ASTM F2764/F2764M-23

Standard Specification for 6 in. to 60 in. [150 mm to 1500 mm] Polypropylene (PP) Corrugated Double and Triple Wall Pipe and Fittings for Non-Pressure Sanitary Sewer Applications

ABSTRACT
This specification covers requirements and test methods for triple wall polypropylene pipe and fittings with nominal inside diameters of 30 to 60 in. [750 to 1600 mm]. These requirements are intended to provide pipe and fittings suitable for underground use for non-pressure sanitary sewer systems. Pipe and fittings produced in accordance with this specification shall be installed in compliance with Practice D2321. Pipe and fittings with a interior wall, a exterior wall and an annular corrugated profile middle wall are covered by this specification.
SCOPE
1.1 This specification covers requirements and test methods for corrugated double and triple wall polypropylene pipe and fittings. The nominal inside diameters covered are 6 in. to 60 in. [150 mm to 1500 mm].  
1.2 The requirements of this specification are intended to provide pipe and fittings for underground use for non-pressure sanitary sewer systems. Pipe and fittings produced in accordance with this specification shall be installed in compliance with Practice D2321.  
1.3 This specification covers pipe and fittings with an annular corrugated wall and an essentially smooth interior wall (that is, double wall) (Fig. 1) and pipe and fittings with an annular corrugated wall and an essentially smooth interior and exterior wall (that is, triple wall) (Fig. 2).
FIG. 1 Typical Corrugated Double Wall Pipe
FIG. 2 Typical Corrugated Triple Wall Pipe  
1.4 The values stated in either SI units or inch-pound units are to be regarded separately as standard. The values stated in each system may not be exact equivalents; therefore, each system shall be used independently of the other. Combining values from the two systems may result in non-conformance with the standard.  
1.5 The following precautionary statement applies only to Section 7 of this specification. This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.6 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

General Information

• Status: Published
• Publication Date: 31-Jan-2023
• ICS: 91.140.80 - Drainage systems
• Technical Committee: F17 - Plastic Piping Systems
• Drafting Committee: F17.62 - Sewer

Relations

• Refers: ASTM D4101-24 - Standard Classification System and Basis for Specification for Polypropylene Injection and Extrusion Materials
• Effective Date: 01-Feb-2024
• Refers: ASTM F2136-18(2024) - Standard Test Method for Notched, Constant Ligament-Stress (NCLS) Test to Determine Slow-Crack-Growth Resistance of HDPE Resins or HDPE Corrugated Pipe
• Effective Date: 01-Feb-2024
• Refers: ASTM D1238-23a - Standard Test Method for Melt Flow Rates of Thermoplastics by Extrusion Plastometer
• Effective Date: 15-Nov-2023
• Refers: ASTM F412-20 - Standard Terminology Relating to Plastic Piping Systems
• Effective Date: 01-Apr-2020
• Refers: ASTM D2321-20 - Standard Practice for Underground Installation of Thermoplastic Pipe for Sewers and Other Gravity-Flow Applications
• Effective Date: 15-Mar-2020
• Refers: ASTM D4218-20 - Standard Test Method for Determination of Carbon Black Content in Polyethylene Compounds by the Muffle-Furnace Technique
• Effective Date: 01-Feb-2020
• Refers: ASTM F412-19 - Standard Terminology Relating to Plastic Piping Systems
• Effective Date: 01-Jan-2019
• Refers: ASTM D2321-18 - Standard Practice for Underground Installation of Thermoplastic Pipe for Sewers and Other Gravity-Flow Applications
• Effective Date: 01-Mar-2018
• Refers: ASTM F2136-18 - Standard Test Method for Notched, Constant Ligament-Stress (NCLS) Test to Determine Slow-Crack-Growth Resistance of HDPE Resins or HDPE Corrugated Pipe
• Effective Date: 15-Feb-2018
• Refers: ASTM D1600-18 - Standard Terminology for Abbreviated Terms Relating to Plastics (Withdrawn 2024)
• Effective Date: 01-Jan-2018
• Refers: ASTM D2444-17 - Standard Practice for Determination of the Impact Resistance of Thermoplastic Pipe and Fittings by Means of a Tup (Falling Weight)
• Effective Date: 15-Nov-2017
• Refers: ASTM F412-17a - Standard Terminology Relating to Plastic Piping Systems
• Effective Date: 01-Aug-2017
• Refers: ASTM D790-17 - Standard Test Methods for Flexural Properties of Unreinforced and Reinforced Plastics and Electrical Insulating Materials
• Effective Date: 01-Jul-2017
• Refers: ASTM D2990-17 - Standard Test Methods for Tensile, Compressive, and Flexural Creep and Creep-Rupture of Plastics
• Effective Date: 01-Mar-2017
• Refers: ASTM F412-17 - Standard Terminology Relating to Plastic Piping Systems
• Effective Date: 01-Feb-2017

Overview

ASTM F2764/F2764M-23 is the globally recognized standard specification developed by ASTM International for polypropylene (PP) corrugated double and triple wall pipe and fittings, covering nominal inside diameters from 6 inches to 60 inches (150 mm to 1500 mm). This specification sets forth material, manufacturing, performance, and testing requirements to ensure the production of durable and structurally reliable PP piping systems specifically designed for underground non-pressure sanitary sewer applications. Both double wall and triple wall pipe constructions are addressed, and all products must be installed in line with ASTM Practice D2321 for proper underground placement.

Key Topics

• Pipe Types Covered
  • Double wall pipes: Corrugated exterior with a smooth interior liner.
  • Triple wall pipes: Smooth interior and exterior liners with an annular corrugated profile wall in between.
• Material Requirements
  • High-quality polypropylene resins, either colored (with UV stabilizers) or black (with specified carbon black content).
  • Permits manufacturer rework material if it meets all physical property requirements.
• Dimensional and Structural Criteria
  • Covers inside diameters from 6 in. to 60 in. [150 mm to 1500 mm].
  • Specifies minimum inside diameters, wall thickness, and pipe stiffness at 5% deflection.
• Testing and Performance
  • Pipes and fittings must pass standardized tests for impact strength, flattening, creep rupture, and tensile creep modulus.
  • Joint performance and watertightness verified per related ASTM specifications.
• Marking and Quality Assurance
  • Product must be clearly marked with standard designation, dimensions, wall type, manufacturer details, and date of manufacture for traceability.

Applications

ASTM F2764/F2764M-23 pipes and fittings are engineered for underground gravity-flow, non-pressure sanitary sewer systems, offering advantages of strength, durability, and corrosion resistance. Their use is ideal in:

• Municipal and residential sanitary sewage collection systems
• Industrial facilities requiring reliable wastewater conveyance
• Infrastructure projects where long-term material performance and watertight integrity are essential

Double wall and triple wall PP pipes deliver high structural stability and flexibility, beneficial for varied soil and traffic load conditions. This specification’s focus on robust jointing systems ensures watertightness, critical for protecting groundwater and maintaining environmental compliance.

Related Standards

• ASTM D2321: Practice for Underground Installation of Thermoplastic Pipe for Sewers
• ASTM D3212: Specification for Joints for Drain and Sewer Plastic Pipes Using Flexible Elastomeric Seals
• ASTM F477: Specification for Elastomeric Seals (Gaskets) for Joining Plastic Pipe
• ASTM D638, D790, D792, D1238, D1505: Various test methods for plastics properties
• AASHTO LRFD Bridge Design Section 12: Design requirements for buried structures, referenced for structural safety

Practical Value

Adoption of ASTM F2764/F2764M-23 assures stakeholders of the use of PP sanitary sewer pipe and fittings that consistently meet stringent quality, structural, and performance benchmarks. The standard supports project longevity, minimizes maintenance needs, and facilitates compliance with local and international installation and performance requirements. Its detailed testing and marking requirements promote confidence among engineers, specifiers, and municipal authorities, fostering better infrastructure built on durable, corrosion-resistant, and watertight polypropylene piping solutions.

Keywords: polypropylene pipe, double wall PP, triple wall PP, sanitary sewer, underground pipe, ASTM F2764/F2764M-23, corrugated pipe, non-pressure sewer systems.

Standards Content (Sample)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: F2764/F2764M − 23
Standard Specification for
6 in. to 60 in. [150 mm to 1500 mm] Polypropylene (PP)
Corrugated Double and Triple Wall Pipe and Fittings for
Non-Pressure Sanitary Sewer Applications
This standard is issued under the fixed designation F2764/F2764M; the number immediately following the designation indicates the year
of original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval.
A superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope* 2. Referenced Documents
1.1 This specification covers requirements and test methods 2.1 ASTM Standards:
for corrugated double and triple wall polypropylene pipe and A666 Specification for Annealed or Cold-Worked Austenitic
fittings. The nominal inside diameters covered are 6 in. to 60 Stainless Steel Sheet, Strip, Plate, and Flat Bar
in. [150 mm to 1500 mm]. D256 Test Methods for Determining the Izod Pendulum
Impact Resistance of Plastics
1.2 The requirements of this specification are intended to
D578/D578M Specification for Glass Fiber Strands
provide pipe and fittings for underground use for non-pressure
D618 Practice for Conditioning Plastics for Testing
sanitary sewer systems. Pipe and fittings produced in accor-
D638 Test Method for Tensile Properties of Plastics
dance with this specification shall be installed in compliance
D790 Test Methods for Flexural Properties of Unreinforced
with Practice D2321.
and Reinforced Plastics and Electrical Insulating Materi-
1.3 This specification covers pipe and fittings with an
als
annular corrugated wall and an essentially smooth interior wall
D792 Test Methods for Density and Specific Gravity (Rela-
(that is, double wall) (Fig. 1) and pipe and fittings with an
tive Density) of Plastics by Displacement
annular corrugated wall and an essentially smooth interior and
D1238 Test Method for Melt Flow Rates of Thermoplastics
exterior wall (that is, triple wall) (Fig. 2).
by Extrusion Plastometer
1.4 The values stated in either SI units or inch-pound units D1505 Test Method for Density of Plastics by the Density-
Gradient Technique
are to be regarded separately as standard. The values stated in
each system may not be exact equivalents; therefore, each D1600 Terminology for Abbreviated Terms Relating to Plas-
system shall be used independently of the other. Combining tics
D2122 Test Method for Determining Dimensions of Ther-
values from the two systems may result in non-conformance
with the standard. moplastic Pipe and Fittings
D2321 Practice for Underground Installation of Thermoplas-
1.5 The following precautionary statement applies only to
tic Pipe for Sewers and Other Gravity-Flow Applications
Section 7 of this specification. This standard does not purport
D2412 Test Method for Determination of External Loading
to address all of the safety concerns, if any, associated with its
Characteristics of Plastic Pipe by Parallel-Plate Loading
use. It is the responsibility of the user of this standard to
D2444 Practice for Determination of the Impact Resistance
establish appropriate safety, health, and environmental prac-
of Thermoplastic Pipe and Fittings by Means of a Tup
tices and determine the applicability of regulatory limitations
(Falling Weight)
prior to use.
D2990 Test Methods for Tensile, Compressive, and Flexural
1.6 This international standard was developed in accor-
Creep and Creep-Rupture of Plastics
dance with internationally recognized principles on standard-
D3212 Specification for Joints for Drain and Sewer Plastic
ization established in the Decision on Principles for the
Pipes Using Flexible Elastomeric Seals
Development of International Standards, Guides and Recom-
D3895 Test Method for Oxidative-Induction Time of Poly-
mendations issued by the World Trade Organization Technical
olefins by Differential Scanning Calorimetry
Barriers to Trade (TBT) Committee.
D4101 Classification System and Basis for Specification for
This specification is under the jurisdiction of ASTM Committee F17 on Plastic
Piping Systems and is the direct responsibility of Subcommittee F17.62 on Sewer. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved Feb. 1, 2023. Published April 2023. Originally contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
approved in 2010. Last previous edition approved in 2019 as F2764/F2764M–19. Standards volume information, refer to the standard’s Document Summary page on
DOI:10.1520/F2764_F2764M–23. the ASTM website.
*A Summary of Changes section appears at the end of this standard
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
F2764/F2764M − 23
FIG. 1 Typical Corrugated Double Wall Pipe
FIG. 2 Typical Corrugated Triple Wall Pipe
Polypropylene Injection and Extrusion Materials diametrical deformation. The corrugation wall is exposed to
D4218 Test Method for Determination of Carbon Black the soil side of the pipe and is its exterior wall.
Content in Polyethylene Compounds by the Muffle-
3.2.2 triple wall pipe, n—In this case, the triple pipe wall
Furnace Technique
construction provides an interior wall in the waterway, an
D6992 Test Method for Accelerated Tensile Creep and
exterior wall to the soil, and includes corrugations, which can
Creep-Rupture of Geosynthetic Materials Based on Time-
be either solid (with a liner) or hollow (with no liner), that
Temperature Superposition Using the Stepped Isothermal
helps brace the pipe against diametrical deformation.
Method
F412 Terminology Relating to Plastic Piping Systems
4. Ordering Information
F477 Specification for Elastomeric Seals (Gaskets) for Join-
4.1 Orders for product made to this specification shall
ing Plastic Pipe
include the following information to adequately describe the
F2136 Test Method for Notched, Constant Ligament-Stress
desired product:
(NCLS) Test to Determine Slow-Crack-Growth Resis-
4.1.1 This ASTM designation and year of issue,
tance of HDPE Resins or HDPE Corrugated Pipe
4.1.2 Diameters,
2.2 AASHTO Standards:
4.1.3 Total footage of each pipe diameter involved,
LRFD, Section 12 AASHTO LRFD Bridge Design Specifi-
4.1.4 Pipe laying length,
cations Section 12 – Buried Structures and Tunnel Liners
4.1.5 Fitting type(s):
2.3 Federal Standard:
4.1.5.1 Size and type of fittings, including mainline and
Fed. Std. No. 123 Marking for Shipment (Civil Agencies)
branch diameters, and
2.4 Military Standard:
4.1.5.2 Number of fittings per diameter.
MIL-STD-129 Marking for Shipment and Storage
2.5 NCHRP (National Cooperative Highway Research Pro- 5. Materials and Manufacture
gram) Report:
5.1 Pipe and Fabricated Fittings—Polypropylene Com-
NCHRP Report 631 Updated Test and Design Methods for
pounds – Polypropylene compounds used in the manufacture
Thermoplastic Drainage Pipe
of the dual wall pipe and fittings shall have the minimum
properties as shown in Table 1. Polypropylene compounds
3. Terminology
shall be comprised of base polypropylene copolymer virgin
3.1 Definitions are in accordance with Terminology F412
resin, and all additives, colorants, process aids, modifiers, UV
and abbreviations are in accordance with Terminology D1600,
inhibitors and stabilizers. Conditioning, sampling, preparation
unless otherwise specified. The abbreviation for polypropylene
and testing of molded specimens shall be in accordance with
is PP.
the requirements in Classification D4101. Compounds shall be
tested and validated on an annual basis or for any new
3.2 Definitions of Terms Specific to This Standard:
formulations. Compounds that have higher performance prop-
3.2.1 double wall pipe, n—In this case, the profile pipe wall
erties shall be permitted provided the density of the final
construction provides an interior liner in the waterway and
3 3
formulation shall not exceed 0.0509 lbs/in. (1.410 g/cm ) and
includes corrugations, which can be either solid (with a liner)
all other product requirements are met.
or hollow (with no liner), that helps brace the pipe against
5.2 Color and Ultraviolet Stabilization for Pipe and
3 Fittings—The pipe shall be colored or black. Black polypro-
Available from American Association of State Highway and Transportation
pylene compounds shall have between 2.0 and 3.0 percent
Officials (AASHTO), 444 N. Capitol St., NW, Suite 249, Washington, DC 20001,
http://www.transportation.org.
carbon black when tested in accordance with the procedures in
DLA Document Services Building 4/D 700 Robbins Avenue Philadelphia, PA
Test Method D4218. Colored polypropylene compounds shall
19111-5094 http://quicksearch.dla.mil/
be protected from Ultraviolet (UV) degradation with UV
The National Academies of Sciences, Engineering, and Medicine 500 Fifth
Street, NW Washington, DC 20001 http://www.national-academies.org stabilizers.
F2764/F2764M − 23
TABLE 1 Polypropylene Compound Properties
Property ASTM Units [SI Units] Minimum Value
Test
Method
Melt Flow Rate D1238 g/10 min 0.15 at 230 °C
3 3
Density D792, D1505 lb/in [g/cm ] 0.0325 [0.900]
Tensile Strength at Yield D638 psi [N/mm ] 3500 [24]
Elongation at Yield D638 % (%) 5 [5]
Flexural Modulus (1% secant) D790B psi [N/mm ] 175 000 [1,200]
IZOD Impact Strength (73.0 °F D256 ft-lb/in [J/m] 8 [427]
[23.0 °C])
Oxidative-Induction Time (392 °F D3895 min 25
[200 °C])
Long-Term Modulus of Elasticity (50- D2990 psi [MPa] 27 000 [186]
yr)
Long-Term Tensile Strength (50-yr) D2990 psi [MPa] 1000 [7]
5.3 Rework Plastic—Clean polypropylene rework plastic, 6.2 Dimensions and Tolerance:
generated from the manufacturer’s own production of the 6.2.1 Nominal Size—The nominal size for the pipe and
product and having the same minimum physical properties, fittings shall be the inside diameter shown in Table 2.
may be used by the manufacturer, provided that the pipe 6.2.2 Minimum Inside Diameter—The minimum inside di-
produced meets all the requirements of this specification. ameter shall be as shown in Table 2, when measured in
accordance with 7.3.3. In no case shall the manufacturer’s
5.4 Elastomeric Seal Materials—Elastomeric compounds
stated inside diameter minus the tolerance in Table 2 be less
and thermoplastic elastomeric compounds used in the manu-
than the required minimum inside diameter.
facture of sealing rings or gaskets shall meet the requirements
of Specification F477.
NOTE 2—The manufacturer’s stated inside diameter is the nominal
diameter plus or minus the inside diameter tolerances. The minimum
5.5 Lubricant—The lubricant used for assembly of gasketed
inside diameter is the smallest diameter the pipe can be with these
joints shall have no detrimental effect of the gasket or on the
tolerances and is used for the hydraulic design of the pipe.
pipe. NOTE 3—The outside diameters and the corrugation pitch of products
manufactured to this specification are not specified; therefore, compatibil-
5.6 Optional Bell Retaining Bands or External Wraps—
ity between pipe and fittings made to this specification from different
Monolithically formed bands or stiffening wraps in or on the
manufacturers should be verified.
external wall of the bell, when used, shall provide tensile
6.2.3 Laying Length—The pipe shall be supplied in any
restraint to bell expansion due to gasket insertion or internal
laying length agreeable to both the owner and the manufac-
hydrostatic pressure in accordance with 6.6.4. These bands
turer. Laying length shall not be less than 99 % of stated
shall be made of corrosion resistant materials such as fiberglass
quantity when measured in accordance with 7.3.2.
(Specification D578/D578M) or stainless steel (Specification
6.2.4 Minimum Wall, Crest, Valley and Liner Thickness—
A666). All metallic mechanical devices, including castings and
The minimum thickness of pipe sections shall meet the
bolt assemblies used to mechanically restrain the bell shall be
requirements given in Table 2 when measured in accordance
constructed of corrosion resistant stainless steel materials
with 7.3.3.
meeting the physical properties and chemical composition
6.3 Pipe Stiffness—Minimum pipe stiffness at 5 % deflec-
requirements of A666, Type 302 through Type 316.
tion shall meet the requirements given in Table 2 when tested
5.6.1 The D578/D578M fiberglass roving or chopped strand
in accordance with 7.4.
shall be an E or S type glass, free of any alkali, dirt or other
impurities. The band shall consist of overlapping continuous or
NOTE 4—The 5 % deflection criterion, which was selected for testing
chopped filament fiber strand and not a fabric.
convenience, is not a limitation with respect to in-use deflection. The
engineer is responsible for establishing the acceptable deflection limit.
NOTE 1—Compound and material properties are typically tested to
6.4 Pipe Flattening—There shall be no evidence of
validate a formulation; they are not routine quality assurance tests. Users
requiring such testing for quality assurance purposes should insert these splitting, cracking, breaking, separation of seams, separation of
criteria in their project specifications.
the outer and inner wall, or combinations thereof, when tested
in accordance with 7.5. Additionally, at or below the average
6. General Requirements
deflection limit defined in Eq 1 and Eq 2 for dual wall and
6.1 Workmanship—The pipe and fittings shall be homoge-
triple wall profiles, respectively, the specimen shall be consid-
neous throughout and be as uniform as commercially practical
ered as failing this test when the load does not increase
in color, opacity, and density. The pipe walls shall be free of
continuously with increasing deflection.
cracks, holes, blisters, voids, foreign inclusions, or other
Buckling Defection Limit:
defects that are visible to the naked eye and that may affect the
Double Wall:
wall integrity. The ends shall be cut cleanly and squarely
D
through valleys.
Δ 5 1.07%· (1)
S D
0.5~D 2 D !
o i
6.1.1 Visible defects, cracks, creases, splits, in pipe are not
permissible. Triple Wall:
F2764/F2764M − 23
TABLE 2 Pipe Stiffness and Pipe Dimensions
Pipe Inside Profile Minimum Inside Minimum Minimum Minimum Minimum Minimum
A B
Diameter Type Inside Diameter Pipe Stiffness Inner Liner Outer Liner Valley Crown
Diameter Tolerances at 5 % Thickness Thickness Thickness Thickness
Deflection
in. [mm] in. [mm] in. [mm] lb/in/in [kPa] in. [mm] in. [mm] in. [mm] in. [mm]
6 [150] D 5.61 [142] +0.04/-0.04 [+1.0/-1.0] 46 [317] 0.040 [1.0] . . . . . .
8 [200] D 7.70 [196] +0.05/-0.05 [+1.1/-1.1] 46 [317] 0.045 [1.1] . . . . . .
10 [250] D 9.70 [246] +0.06/-0.06 [+1.4/-1.4] 46 [317] 0.050 [1.3] . . . . . .
12 [300] D 11.90 [302] +010/-0.10 [+2.5/-2.5] 46 [317] 0.054 [1.4] . . . . . .
15 [375] D 14.85 [377] +0.15/-0.15 [+3.8/-3.8] 46 [317] 0.065 [1.7] . . . . . .
18 [450] D 17.93 [455] +0.17/-0.17 [+4.3/-4.3] 46 [317] 0.075 [1.9] . . . . . .
21 [530] D 20.75 [527] +0.17/-0.17 [+4.3/-4.3] 46 [317] 0.077 [2.0] . . . . . .
24 [600] D 23.90 [607] +0.23/-0.23 [+5.8/-58] 46 [317] 0.086 [2.2] . . . . . .
30 [750] D 29.79 [757] +0.24/-0.24 [+6.1/-6.1] 46 [317] 0.094 [2.4] . . . . . .
30 [750] T 29.62 [752] +0.18/- 0.18 [+4.6/-4.6] 46 [317] 0.070 [1.8] 0.070 [1.8] 0.081 [2.1] 0.115 [2.9]
36 [900] D 35.40 [899] +0.21/- 0.21 [+5.3/-5.3] 46 [317] 0.102 [2.6] . . . . . .
36 [900] T 35.40 [899] +0.21/- 0.21 [+5.3/-5.3] 46 [317] 0.095 [2.4] 0.095 [2.4] 0.109 [2.8] 0.165 [4.2]
42 [1050] D 41.31 [1049] +0.22/- 0.22 [+5.6/-5.6] 46 [317] 0.105 [2.7] . . . . . .
42 [1050] T 41.31 [1049] +0.22/- 0.22 [+5.6/-5.6] 46 [317] 0.105 [2.7] 0.105 [2.7] 0.121 [3.1] 0.165 [4.2]
48 [1200] D 47.31 [1201] +0.27/- 0.27 [+6.9/-6.9] 46 [317] 0.105 [2.7] . . . . . .
48 [1200] T 47.31 [1201] +0.27/- 0.27 [+6.9/-6.9] 46 [317] 0.105 [2.7] 0.105 [2.7] 0.126 [3.2] 0.170 [4.3]
54 [1350] D 53.32 [1354] +0.27/- 0.27 [+6.9/-6.9] 46 [317] 0.105 [2.7] . . . . . .
54 [1350] T 53.32 [1354] +0.27/- 0.27 [+6.9/-6.9] 46 [317] 0.105 [2.7] 0.105 [2.7] 0.131 [3.3] 0.170 [4.3]
60 [1500] D 59.30 [1506] +0.31/- 0.31 [+7.9/-7.9] 46 [317] 0.115 [2.9] . . . . . .
60 [1500] T 59.30 [1506] +0.31/- 0.31 [+7.9/-7.9] 46 [317] 0.105 [2.7] 0.105 [2.7] 0.137 [3.5] 0.210 [5.3]
A
Where the dimensions for the outer liner thickness are defined, all the associated dimensions shall only pertain to the triple wall profile pipe.
B
D profile type represents double wall profile pipe. T profile type represents triple wall profile pipe.
D of the fitting (run plus branch(es) as applicable) that is loaded
Δ 5 1.29%· (2)
S D
0.5~D 2 D ! by the upper plate. Testing shall be for equivalent load, not
o i
deflection. Acceptance criteria shall be in accordance with 6.4.
where:
NOTE 6—Installation orientation means that the fitting testing orienta-
Δ = minimum buckling deflection limit (%)
tion is as though it were installed in a pipeline, for example, an elbow or
D = mean diameter (centroid) of pipe (in [mm])
tee with the directional outlet(s) to the side. In accordance with an
0.5 (D – D ) = height of the corrugation (outside diameter
o i
established quality program, fittings should be tested to only qualify the
minus inside diameter) (in [mm])
overall design and integrity of the unit. As unique structures, testing of
NOTE 5—Eq 1 and Eq 2 are based on the results from NCHRP Report
every angle orientation is not necessary.
631 and is defined as being derived from the standard parallel plate test
6.6.1.2 The fitting body in an installation orientation shall
equation and modified for polypropylene. The values for the diameter
measurements are based on each producer’s specific corrugation dimen-
be impact tested in accordance with 7.6. Acceptance criteria
sions.
shall be in accordance with 6.5.
6.5 Pipe Impact Strength—There shall be no evidence of
6.6.2 The joining system(s) between pipe and between pipe
splitting, cracking, breaking, separation of seams, separation of
and fittings shall be of a design that preserves pipeline slope
the outer and inner wall, or combinations thereof, when
and alignment during construction and prevents separation at
conditioned in accordance with 7.1 and tested in accordance
the joints while maintaining watertight requirements in accor-
with 7.6 and examined under normal light and the unaided eye.
dance with 6.6.3. Fittings shall be tested in an installation
The minimum pipe impact strength at 73 °F [23 °C] shall be
orientation, shall be uniformly supported (body and outlet(s))
140 ft-lbf [190 J].
by the lower plate, and uniformly loaded (body and outlet(s))
by the upper plate.
6.6 Fittings and Joining Systems:
6.6.3 Pipe and fittings shall have a watertight bell/spigot
6.6.1 Fittings shall be fabricated by the pipe manufacturer
joint that complies with the laboratory tests defined and
from pipe made in accordance with this standard. Fittings
described in Specification D3212 and utilizes a gasket that
fabricated from double-wall pipe shall be used with double-
complies with the requirements of Specification F477. Note
wall pipe. Fittings fabricated from triple-wall pipe shall be
that special provisions must be taken in order to join field cut
used with triple-wall pipe. Fitting material shall comply with
pipe that meets the requirements of Specification D3212. Any
5.1, 5.2 and 5.3.
component used in the joining material shall be resistant to
6.6.1.1 Fittings shall be tested in an installation orientation,
effluents being carried in the pipe.
shall be uniformly supported (body and outlet(s)) by the l
...

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: F2764/F2764M − 19 F2764/F2764M − 23
Standard Specification for
66 in. to 60 in. [150[150 mm to 1500 mm] Polypropylene (PP)
Corrugated Double and Triple Wall Pipe and Fittings for
Non-Pressure Sanitary Sewer Applications
This standard is issued under the fixed designation F2764/F2764M; the number immediately following the designation indicates the year
of original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval.
A superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope*
1.1 This specification covers requirements and test methods for corrugated double and triple wall polypropylene pipe and fittings.
The nominal inside diameters covered are 66 in. to 60 in. [150[150 mm to 1500 mm].
1.2 The requirements of this specification are intended to provide pipe and fittings for underground use for non-pressure sanitary
sewer systems. Pipe and fittings produced in accordance with this specification shall be installed in compliance with Practice
D2321.
1.3 This specification covers pipe and fittings with an annular corrugated wall and an essentially smooth interior wall (that is,
double wall) (Fig. 1) and pipe and fittings with an annular corrugated wall and an essentially smooth interior and exterior wall (that
is, triple wall) (Fig. 2).
1.4 The values stated in either SI units or inch-pound units are to be regarded separately as standard. The values stated in each
system may not be exact equivalents; therefore, each system shall be used independently of the other. Combining values from the
two systems may result in non-conformance with the standard.
1.5 The following precautionary statement applies only to Section 7 of this specification. This standard does not purport to
address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish
appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.
1.6 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
2. Referenced Documents
2.1 ASTM Standards:
A666 Specification for Annealed or Cold-Worked Austenitic Stainless Steel Sheet, Strip, Plate, and Flat Bar
D256 Test Methods for Determining the Izod Pendulum Impact Resistance of Plastics
D578/D578M Specification for Glass Fiber Strands
D618 Practice for Conditioning Plastics for Testing
This specification is under the jurisdiction of ASTM Committee F17 on Plastic Piping Systems and is the direct responsibility of Subcommittee F17.62 on Sewer.
Current edition approved April 1, 2019Feb. 1, 2023. Published May 2019April 2023. Originally approved in 2010. Last previous edition approved in 20182019 as
F2764/F2764M–18a. DOI:10.1520/F2764_F2764M–19. –19. DOI:10.1520/F2764_F2764M–23.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
*A Summary of Changes section appears at the end of this standard
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
F2764/F2764M − 23
FIG. 1 Typical Corrugated Double Wall Pipe
FIG. 2 Typical Corrugated Triple Wall Pipe
D638 Test Method for Tensile Properties of Plastics
D790 Test Methods for Flexural Properties of Unreinforced and Reinforced Plastics and Electrical Insulating Materials
D792 Test Methods for Density and Specific Gravity (Relative Density) of Plastics by Displacement
D1238 Test Method for Melt Flow Rates of Thermoplastics by Extrusion Plastometer
D1505 Test Method for Density of Plastics by the Density-Gradient Technique
D1600 Terminology for Abbreviated Terms Relating to Plastics
D2122 Test Method for Determining Dimensions of Thermoplastic Pipe and Fittings
D2321 Practice for Underground Installation of Thermoplastic Pipe for Sewers and Other Gravity-Flow Applications
D2412 Test Method for Determination of External Loading Characteristics of Plastic Pipe by Parallel-Plate Loading
D2444 Practice for Determination of the Impact Resistance of Thermoplastic Pipe and Fittings by Means of a Tup (Falling
Weight)
D2990 Test Methods for Tensile, Compressive, and Flexural Creep and Creep-Rupture of Plastics
D3212 Specification for Joints for Drain and Sewer Plastic Pipes Using Flexible Elastomeric Seals
D3895 Test Method for Oxidative-Induction Time of Polyolefins by Differential Scanning Calorimetry
D4101 Classification System and Basis for Specification for Polypropylene Injection and Extrusion Materials
D4218 Test Method for Determination of Carbon Black Content in Polyethylene Compounds by the Muffle-Furnace Technique
D6992 Test Method for Accelerated Tensile Creep and Creep-Rupture of Geosynthetic Materials Based on Time-Temperature
Superposition Using the Stepped Isothermal Method
F412 Terminology Relating to Plastic Piping Systems
F477 Specification for Elastomeric Seals (Gaskets) for Joining Plastic Pipe
F2136 Test Method for Notched, Constant Ligament-Stress (NCLS) Test to Determine Slow-Crack-Growth Resistance of HDPE
Resins or HDPE Corrugated Pipe
2.2 AASHTO Standards:
LRFD, Section 12 AASHTO LRFD Bridge Design Specifications Section 12 – Buried Structures and Tunnel Liners
2.3 Federal Standard:
Fed. Std. No. 123 Marking for Shipment (Civil Agencies)
2.4 Military Standard:
MIL-STD-129 Marking for Shipment and Storage
2.5 NCHRP (National Cooperative Highway Research Program) Report:
NCHRP Report 631 Updated Test and Design Methods for Thermoplastic Drainage Pipe
3. Terminology
3.1 Definitions are in accordance with Terminology F412 and abbreviations are in accordance with Terminology D1600, unless
otherwise specified. The abbreviation for polypropylene is PP.
3.2 Definitions of Terms Specific to This Standard:
Available from American Association of State Highway and Transportation Officials (AASHTO), 444 N. Capitol St., NW, Suite 249, Washington, DC 20001,
http://www.transportation.org.
DLA Document Services Building 4/D 700 Robbins Avenue Philadelphia, PA 19111-5094 http://quicksearch.dla.mil/
The National Academies of Sciences, Engineering, and Medicine 500 Fifth Street, NW Washington, DC 20001 http://www.national-academies.org
F2764/F2764M − 23
3.2.1 double wall pipe, n—In this case, the profile pipe wall construction provides an interior liner in the waterway and includes
corrugations, which can be either solid (with a liner) or hollow (with no liner), that helps brace the pipe against diametrical
deformation. The corrugation wall is exposed to the soil side of the pipe and is its exterior wall.
3.2.2 triple wall pipe, n—In this case, the triple pipe wall construction provides an interior wall in the waterway, an exterior wall
to the soil, and includes corrugations, which can be either solid (with a liner) or hollow (with no liner), that helps brace the pipe
against diametrical deformation.
4. Ordering Information
4.1 Orders for product made to this specification shall include the following information to adequately describe the desired
product:
4.1.1 This ASTM designation and year of issue,
4.1.2 Diameters,
4.1.3 Total footage of each pipe diameter involved,
4.1.4 Pipe laying length,
4.1.5 Fitting type(s):
4.1.5.1 Size and type of fittings, including mainline and branch diameters, and
4.1.5.2 Number of fittings per diameter.
5. Materials and Manufacture
5.1 Pipe and Fabricated Fittings—Polypropylene Compounds – Polypropylene compounds used in the manufacture of the dual
wall pipe and fittings shall have the minimum properties as shown in Table 1. Polypropylene compounds shall be comprised of
the base polypropylene copolymer virgin resin, and all additives, colorants, process aids, modifiers, UV inhibitors and stabilizers.
Compounds that have higher performance properties shall be permitted provided the density of the base resin shall not exceed
3 3
0.0343 lb/inConditioning, (0.950 g/cm ) and all other product requirements are met. Conditioning sampling, preparation,
sampling, preparation and testing of molded specimens shall be in accordance with the requirements in SpecificationClassification
D4101. For slow crack-growth resistance of the pipe corrugation, and inner and exterior walls, PP compounds shall be evaluated
using the notched constant ligament stress (NCLS) test according to the procedure described in 7.7.1. The average failure time of
the five test specimens shall exceed 100 h with no single test specimen’s failure time less than 71 h. Compounds shall be tested
and validated on an annual basis or for any new formulations. The minimum long-term (50-year) design values for modulus of
elasticity and tensile strength for the PP compounds shall be 27 000 psi [186 MPa] Compounds that have higher performance
3 3
properties shall be permitted provided the density of the final formulation shall not exceed 0.0509 lbs/in. (1.410 g/cm and 1,000
psi [7.0 MPa], respectively. ) and all other product requirements are met.
TABLE 1 Polypropylene Compound Properties
Property ASTM Units [SI Units] Minimum Value
Test
Method
Melt Flow Rate D1238 g/10 min 0.15 @ 230 °C
Melt Flow Rate D1238 g/10 min 0.15 at 230 °C
3 3
Density D792, D1505 lb/in [g/cm ] 0.0325 [0.900]
Tensile Strength at Yield D638 psi [N/mm ] 3500 [24]
Elongation at Yield D638 % (%) 5 [5]
Flexural Modulus (1% secant) D790B psi [N/mm ] 175 000 [1,200]
IZOD Impact Strength (73.0 °F D256 ft-lb/in [J/m] 8 [427]
[23.0 °C])
Oxidative-Induction Time (392 °F D3895 min 25
[200 °C])
Long-Term Modulus of Elasticity (50- D2990 psi [MPa] 27 000 [186]
yr)
Long-Term Tensile Strength (50-yr) D2990 psi [MPa] 1000 [7]
F2764/F2764M − 23
5.2 Color and Ultraviolet Stabilization for Pipe and Fittings—The pipe shall be colored or black. Black polypropylene compounds
shall have between 2.0 and 3.0 percent carbon black when tested in accordance with the procedures in Test Method D4218. Colored
polypropylene compounds shall be protected from Ultraviolet (UV) degradation with UV stabilizers.
5.3 Rework Plastic—Clean polypropylene rework plastic, generated from the manufacturer’s own production of the product and
having the same minimum physical properties, may be used by the manufacturer, provided that the pipe produced meets all the
requirements of this specification.
5.4 Elastomeric Seal Materials—Elastomeric compounds and thermoplastic elastomeric compounds used in the manufacture of
sealing rings or gaskets shall meet the requirements of Specification F477.
5.5 Lubricant—The lubricant used for assembly of gasketed joints shall have no detrimental effect of the gasket or on the pipe.
5.6 Optional Bell Retaining Bands or External Wraps—Monolithically formed bands or stiffening wraps in or on the external wall
of the bell, when used, shall provide tensile restraint to bell expansion due to gasket insertion or internal hydrostatic pressure in
accordance with 6.6.4. These bands shall be made of corrosion resistant materials such as fiberglass (Specification D578/D578M)
or stainless steel (Specification A666). All metallic mechanical devices, including castings and bolt assemblies used to
mechanically restrain the bell shall be constructed of corrosion resistant stainless steel materials meeting the physical properties
and chemical composition requirements of A666, Type 302 through Type 316.
5.6.1 The D578/D578M fiberglass roving or chopped strand shall be an E or S type glass, free of any alkali, dirt or other
impurities. The band shall consist of overlapping continuous or chopped filament fiber strand and not a fabric.
NOTE 1—Compound and material properties are typically tested to validate a formulation; they are not routine quality assurance tests. Users requiring
such testing for quality assurance purposes should insert these criteria in their project specifications.
6. General Requirements
6.1 Workmanship—The pipe and fittings shall be homogeneous throughout and be as uniform as commercially practical in color,
opacity, and density. The pipe walls shall be free of cracks, holes, blisters, voids, foreign inclusions, or other defects that are visible
to the naked eye and that may affect the wall integrity. The ends shall be cut cleanly and squarely through valleys.
6.1.1 Visible defects, cracks, creases, splits, in pipe are not permissible.
6.2 Dimensions and Tolerance:
6.2.1 Nominal Size—The nominal size for the pipe and fittings shall be the inside diameter shown in Table 2.
6.2.2 Minimum Inside Diameter—The minimum inside diameter shall be as shown in Table 2, when measured in accordance with
section 7.3.3. In no case shall the manufacturer’s stated inside diameter minus the tolerance in Table 2 be less than the required
minimum inside diameter.
NOTE 2—The manufacturer’s stated inside diameter is the nominal diameter plus or minus the inside diameter tolerances. The minimum inside diameter
is the smallest diameter the pipe can be with these tolerances and is used for the hydraulic design of the pipe.
NOTE 3—The outside diameters and the corrugation pitch of products manufactured to this specification are not specified; therefore, compatibility between
pipe and fittings made to this specification from different manufacturers should be verified.
6.2.3 Laying Length—The pipe shall be supplied in any laying length agreeable to both the owner and the manufacturer. Laying
length shall not be less than 99 % of stated quantity when measured in accordance with 7.3.2.
6.2.4 Minimum Wall, Crest, Valley and Liner Thickness—The minimum thickness of pipe sections shall meet the requirements
given in Table 2 when measured in accordance with 7.3.3.
F2764/F2764M − 23
TABLE 2 Pipe Stiffness and Pipe Dimensions
Pipe Inside Profile Minimum Inside Minimum Minimum Minimum Minimum Minimum
A B
Diameter Type Inside Diameter Pipe Stiffness Inner Liner Outer Liner Valley Crown
Diameter Tolerances at 5 % Thickness Thickness Thickness Thickness
Deflection
in. [mm] in. [mm] in. [mm] lb/in/in [kPa] in. [mm] in. [mm] in. [mm] in. [mm]
6 [150] D 5.61 [142] +0.04/-0.04 [+1.0/-1.0] 46 [317] 0.040 [1.0] . . . . . .
8 [200] D 7.70 [196] +0.05/-0.05 [+1.1/-1.1] 46 [317] 0.045 [1.1] . . . . . .
10 [250] D 9.70 [246] +0.06/-0.06 [+1.4/-1.4] 46 [317] 0.050 [1.3] . . . . . .
12 [300] D 11.90 [302] +010/-0.10 [+2.5/-2.5] 46 [317] 0.054 [1.4] . . . . . .
15 [375] D 14.85 [377] +0.15/-0.15 [+3.8/-3.8] 46 [317] 0.065 [1.7] . . . . . .
18 [450] D 17.93 [455] +0.17/-0.17 [+4.3/-4.3] 46 [317] 0.075 [1.9] . . . . . .
21 [530] D 20.75 [527] +0.17/-0.17 [+4.3/-4.3] 46 [317] 0.077 [2.0] . . . . . .
24 [600] D 23.90 [607] +0.23/-0.23 [+5.8/-58] 46 [317] 0.086 [2.2] . . . . . .
30 [750] D 29.79 [757] +0.24/-0.24 [+6.1/-6.1] 46 [317] 0.094 [2.4] . . . . . .
30 [750] T 29.62 [752] +0.18/- 0.18 [+4.6/-4.6] 46 [317] 0.070 [1.8] 0.070 [1.8] 0.081 [2.1] 0.115 [2.9]
36 [900] D 35.40 [899] +0.21/- 0.21 [+5.3/-5.3] 46 [317] 0.102 [2.6] . . . . . .
36 [900] T 35.40 [899] +0.21/- 0.21 [+5.3/-5.3] 46 [317] 0.095 [2.4] 0.095 [2.4] 0.109 [2.8] 0.165 [4.2]
42 [1050] D 41.31 [1049] +0.22/- 0.22 [+5.6/-5.6] 46 [317] 0.105 [2.7] . . . . . .
42 [1050] T 41.31 [1049] +0.22/- 0.22 [+5.6/-5.6] 46 [317] 0.105 [2.7] 0.105 [2.7] 0.121 [3.1] 0.165 [4.2]
48 [1200] D 47.31 [1201] +0.27/- 0.27 [+6.9/-6.9] 46 [317] 0.105 [2.7] . . . . . .
48 [1200] T 47.31 [1201] +0.27/- 0.27 [+6.9/-6.9] 46 [317] 0.105 [2.7] 0.105 [2.7] 0.126 [3.2] 0.170 [4.3]
54 [1350] D 53.32 [1354] +0.27/- 0.27 [+6.9/-6.9] 46 [317] 0.105 [2.7] . . . . . .
54 [1350] T 53.32 [1354] +0.27/- 0.27 [+6.9/-6.9] 46 [317] 0.105 [2.7] 0.105 [2.7] 0.131 [3.3] 0.170 [4.3]
60 [1500] D 59.30 [1506] +0.31/- 0.31 [+7.9/-7.9] 46 [317] 0.115 [2.9] . . . . . .
60 [1500] T 59.30 [1506] +0.31/- 0.31 [+7.9/-7.9] 46 [317] 0.105 [2.7] 0.105 [2.7] 0.137 [3.5] 0.210 [5.3]
A
Where the dimensions for the outer liner thickness are defined, all the associated dimensions shall only pertain to the triple wall profile pipe.
B
D profile type represents double wall profile pipe. T profile type represents triple wall profile pipe.
6.3 Pipe Stiffness—Minimum pipe stiffness at 5 % deflection shall meet the requirements given in Table 2 when tested in
accordance with 7.4.
NOTE 4—The 5 % deflection criterion, which was selected for testing convenience, is not a limitation with respect to in-use deflection. The engineer is
responsible for establishing the acceptable deflection limit.
6.4 Pipe Flattening—There shall be no evidence of splitting, cracking, breaking, separation of seams, separation of the outer and
inner wall, or combinations thereof, when tested in accordance with 7.5. Additionally, at or below the average deflection limit
defined in Eq 1 and Eq 2 for dual wall and triple wall profiles, respectively, the specimen shall be considered as failing this test
when the load does not increase continuously with increasing deflection.
Buckling Defection Limit:
Double Wall:
D
∆5 1.07%· (1)
S D
0.5 D 2 D
~ !
o i
Triple Wall:
D
∆5 1.29%· (2)
S D
0.5~D 2 D !
o i
where:
Δ = minimum buckling deflection limit (%)
D = mean diameter (centroid) of pipe (in [mm])
0.5 (D – D ) = height of the corrugation (outside diameter minus inside diameter) (in [mm])
o i
NOTE 5—Eq 1 and Eq 2 are based on the results from NCHRP Report 631 and is defined as being derived from the standard parallel plate test equation
and modified for polypropylene. The values for the diameter measurements are based on each producer’s specific corrugation dimensions.
6.5 Pipe Impact Strength—There shall be no evidence of splitting, cracking, breaking, separation of seams, separation of the outer
and inner wall, or combinations thereof, when conditioned in accordance with 7.1 and tested in accordance with 7.6 and examined
under normal light and the unaided eye. The minimum pipe impact strength at 73 °F [23 °C] shall be 140 ft-lbf [190 J].
6.6 Fittings and Joining Systems:
F2764/F2764M − 23
6.6.1 Fittings shall be fabricated by the pipe manufacturer from pipe made in accordance with this standard. Fittings fabricated
from double-wall pipe shall be used with double-wall pipe. Fittings fabricated from triple-wall pipe shall be used with triple-wall
pipe. Fitting material shall comply with 5.1, 5.2 and 5.3.
6.6.1.1 Fittings shall be tested in an installation orientation, shall be uniformly supported (body and outlet(s)) by the lower plate,
and uniformly loaded (body and outlet(s)) by the upper plate. Fittings shall meet or exceed a vertical load equivalent to the 5%
deflection stiffness in accordance with Table 2 for pipe to which the fitting is to be joined. The equivalent maximum load shall be
the 5% deflection stiffness in accordance with Table 2 unit load (psi/in or [kPa /mm]) multiplied by the length of the fitting (run
plus branch(es) as applicable) that is loaded by the upper plate. Testing shall be for equivalent load, not deflection. Acceptance
criteria shall be in accordance with 6.4.
NOTE 6—Installation orientation means that the fitting testing orientation is as though it were installed in a pipeline, for example, an elbow or tee with
the directional outlet(s) to the side. In accordance with an established quality program, fittings should be tested to only qualify the overall design and
integrity of the unit. As unique structures, testing of every angle orientation is not necessary.
6.6.1.2 The fitting body in an installation orientation shall be impact tested in accordance with 7.6. Acceptance criteria shall be
in accordance with 6.5.
6.6.2 The joining system(s) between pipe and between pipe and fittings shall be of a design that preserves pipeline slope and
alignment during construction and prevents separation at the joints while maintaining watertight requirements in accordance with
6.6.3. Fittings shall be tested in an installation orientation, shall be uniformly supported (body and outlet(s)) by the lower
...