ASTM F2787-13(2018)

Standard Practice for Structural Design of Thermoplastic Corrugated Wall Stormwater Collection Chambers

SIGNIFICANCE AND USE
4.1 This practice provides a rational method for structural design of thermoplastic stormwater chambers. The loads, capacities, and limit states are based on accepted load and resistance factor design for thermoplastic pipes; however, existing design specifications for thermoplastic pipes do not adequately address the design of chambers due to (1) open-bottom geometry, (2) support on integral foot, (3) varying circumferential corrugation geometry, and (4)  manufacture with alternative thermoplastic resin. This practice standardizes recommendations for designers to adequately address these aspects of chamber design.  
4.2 This practice is written to allow chamber manufacturers to evaluate chambers meeting existing classifications and to design chambers for new classifications as they are developed.
SCOPE
1.1 This practice standardizes structural design of thermoplastic corrugated wall arch-shaped chambers used for collection, detention, and retention of stormwater runoff. The practice is for chambers installed in a trench or bed and subjected to earth and live loads. Structural design includes the composite system made up of the chamber arch, the chamber foot, and the soil envelope. Relevant recognized practices include design of thermoplastic culvert pipes and design of foundations.  
1.2 This practice standardizes methods for manufacturers of buried thermoplastic structures to design for the time dependent behavior of plastics using soil support as an integral part of the structural system. This practice is not applicable to thermoplastic structures that do not include soil support as a component of the structural system.  
1.3 This practice is limited to structural design and does not provide guidance on hydraulic, hydrologic, or environmental design considerations that may need to be addressed for functional use of stormwater collection chambers.  
1.4 Stormwater chambers are most commonly embedded in open graded, angular aggregate which provide both structural support and open porosity for water storage. Should soils other than open graded, angular aggregate be specified for embedment, other installation and functional concerns may need to be addressed that are outside the scope of this practice.  
1.5 Chambers are produced in arch shapes to meet classifications that specify chamber rise, chamber span, minimum foot width, minimum wall thickness, and minimum arch stiffness constant. Chambers are manufactured with integral footings.  
1.6 Polypropylene chamber classifications are found in Specification F2418. Specification F2418 also specifies chamber manufacture and qualification.  
1.7 The values stated in inch-pound units are to be regarded as standard. The values given in parentheses are mathematical conversions to SI units that are provided for information only and are not considered standard.  
1.8 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.  
1.9 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-2018
• ICS: 83.140.99 - Other rubber and plastics products
• Technical Committee: F17 - Plastic Piping Systems
• Drafting Committee: F17.65 - Land Drainage

Relations

• Replaces: ASTM F2787-13 - Standard Practice for Structural Design of Thermoplastic Corrugated Wall Stormwater Collection Chambers
• Effective Date: 01-Feb-2018
• Refers: ASTM F2418-23 - Standard Specification for Polypropylene (PP) Corrugated Wall Stormwater Collection Chambers
• Effective Date: 01-Sep-2023
• Refers: ASTM D2487-17e1 - Standard Practice for Classification of Soils for Engineering Purposes (Unified Soil Classification System)
• Effective Date: 15-Dec-2017
• Refers: ASTM D2487-17 - Standard Practice for Classification of Soils for Engineering Purposes (Unified Soil Classification System)
• Effective Date: 15-Dec-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 F2418-16a - Standard Specification for Polypropylene (PP) Corrugated Wall Stormwater Collection Chambers
• Effective Date: 01-Aug-2016
• Refers: ASTM F2418-16 - Standard Specification for Polypropylene (PP) Corrugated Wall Stormwater Collection Chambers
• Effective Date: 01-Apr-2016
• Refers: ASTM D6992-03(2015) - Standard Test Method for Accelerated Tensile Creep and Creep-Rupture of Geosynthetic Materials Based on Time-Temperature Superposition Using the Stepped Isothermal Method
• Effective Date: 01-May-2015
• Refers: ASTM F2418-13 - Standard Specification for Polypropylene (PP) Corrugated Wall Stormwater Collection Chambers
• Effective Date: 01-Aug-2013
• Refers: ASTM F2418-12 - Standard Specification for Polypropylene (PP) Corrugated Wall Stormwater Collection Chambers
• Effective Date: 01-Feb-2012
• Refers: ASTM D2487-11 - Standard Practice for Classification of Soils for Engineering Purposes (Unified Soil Classification System)
• Effective Date: 01-May-2011
• Refers: ASTM F2418-11 - Standard Specification for Polypropylene (PP) Corrugated Wall Stormwater Collection Chambers
• Effective Date: 01-Apr-2011
• Refers: ASTM D2487-10 - Standard Practice for Classification of Soils for Engineering Purposes (Unified Soil Classification System)
• Effective Date: 01-Jan-2010
• Refers: ASTM F2418-09a - Standard Specification for Polypropylene (PP) Corrugated Wall Stormwater Collection Chambers
• Effective Date: 01-Dec-2009
• Refers: ASTM D2990-09 - Standard Test Methods for Tensile, Compressive, and Flexural Creep and Creep-Rupture of Plastics
• Effective Date: 01-Sep-2009

Overview

ASTM F2787-13(2018) is a standard published by ASTM International that establishes recommended practices for the structural design of thermoplastic corrugated wall stormwater collection chambers. These chambers are primarily used for the collection, detention, and retention of stormwater runoff and are commonly installed in trenches or beds beneath the earth, where they are subjected to both earth and live loads.

This standard addresses structural considerations unique to thermoplastic stormwater chambers-such as their open-bottom geometry, support on integral feet, varied circumferential corrugation, and potential manufacture with alternative thermoplastic resins. ASTM F2787 provides designers and manufacturers with a rational, standardized design methodology, supplementing established practices for thermoplastic pipes and buried structures.

Key Topics

• Structural System Components: Considers the chamber arch, the chamber foot, and the soil envelope as a composite system for supporting loads.
• Load Types: Addresses design for both dead loads (permanent soil cover) and live loads (vehicular and transient surface loads), referencing load calculations from recognized bridge and pipe standards.
• Time-Dependent Behavior: Provides standardized methods to account for the viscoelastic, time-dependent properties of plastics, particularly creep, utilizing soil support as an integral system component.
• Material and Soil Considerations: Outlines the need to specify proper soil class, backfill, and embedment materials-most commonly open-graded, angular aggregates-for structural support and water storage.
• Chamber Classification: Refers to chamber classifications (rise, span, foot width, wall thickness, arch stiffness) and manufacturing requirements detailed in ASTM F2418.
• Design Limitations: The standard focuses solely on structural design, explicitly excluding guidance on hydraulic, hydrologic, or environmental factors.
• Safety and Quality Assurance: Emphasizes the manufacturer’s responsibility to ensure appropriate safety, health, and environmental practices and to comply with relevant regulatory limitations. Requires design validation through analysis and testing.

Applications

The standard is intended for:

• Designers of stormwater management systems: Enabling the structural design of buried thermoplastic chambers used in collection, detention, and retention of stormwater runoff.
• Manufacturers of thermoplastic stormwater chambers: Providing criteria to evaluate existing product lines and to design new chamber types for evolving regulatory and project needs.
• Civil and geotechnical engineers: Offering guidance complementary to soil classification (ASTM D2487) and foundation design for subsurface installations.
• Municipalities and public works: Supporting specification and quality assurance of underground stormwater infrastructure within roadway or urban development projects.

Common applications include underground stormwater management beneath parking lots, roadways, and landscaped areas where reliable structural performance under varying load conditions and site-specific soils is required.

Related Standards

• ASTM F2418: Specification for polypropylene corrugated wall stormwater collection chambers, including manufacturing and qualification requirements.
• ASTM D2487: Practice for classification of soils for engineering purposes using the Unified Soil Classification System.
• ASTM D2990 & D6992: Test methods for assessing the creep behavior of plastics and geosynthetics.
• AASHTO LRFD Bridge Design Specifications: Structural design criteria for loads and foundation elements in civil works.
• AASHTO M43 & M145: Specifications for suitable aggregates and soil classification in construction projects.
• AWWA M45: Provides guidance on the design of fiberglass pipes, relevant for analogous statics and soil-structure interactions in plastic chambers.

Practical Value

Adopting ASTM F2787-13(2018) ensures:

• Consistency and reliability in the structural design of thermoplastic stormwater chambers across diverse infrastructure projects.
• Designs that account for material-specific behavior and composite action with the supporting soil, enhancing structural safety and service life.
• Compatibility with current industry practices and regulatory frameworks for stormwater management and buried utilities.
• Streamlined qualification and certification processes for new chamber products, facilitating confidence for designers, specifiers, and regulators.

Keywords

Thermoplastic stormwater chambers, structural design, corrugated wall, ASTM F2787, plastic pipes, underground infrastructure, stormwater management, load resistance, soil support, chamber classification, live load, dead load, civil engineering standards.

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: F2787 − 13 (Reapproved 2018)
Standard Practice for
Structural Design of Thermoplastic Corrugated Wall
Stormwater Collection Chambers
This standard is issued under the fixed designation F2787; 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* 1.7 The values stated in inch-pound units are to be regarded
as standard. The values given in parentheses are mathematical
1.1 This practice standardizes structural design of thermo-
conversions to SI units that are provided for information only
plastic corrugated wall arch-shaped chambers used for
and are not considered standard.
collection, detention, and retention of stormwater runoff. The
1.8 This standard does not purport to address all of the
practice is for chambers installed in a trench or bed and
safety concerns, if any, associated with its use. It is the
subjected to earth and live loads. Structural design includes the
responsibility of the user of this standard to establish appro-
composite system made up of the chamber arch, the chamber
priate safety, health, and environmental practices and deter-
foot, and the soil envelope. Relevant recognized practices
mine the applicability of regulatory limitations prior to use.
include design of thermoplastic culvert pipes and design of
1.9 This international standard was developed in accor-
foundations.
dance with internationally recognized principles on standard-
1.2 This practice standardizes methods for manufacturers of
ization established in the Decision on Principles for the
buried thermoplastic structures to design for the time depen-
Development of International Standards, Guides and Recom-
dent behavior of plastics using soil support as an integral part
mendations issued by the World Trade Organization Technical
of the structural system. This practice is not applicable to
Barriers to Trade (TBT) Committee.
thermoplastic structures that do not include soil support as a
component of the structural system.
2. Referenced Documents
1.3 This practice is limited to structural design and does not 2.1 ASTM Standards:
provide guidance on hydraulic, hydrologic, or environmental D2487 Practice for Classification of Soils for Engineering
design considerations that may need to be addressed for Purposes (Unified Soil Classification System)
functional use of stormwater collection chambers. D2990 Test Methods for Tensile, Compressive, and Flexural
Creep and Creep-Rupture of Plastics
1.4 Stormwater chambers are most commonly embedded in
D6992 Test Method for Accelerated Tensile Creep and
open graded, angular aggregate which provide both structural
Creep-Rupture of Geosynthetic Materials Based on Time-
support and open porosity for water storage. Should soils other
Temperature Superposition Using the Stepped Isothermal
than open graded, angular aggregate be specified for
Method
embedment, other installation and functional concerns may
F2418 SpecificationforPolypropylene(PP)CorrugatedWall
need to be addressed that are outside the scope of this practice.
Stormwater Collection Chambers
1.5 Chambers are produced in arch shapes to meet classifi-
2.2 AASHTO LRFD Bridge Design Specifications:
cationsthatspecifychamberrise,chamberspan,minimumfoot
Section3LoadsandLoadFactors, 3.5PermanentLoads;3.6
width, minimum wall thickness, and minimum arch stiffness
Live Loads
constant. Chambers are manufactured with integral footings.
Section 10 Foundations, 10.6 Spread Footings
Section 12 Buried Structures and Tunnel Liners, 12.12
1.6 Polypropylene chamber classifications are found in
Thermoplastic Pipes
Specification F2418. Specification F2418 also specifies cham-
ber manufacture and qualification.
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
This practice is under the jurisdiction of ASTM Committee F17 on Plastic the ASTM website.
Piping Systems and is the direct responsibility of Subcommittee F17.65 on Land AASHTO LRFD Bridge Design Specifications-Dual Units, 4th Edition, 2007
Drainage. and AASHTO Standard Specifications for Transportation Materials and Sampling,
Current edition approved Feb. 1, 2018. Published March 2018. Originally 28th edition, 2008. Available from American Association of State Highway and
approved in 2009. Last previous edition approved in 2013 as F2787–13. DOI: Transportation Officials (AASHTO), 444 N. Capitol St., NW, Suite 249,
10.1520/F2787-13R18. Washington, DC 20001.
*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
F2787 − 13 (2018)
2.3 AASHTO Standard Specifications: 3.1.7 embedment—backfill material against the sides of
M43 Standard Specification for Size ofAggregate for Road chambers and end caps and in between rows of chambers from
and Bridge Construction the foundation stone below to a specified dimension over the
M 145 Standard Specification for Classification of Soils and top of the chambers (see Fig. 3).
Soil-Aggregate Mixtures for Highway Construction Pur-
3.1.8 end cap—a bulkhead provided to begin and terminate
poses
a chamber, or row of chambers, and prevent intrusion of
T99 Standard Method of Test for Moisture-Density Rela-
surrounding embedment materials.
tions of Soils Using a 2.5-kg (5.5-lb) Rammer and a
3.1.9 foot—a flat, turned out section that is manufactured
305-mm (12-in.) Drop
with the chamber to provide a bearing surface for transfer of
2.4 AWWA Manual:
vertical loads to the foundation (see Fig. 1).
M45 Manual of Water Supply Practices: Fiberglass Pipe
3.1.10 foot area—the actual contact area of the foot with the
Design
foundation.
3. Terminology
3.1.11 local buckling—compression failure of built-up plate
sections with high width-to-thickness ratios.
3.1 Definitions:
3.1.12 nominal height—a designation describing the ap-
3.1.1 Definitions used in this specification are in accordance
with the definitions in Terminology F412, and abbreviations proximate outside vertical dimension of the chamber at its
are in accordance with Terminology D1600, unless otherwise crown (see Fig. 1).
indicated.
3.1.13 nominal width—a designation describing the ap-
3.1.2 chamber—an arch-shaped structure manufactured of
proximate outside horizontal dimension of the chamber at its
thermoplastic with an open-bottom that is supported on feet
feet (see Fig. 1).
and may be joined into rows that begin with, and are termi-
3.1.14 rise—the vertical distance from the chamber base
nated by, end caps (see Fig. 1).
(bottom of the chamber foot) to the inside of a chamber wall
3.1.3 classification—the chamber model specification that
valley element at the crown as depicted in Fig. 1.
identifies nominal height, nominal width, rise, span, minimum
3.1.15 span—the horizontal distance from the interior of
foot width, wall thickness, and arch stiffness constant.
one sidewall valley element to the interior of the other sidewall
3.1.4 corrugated wall—a wall profile consisting of a regular
valley element as depicted in Fig. 1.
pattern of alternating crests and valleys connected by web
3.1.16 valley—the element of a corrugation located at the
elements (see Fig. 2).
interior surface of a chamber wall, spanning between two web
3.1.5 crest—the element of a corrugation located at the
elements (see Fig. 2).
exterior surface of the chamber wall, spanning between two
3.1.17 viscoelasticity—the response of a material to load
web elements (see Fig. 2).
thatisdependentbothonloadmagnitude(elastic)andloadrate
3.1.6 crown—the center section of a chamber typically
(viscous).
located at the highest point as the chamber is traversed
3.1.18 web—the element of a corrugated wall that connects
circumferentially.
a crest element to a valley element (see Fig. 2).
4. Significance and Use
AWWA Manual of Water Supply Practices M45: Fiberglass Pipe Design, 2nd
4.1 This practice provides a rational method for structural
Edition, 2005. Available from the American Water Works Association (AWWA),
design of thermoplastic stormwater chambers. The loads,
6666 W. Quincy Ave., Denver, CO 80235.
NOTE 1—The model chamber shown in this standard is intended only as a general illustration.
FIG. 1 Chamber Terminology (Typical)
F2787 − 13 (2018)
NOTE 1—The corrugation profile shown in this standard is intended only as a general illustration.
FIG. 2 Corrugation Terminology (Typical)
FIG. 3 Installation Terminology (Typical)
capacities, and limit states are based on accepted load and 5.3.1 Service Limit State—Servicedesignshalllimitvertical
resistance factor design for thermoplastic pipes; however, displacements at the ground surface. Chambers shall be evalu-
existing design specifications for thermoplastic pipes do not
ated for detrimental structural deformation.
adequately address the design of chambers due to (1) open-
5.3.2 Safety Against Structural Failure—Structural design
bottom geometry, (2) support on integral foot, (3) varying
shall evaluate chambers for buckling, compression, tension,
circumferential corrugation geometry, and (4) manufacture
and foundation bearing.
with alternative thermoplastic resin. This practice standardizes
5.4 Buckling capacity is based on material stress limits.
recommendations for designers to adequately address these
Compression and tension capacities are based on material
aspects of chamber design.
strain limits. Foundation bearing capacity is based on soil
4.2 This practice is written to allow chamber manufacturers
ultimate bearing capacity.
to evaluate chambers meeting existing classifications and to
5.5 Chambers shall be designed using closed-form solutions
design chambers for new classifications as they are developed.
(verified by analysis) or finite element analysis (FEA). Designs
shall be validated by testing.
5. Basis of Design
NOTE 1—The soil-chamber system complexity generally precludes the
5.1 Design is based on AASHTO LRFD Bridge Design
use of closed-form solutions for determination of design force effects.
Specifications and publications for static soil-structure-
While specific solutions may be developed for individual chamber
interaction analysis for thermoplastic pipes. Users should
geometries, general solutions have not been developed to accurately
verify that these recommendations meet particular project predict behavior for the many possible variations in chamber geometry. In
most cases FEAmust be employed to calculate design force effects on the
needs.
chamber or as verification of closed-form solutions.
5.2 Chamber installations shall be designed for the critical
5.6 Chamber material properties shall be based on tests.
combination of live load and dead load, see Section 7.
5.3 Chambers shall be designed for service limit states and 5.7 Chamber section properties shall be calculated from the
safety against structural failure, see Section 8. geometry of the chamber cross-section.
F2787 − 13 (2018)
5.8 Soil properties shall be based on generally accepted 7.2 Dead Load (DL)—Dead load shall be computed from
published properties for the specified soil classifications or by permanent soil cover over chambers.The soil unit weight shall
3 3
tests on site-specific materials. not be less than 120 lb/ft (18.9 kN/m ) unless otherwise
determined by tests. Dead load shall be calculated for each
6. Analysis for Design
installation.
6.1 The design shall include structural modeling of the
7.3 Dead Load Factor (γ )—The dead load factor shall be
DL
chamberunderloadsintheinstalledsoilenvironment.Analysis
1.95.
models shall include critical anticipated live loads and soil
7.4 Live Load (LL)—Live load calculation is provided in
cover heights that provide deflections for serviceability design
Annex A1. Live load includes transient loads (passing ve-
and force effects to design for safety against structural failure.
hicles) or sustained loads (stationary non-permanent loads).
6.2 Analysis shall consider the following:
Live load computation is based on theAASHTO HL-93 design
6.2.1 Chamber Structure—Two-dimensional FEA shall use
vehicular live load applied to a single-loaded lane.
beam elements with effective section properties to model the
7.4.1 HL-93—The HL-93 load is a combination of the
chamber wall. Each beam element shall represent not more
design truck or design tandem, whichever is critical, applied
than 10 degrees of the chamber circumference. Nodes at beam
with the design lane load.
ends shall be located at the center of the gravity (cg) of the
7.4.2 Design Truck—The design truck shall be the
corrugated chamber wall cross-section. Three-dimensional
AASHTO Design Truck as specified in AASHTO LRFD
FEA shall employ shell elements.
Bridge Design Specifications, Section 3.6.1.2.2.
6.2.2 FEA Program—Acceptable FEAprograms include (1)
7.4.3 Design Tandem—The design tandem shall be the
CANDE (Culvert Analysis and Design), (2) similarly featured
AASHTO Design Tandem as specified in AASHTO LRFD
and verified culvert design software, or (3) general purpose
Bridge Design Specifications, Section 3.6.1.2.3.
finite element analysis software with capability to model
7.4.4 Thermoplastic chamber structures have a structural
nonlinear static soil-structure-interaction.
response that is dependent on load duration. Chamber response
6.2.3 Creep—The time-dependent response (creep) of ther-
to live load is computed using appropriate creep moduli for
moplastic chamber materials shall be included in the analysis.
instantaneous response (transient loads) and longer-duration
Acceptable methods are (1) multiple linear-elastic models with
response (sustained loads).As a minimum, design for live load
successive stiffness reductions for creep effects, and (2) non-
shall include evaluation of instantaneous response (due to
linear chamber models that include the creep response. Values
moving vehicles), using a short duration (≤ 1 min) creep
of creep modulus shall be determined by test in accordance
modulus, with multiple presence and impact factors in the live
with Test Methods D2990 or Test Method D6992.
loadcomputation,andasustainedloadresponse(duetoparked
6.2.4 Soil—Models shall include accurate representation of
vehicle) using a 1 week creep modulus with no multiple
the structural backfill envelope and boundary conditions. The
presence or impact factors included in the live load computa-
backfill envelope includes foundation, embedment, and cover.
tion.
Boundary conditions typically include the size of the soil
7.5 Live Load Factor (γ )—The live load factor shall be
LL
embedment zone, distance to trench walls, subgrade under the
1.75.
backfill envelope, weight and stiffness of soils above the
backfill envelope, and boundary for application of live loads.
8. Structural Design
Structural backfill soils shall be modeled with nonlinear
8.1 The resistance of a chamber to design loads shall be
properties that incorporate the effects of confinement. Accept-
based on the critical limit state for (1) serviceability
ablesoilmodelsinclude(1)soilhardeningmodelsthatincrease
requirements, (2) stability of the chamber to global buckling,
soil stiffness for confinement, (2) elastic-plastic models that
(3) strength of the chamber to local buckling, (4) strength of
allow failure in shear, or (3) large-deformation models. Soils
the chamber material relative to tensile strain limits, (5)
outside the backfill envelope and further than two times the
capacity of the foundation material to bearing from the
chamber span from the chamber may be modeled as linear-
chamber foot, and (6) capacity of the subgrade material to
elastic. Soil continuum elements shall be either fully bonded to
bearing from the foundation.
the chamber beam elements or modeled with a friction inter-
8.2 Serviceability—Chambers shall be designed to limit
face.
deflections that could adversely affect (1) displacements at the
6.2.5 Live Load—Models shall include live loads, see Sec-
ground surface, (2) distribution of loads assumed in the
tion 7.
analysis, or (3) hydraulic function. Deflection predictions shall
6.2.6 Chamber Beds—Structural effects of adjacent cham-
be obtained from chamber design models using service loads.
bers shall be analyzed. When two-dimensional plane-strain
Unless otherwise specified, deflections (change in rise and
analysis is used, changes in geometry along the length of
span) shall be limited to 2.5 % of the nominal rise and span.
chamber runs, including intermediate stiffeners or diaphragms,
shall be addressed using separate models.
8.3 Compression Strength Capacity—The chamber is de-
signed for compression local buckling by determination of an
7. Structural Loads
effective area to carry factored loads. The effective area is
7.1 The design load on a chamber shall include dead load calculated by idealizing the corrugation into rectangular plates.
and live load. The design is evaluated for the thrust only case, and for the
F2787 − 13 (2018)
combined thrust and bending case. The resulting safety factor where:
is the ratio of allowable material strain to induced strain
ε = first-order strain at a wall cross-section due to axial
T
calculated by this procedure. The following steps provide the
thrust (in./in.),
design procedure (for design example see Appendix X1). ε = first-order strain in each element at a wall cross-
Mi
section due to combined axial thrust and bending
8.3.1 IdealizedWallProfile—Corrugatedwallcross-sections
moment (in./in.),
shall be idealized as straight (plate) elements. Each element is
T = DL thrust at a wall cross-section from models
DL
assigned a width based on the clear distance between the
(lb/in.),
adjoining elements and the thickness at the center of the
T = LL thrust at a wall cross-section from models (lb/
LL
element. Fig. 4 illustrates idealization of a model corrugation.
in.),
Where the cross-section is non-uniform around the chamber
M = DL bending moment at a wall cross-section from
DL
circumference, calculate idealized cross-section properties at
models (in.-lb/in.),
locations separated not more than 30 degrees around the
M = LL bending moment at a wall cross-section from
LL
circumference.
models (in.-lb/in.),
c = distance to each element center of gravity from the
8.3.2 First-Order Wall Strain—The first-order strain due to
i
center of gravity of the wall cross-section (in.),
axial thrust, ε , at a wall cross-section is given in Eq 1. The
T
E = thermoplastic modulus of elasticity used in the
t
first-order strain due to combined axial thrust and bending
model; t indicates load duration dependency (lb/
moment, ε , for each element at a wall cross-section is given
Mi
in. ),
in Eq 2. Strains are positive for compression.
A = gross area of the chamber wall cross-section (in. /
γ T 1γ T
DLmax DL LL LL in.), and
ε 5 (1)
T
AE
t I = moment of inertia of the chamber wall cross-section
(in. /in.)
γ T 1γ T γ M 1γ M c
~ !
DLmax DL LL LL DLmax DL LL LL i
ε 5 1 .0 (2)
Mi
AE IE
t t
FIG. 4 Typical and Idealized Cross-Section of Corrugated Wall
F2787 − 13 (2018)
8.3.3 Slenderness and Effective Width—The effective width, mined from material compression tests. Compression strength
b, of each element in the cross-section for buckling shall be is satisfied if Eq 9 and 10 are met.
i
determined by Eq 3.
ε
cy
$1 (9)
b 5 ρ w (3)
ε
i i i Tf
0.22
1.5ε
cy
1 2 $1 (10)
S D
λ ε
i Mf
ρ 5 #1 (4)
i
λ
i
where:
w ε
ε = chamber thermoplastic compression yield strain
i i
cy
λ 5 .0.673 (5)
S DŒ
i
t k
(in./in.).
i i
NOTE 3—For typical thermoplastics, the values of stiffness and strength
where:
vary with temperature, load level, and load rate. However, research,
b = effective width of each element (in.),
i testing, and analysis have shown that these same thermoplastics fail at a
ρ = effective width factor,
i constant strain that is approximately independent of load application rate
λ = slenderness factor, orduration.Thestrainisafunctionoftheresin.Thelimitingstrainstheory
i
is used for design of thermoplastic culvert pipes in AASHTO LRFD
ε = strain in each element, evaluated for Thrust and Thrust
i
Bridge Design Specifications.
+ Moment (in./in.),
k = plate buckling edge support coefficient,
i
8.4 Tensile Strength Capacity—At any given wall cross-
t = thickness of each element (in.), and
i
section, the maximum factored tensile strain shall not exceed
w = total clear width of element between supporting ele-
i
the material tensile yield strain as in Eq 11.
ments (in.).
ε
NOTE 2—The plate buckling edge support coefficient can be approxi- ty
$1 (11)
mated as 4.0 for simply supported edges, or 0.43 for free edges. A more ε
t
exact value can be determined for specific cases based on methods
γ T 1γ T γ M 1γ M c
5 ~ !
DL DL LL LL DL DL LL LL t
presented in Timoshenko and Gere.
ε 5 1 ,0 (12)
t
AE IE
t t
8.3.4 Effective Area—The total effective area is determined
where:
as the summation of effective element areas in Eq 6.
ε = chamber thermoplastic tension yield strain (in./in.),
ty
~1 2 ρ !w t
( i i i
A 5 A 2 (6) ε = maximumtensilestraininthechamberwall;useγ
t DLmax
eff
ω
or γ to get maximum tension strain (in./in.), and
DLmin
where: c = distance to extreme outer fiber from the center of
t
gravityofthewallcross-section,fortensionstrain(in.).
A = effective area of wall cross-section (in. /in.), and
eff
ω = period of corrugation (in.).
8.5 Global Buckling:
8.3.5 Total Factored Strain—The total factored strains are
8.5.1 At any given wall cross-section, the critical buckling
given in Eq 7 and 8. The total factored strains are calculated at
thrust, T , shall be greater than the maximum factored thrust
CR
the extreme outer fiber of the cross-section.
due to dead and live loads as shown in Eq 13. The thrust shall
be obtained from chamber design models using service loads.
γ T 1γ T
DLmax DL LL LL
ε 5 (7)
Tf
Thrust is positive for compression.
A E
eff t
T
γ T 1γ T ~γ M 1γ M !c
CR
DLmax DL LL LL DLmax DL LL LL c
ε 5 1 .0 (8) $1 (13)
Mf
A E IE T
eff t t
T 5 T 1T (14)
where: DL LL
ε = total factored thrust compression strain (in./in.), where:
Tf
ε = total factored combined thrust and bending compres-
Mf
T = maximum thrust due to dead loads and live loads
sion strain (in./in.), and
(lb/in.)
c = distance to extreme outer fiber from the center of
c
T = critical buckling thrust in Eq 15 (lb/in.).
CR
gravity of the wall cross-section, for compression
8.5.2 The critical buckling thrust for a wall cross-section is
strain (in.).
given in Eq 15, following the approach adopted by theAWWA
8.3.6 Compression Strength Check—Chamber capacity is
for global buckling of buried plastic pipe.Table 1
the thermoplastic yield strain, ε . Yield strain may be deter-
cy
0.33 0.67
1.2C ~E I! ~φ M k ! R
n L s s υ h
T 5 (15)
CR
FS
5 11υ 1 2 2υ
~ !~ !
Timoshenko, S. P. and Gere, J. M., Theory of Elastic Stability, McGraw Hill,
k 5 (16)
υ
New York, 1961. 1 2 υ
F2787 − 13 (2018)
A,B
TABLE 1 Constrained ModulusM Based on Soil Type and Compaction Condition
s
P Stress level Sn-100 Sn-95 Sn-90 Sn-85
sp
(ksf) (ksi) (ksi) (ksi) (ksi)
0.15 2.350 2.000 1.275 0.470
0.75 3.450 2.600 1.500 0.520
1.50 4.200 3.000 1.625 0.570
3.00 5.500 3.450 1.800 0.650
6.00 7.500 4.250 2.100 0.825
9.00 9.300 5.000 2.500 1.000
P Stress level Si-95 Si-90 Si-85
sp
(ksf) (ksi) (ksi) (ksi)
0.15 1.415 0.670 0.360
0.75 1.670 0.740 0.390
1.50 1.770 0.750 0.400
3.00 1.880 0.790 0.430
6.00 2.090 0.900 0.510
9.00
P Stress level Cl-95 Cl-90 Cl-85
sp
(ksf) (ksi) (ksi) (ksi)
0.15 0.530 0.255 0.130
0.75 0.625 0.320 0.175
1.50 0.690 0.355 0.200
3.00 0.740 0.395 0.230
6.00 0.815 0.460 0.285
9.00 0.895 0.525 0.345
A
The soil types are defined by a two-letter designation that indicates general soil classification. Sn for sands and gravels, Si for silts, and Cl for clays. Specific soil groups
that fall into these categories, based on ASTM D2487 and AASHTO M 145, are listed in Table 2.
B
The numerical suffix to the soil type indicates the compaction level of the soil as a percentage of maximum dry density determined in accordance with AASHTO T 99.
TABLE 2 Equivalent ASTM and AASHTO Soil Classifications
A ,B
Basic Soil Type ASTM D2487 AASHTO M 145
C C
Sn SW, SP A1, A3
GW, GP
(Gravelly sand, SW)
sands and gravels with 12 % or
less fines
Si GM, SM, ML A-2-4, A-2-5, A4
(Sandy silt, ML) also GC and SC with less than
20 % passing a No. 200 sieve
Cl CL, MH, GC, SC A-2-6, A-2-7, A5, A6
(Silty clay, CL) also GC and SC with more than
20 % passing a No. 200 sieve
A
The soil classification listed in parentheses is the type that was tested to develop the constrained soil modulus values in Table 1. The correlations to other soil types are
approximate.
B
Angular aggregate materials conforming to AASHTO M 43 are classified as Soil Type SN.
C
Uniformly graded materials with an average particle size smaller than a No. 40 sieve shall not be used as backfill for thermoplastic culverts unless specifically allowed
in the contract documents and special precautions are taken to control moisture content and monitor compaction levels.
11.4
h = height of soil cover over the chamber (in.).
R 5 (17)
h
111D/h
~ !
NOTE 4—The critical buckling thrust given by Eq 15 is for cylindrical
pipe. Corrugated stormwater chambers generally have adequate hoop
where:
stiffness that precludes global buckling.
T = maximum thrust due to dead loads and live loads
8.6 Foundation Strength—Bearing of the chamber foot on
(lb/in.)
the foundation and bearing of the foundation on the subgrade
FS = design factor = 2.5,
shallbecheckedversusultimatebearingcapacity.Thechamber
C = scalar calibration factor to account for nonlinear
n
footshallbeidealizedasarectangularspreadfootingwithload
effects = 0.55,
applied to the foundation.The load traveling from the chamber
φ = strength reduction factor for soil = 0.9,
s
and any concentrated adjacent soil column shall be distributed
υ = Poisson’s ratio of the soil; in the absence of specific
through the foundation and applied as a spread footing to the
information, it is common to assume υ = 0.3 giving
subgrade. Calculations for bearing capacity shall be in accor-
k = 0.74,
υ
dance withAASHTO Section 10 for spread footings, with soil
M = constrained soil modulus (lb/in. ), Table 1 ,
s
properties determined by a geotechnical engineer (for founda-
E = 50 yr. tensile creep modulus (lb/in. ),
L
tion design example see Appendix X2).
I = moment of inertia of the chamber wall cross-section
(in. /in.),
8.7 Design of End Closures—Closure pieces at the end of
D = nominal span of chamber (in.), and
chambers such as end caps or end plates may be molded
F2787 − 13 (2018)
integrally with the chamber or may be formed as a separate 9.1.2 Aminimum of two tests shall be conducted including
structure. End closures made as separate structures shall be one sustained earth load test and one live load test (see
designed to interlock with the end corrugation at either end of
Appendix X3).
a chamber row.An end cap may fit either over or under the end
corrugation as long as there is sufficient interlock with the
10. Certification
chamber so that the end cap does not collapse into the chamber
10.1 Design Certification—If requested by the purchaser,
row after the placement of backfill. End closures, whether
the chamber manufacturer shall provide certification that the
integral with, or separate from, the chamber structure, shall be
chamber design meets all requirements of this standard and
designed using the same engineering principles applied to the
submit test reports, calculations, installation specifications, and
chambers.
drawings showing conformance to this standard.
9. Design Qualification
11. Keywords
9.1 Design Qualification—The chamber design shall be
qualified with full-scale installation testing of representative
11.1 chamber; corrugated; creep; local buckling; stormwa-
chambers under design earth and live loads.
ter; structural design; thermoplastic
9.1.1 Testing shall demonstrate safety against structural
failure. Sufficient performance data shall be obtained on which
to verify the design calculations.
ANNEX
(Mandatory Information)
A1. COMPUTATION OF LIVE LOADS
A1.1 Live Load Computation—Live load includes transient wheels for the design truck shall be as specified in Fig. A1.1.
loads (passing vehicles) or sustained loads (stationary non- The design truck has a single 8 kip (kip = 1000 lb) axle
permanent loads). Live load computation is based on the
followed by two 32 kip axles, spaced 14 ft apart. Wheels on a
AASHTO HL-93 design vehicular live load applied to a single
single axle are spaced 6 ft apart. Wheel loads (W) shall be
loaded lane. HL-93 live load is a combination of the design
applied uniformly on tire contact areas.
truck or design tandem, whichever is critical, applied with the
NOTEA1.2—Typical stormwater chamber design will be based on a 32
design lane load.
kip axle, where low cover heights preclude interaction of adjacent axles.
NOTE A1.1—Thermoplastic chamber structures have a structural re-
A1.1.2 Design Tandem—The design tandem is based on the
sponse that is dependent on load duration. Chamber structural design
should include thermoplastic creep modulus that is consistent with the AASHTO Design Tandem. The weights and spacing of axles
anticipated duration of live load. For example, the probable maximum
and wheels for the design tandem shall be as specified in Fig.
duration of parked vehicles over the chambers should be accounted for in
A1.2. The design tandem has two 25 kip axles, spaced 4 ft
selecting the design modulus. Typical values for load duration are as
apart. Wheels on a single axle are spaced 6 ft apart. Wheel
follows: instantaneous (≤ 1 minute) with impact and multiple presence, to
account for normal traffic; 1 week with no impact or multiple presence, to
loads are 12 500 lb on each wheel. Wheel loads (W) shall be
account for a vehicle parked over the chamber for a longer duration.
applied uniformly on tire contact areas.
A1.1.1 Design Truck—The design truck is based on the
NOTE A1.3—Construction vehicles that exceed AASHTO design truck
AASHTO design truck. The weights and spacing of axles and
or design tandem loads must be evaluated on a case-by-case basis.
FIG. A1.1 Characteristics of Design Truck and Design Tire Contact Area
F2787 − 13 (2018)
FIG. A1.2 Characteristics of Design Tandem
A1.1.3 Design Lane Load—The design lane load shall be calculated in Eq A1.4. The truck or tandem live load shall be
appliedasauniformloadof64lb/ft occupyingthefullground applied uniformly on the tire contact area or the live load patch
surface above the chamber. The service design lane load shall area.The design lane load shall be as provided in EqA1.5.The
not be distributed for out-of-plane effects nor shall it be lane load shall be applied as a uniform surface pressure.
increased or reduced for any other effect.
LL 5 LL 1LL (A1.3)
t l
A1.1.4 Tire Contact Area (A )—Wheel load shall be applied
c
IM
LL 5 W*m* 11 (A1.4)
S D
at the ground surface over tire contact areas. The tire contact t
area shall be a single rectangle whose width (w ) is 20 in. and
w
LL 5 64 lb/ft (A1.5)
l
whose length (l ) is 10 in. as in Figs. A1.1 and A1.2. The tire
w
pressure shall be uniformly distributed over the contact area.
where:
The contact area is calculated in Eq A1.1.
LL = total service live load, incl. surface pressure (lb/ft )
and patch load (lb),
A 5 w l (A1.1)
c w w
LL = service live load due to the design truck or tandem
t
where:
(lb),
A = tire contact area = 200 in. ,
LL = service lane load (lb/ft ),
c
l
w = tire width = 20 in., and
W = wheel load from design truck or design tandem (lb),
w
l = tire length = 10 in.
w and
m = multiple presence factor (see A1.2.1).
A1.2 Service Limit State—Live load calculated in this
Annex is used to design for the service limit state. Service live
A1.3 Safety Against Structural Failure—Factored live load
load calculation follows:
effects are used to design for safety against structural failure.
Service live load shall be applied in design models of the
A1.2.1 Multiple Presence Factor (m)—Afactor of 1.2 shall
chamber and resultant internal force effects of axial thrust and
be applied to live load to account for the probability of an
bending moment shall be factored by the live load factor and
overloaded vehicle.
used to design for safety against structural failure. The Live
NOTEA1.4—Typical available stormwater chamber classifications
...