installation irregularities;
viv
dis the negative relative vertical deflection caused by the soil load;
vs
dis the negative relative vertical deflection caused by the weight of the pipe.
vw
NOTE Relative deflection can be converted to % deflection by multiplying by 100.
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© ISO
ISO/TR 10465-3:1999(E)
5.2 Long-term deflection calculated using an ATV-A 127 type design system
The calculated long-term deflection will vary depending whether silo theory or prismatic load is used to calculate the
vertical load.
5.2.1 Soil friction remaining
In ATV-A 12
...