Table Of ContentACI 360R-92
(Reapproved 1997)
Design of Slabs on Grade
Reported by ACI Committee 360
Boyd C. Ringo* H. Platt Thompson*
Chairman Vice Chairman
Robert B. Anderson* F. Ray Rose
Larry Gillengerton A. Fattah Shaikh
Robert I. Gulyas R. Gregory Taylor
Robert D. Johnson William V. Wagner
Jack I. Mann Robert F. Ytterberg
* Designates members of editorial group
Indicates past chairmen of committee
Deceased
2.3-Design and construction variables
This document presents information on the design of slabs on grade, pri- 2.4-Design methods
marily industrial floors and the slabs adjacent to them. The report ad-
2.5-Fiber-reinforced concrete (FRC)
dresses the planning, design, and detailing of the slabs. Background infor-
2.6-Conclusion
mation on design theories is followed by discussion of the soil support
system, loadings, and types of slabs. Design methods are given for plain
concrete, reinforced concrete, shrinkage-compensating concrete, and post- Chapter 3-Soil support systems for slabs on grade, pg.
tensioned concrete slabs, followed by information on shrinkage and curling 360R-8
problems. Design examples appear in an appendix.
3.1-Introduction
3.2-Soil classification and testing
Keywords: Concrete; curling; design; floors on ground; grade floors; in-
dustrial floors; joints; load types; post-tensioned concrete; reinforcement 3.3-Modulus of subgrade reaction
(steel); shrinkage; shrinkage-compensating concrete; slabs; slabs on 3.4-Design of the slab support system
grade; soil mechanics; shrinkage; warping. 3.5-Site preparation
3.6-Inspection and site testing of soil support
3.7-Special problems with slab on grade support
CONTENTS
Chapter 4-Loads, pg. 360R-15
Chapter l-Introduction, pg. 360R-2
4.1-Introduction
l.l-Purpose and scope
4.2-Vehicle loads
1.2-Work of Committee 360 and other relevant
4.3-Concentrated loads
committees
4.4-Uniform loads
1.3-Work of non-ACI organizations
4.5-Line and strip loads
1.4-Design theories for slabs on grade
4.6-Unusual loads
1.5-Overview of subsequent chapters
4.7-Construction loads
4.8-Environmental factors
Chapter 2-Slab types and design methods, pg. 360R-4
4.9-Factors of safety
2.1-Introduction
4.10-Summary
2.2-Slab types
Chapter 5-Design of plain concrete slabs, pg. 360R-19
ACI Committee Reports, Guides, Standard Practices, 5.1-Introduction
and Commentaries are intended for guidance in de-
signing, planning, executing, or inspecting construction,
and in preparing specifications. Reference to these doc- Copyright 1992, American Concrete Institute.
All rights reserved including rights of reproduction and use in any form or by
uments shall not be made in the Project Documents. If
any means, including the making of copies by any photo process, or by any elec-
items found in these documents are desired to be a part tronic or mechanical device, printed, written, or oral, or recording for sound or
of the Project Documents, they should be phrased in visual reproduction for use in any knowledge or retrieval system or device, unless
mandatory language and incorporated into the Project permission in writing is obtained from the copyright proprietors.
Documents.
360R-1
360R-2 ACI COMMITTEE REPORT
5.2-Portland Cement Association (PCA) design pendix, pg. 360R-41
method Al-Design examples using the PCA method
5.3-Wire Reinforcement Institute (WRI) method A2-Slab thickness design by WRI method
5.4-Corps of Engineers (COE) design method A3-Design examples using COE charts
A4-Slab design using post-tensioning
Chapter 6-Design of slabs with shrinkage and temper- A5-Shrinkage-compensating concrete examples
ature reinforcement, pg. 360R-20
6.1-Introduction
6.2-Thickness design methods
6.3-Subgradedrag equation CHAPTER l-INTRODUCTION
6.4-Reinforcement location
l.l-Purpose and scope
Chapter 7-Design of shrinkage-compensating concrete Consistent with the mission of ACI Committee 360,
slabs, pg. 360R-21 this report presents state-of-the-art information on the
7.1-Introduction design of slabs on grade. In this context, design is defined
7.2-Thickness determination as the decision-making process of planning, sizing, detail-
7.3-Typical reinforcement conditions ing, and developing specifications generally preceding
7.4-Design implications construction. Information on other aspects, such as
7.5-Maximum and minimum reinforcement require- materials, construction methods, placement of concrete,
ments and finishing techniques, is included only where it is
7.6-Other considerations needed in making design decisions.
In the context of this report, Committee 360 defines
Chapter 8-Design of post-tensioned slabs on grade, pg. slab on grade as:
360R-27 a slab, continuously supported by ground, whose total
8.1-Notation loading when uniformly distributed would impart a
8.2-Definitions pressure to the grade or soil that is less than 50
8.3-Introduction percent of the allowable bearing capacity thereof.
8.4-Applicable design procedures The slab may be of uniform or variable thickness,
8.5-Data needed for design of reinforced slabs and it may include stiffening elements such as ribs or
8.6-Design for slabs on expansive soils beams. The slab may be plain, reinforced, or pre-
8.7-Design for slabs on compressible soil stressed concrete. The reinforcement or prestressing
8.8-Maximum spacing of post-tensioning tendons in steel may be provided for the effects of shrinkage
normal weight concrete and temperature or for structural loading.
Chapter 9-Reducing the effects of slab shrinkage and This report covers the design of slabs on grade for
curling, pg. 360R-32 loads caused by material stored directly on the slab or on
9.1-Introduction storage racks, as well as static and dynamic loads associ-
9.2-Drying and thermal shrinkage ated with handling equipment and vehicles. Other loads,
9.3-Curling and warping such as loads on the roof transferred through dual pur-
9.4-Factors that affect shrinkage and curling pose rack systems are also covered. ACI Committee 360
9.5-Compressive strength and shrinkage considers use of the information presented in this report
9.6-Compressive strength and abrasion resistance reasonable for slabs on grade which support structural
9.7-Removing restraints to shrinkage loads provided the loading limit of the above definition
9.8-Subgrade and vapor barriers is satisfied.
9.9-Distributed reinforcement to reduce curling and In addition to design of the slab for these loadings,
number of joints the report discusses subgrade-subbase, shrinkage and
9.l0-Thickened edges to reduce curling temperature effects, cracking, curling or warping, and
9.11-Relation between curing and curling other items affecting the design. Although the same gen-
9.12-Warping stresses in relation to joint spacing eral principles are applicable, the report does not spe-
9.13-Warping stresses and deformation cifically address the design of highways, airport pave-
9.14-Effect of eliminating contraction joints with ments, parking lots, and mat foundations.
post-tensioning or shrinkage-compensating
concrete 1.2-Work of ACI Committee 360 and other relevant
9.15-Summary and conclusions committees
1.2.1 ACI 360 mission-Since several engineering
Chapter l0-References, pg. 360R-39 disciplines and construction trades deal with slabs on
l0.1-Recommended references grade, several ACI committees are involved, directly and
10.2-Cited references indirectly. Before the formation of Committee 360, no
DESIGN OF SLABS ON GRADE
ACI committee was specifically charged to cover design. grade come from organizations and individuals outside of
Consequently, ACI 360 was formed with this mission: the American Concrete Institute. The United States
Army Corps of Engineers, the National Academy of
Develop and report on criteria for design of slabs on Science, and the Department of Housing and Urban De-
grade, except highway and airport pavements velopment have developed guidelines for floor slab
design and construction. Several industrial associations,
1.2.2 ACI Committee 302-ACI Committee 302 de- such as the Portland Cement Association, the Wire Rein-
velops recommendations on the construction of floor forcement Institute, the Concrete Reinforcing Steel Inst-
slabs. ACI 302.2R, gives basic information, guidelines, itute, the Post-Tensioning Institute, as well as several
and recommendations on slab construction. It also con- universities and consulting engineers have studied slabs
tains information on thickness and finishing requirements on grade and developed recommendations on their de-
for different classes of slabs. sign and construction. In addition, periodicals such as
1.2.3 ACI Committee 325-ACI Committee 325 is Concrete Construction have continuously disseminated in-
concerned with structural design, construction, main- formation for the use of those involved with slabs on
tenance, and rehabilitation of concrete pavements. The grade. In developing this report, Committee 360 has
committee documents include ACI 325.1R on construc- drawn heavily from these contributions.
tion and ACI 325.3R on foundation and shoulder design.
1.2.4 ACI Committee 318-Although ACI 318 does 1.4-Design theories for slabs on grade
not specifically mention slabs on grade, the commentary 1.4.1 Introduction-Stresses in slabs on grade result
(ACI 318R) notes the exclusion of the soil-supported from both imposed loads and volume changes of the con-
slabs from various requirements in ACI 318 unless such crete. The magnitude of these stresses depends upon fac-
slabs transmit structural loads. Chapter 13 of ACI 318R tors such as the degree of continuity, subgrade strength
states: “. . . Also excluded are soil-supported slabs such and uniformity, method of construction, quality of con-
as ‘slab on grade’ which do not transmit vertical loads struction, and magnitude and position of the loads. In
from other parts of the structure to the soil.” The 318 most cases, the effects of these factors can only be
commentary Chapter 7 on shrinkage and temperature re- evaluated by making simplifying assumptions with respect
inforcement states that its provisions “. . . apply to to material properties and soil-structure interaction. The
structural floor and roof slabs only and not to soil- following sections briefly review some of the theories that
supported slabs, such as ‘slab on grade.“’ have been proposed for the design of soil-supported con-
1.2.5 ACI Committee 332-ACI Committee 332 de- crete slabs.
velops information on the use of concrete in residential 1.4.2 Review of classical design theories-The design
construction. Slabs on grade are important elements in methods for slabs on grade are based on theories origi-
such construction. However, residential slabs generally do nally developed for airport and highway pavements. An
not require detailed design unless poor soil conditions early attempt at a rational approach to design was made
are encountered. Residential slabs placed on poor soils, around 1920, when Westergaard’ proposed the so-called
such as expansive soils, and those slabs that support “corner formula” for stresses. Although the observations
unusual or heavy loads, require more thorough evalua- in the first road test with rigid pavements seemed to be
tion of soil properties and their interaction with the slab in reasonable agreement with the predictions of this for-
structure. mula, its use has been limited.
1.2.6 ACI Committee 336-ACI Committee 336 is Westergaard developed one of the first rigorous
concerned with design and related considerations of theories of structural behavior of rigid pavement in the
foundations which support and transmit substantial loads This theory considers a homogeneous, iso-
from one or more structural members. The design pro- tropic, and elastic slab resting on an ideal subgrade that
cedures for mat foundations are given in ACI 336.2R. exerts, at all points, a vertical reactive pressure pro-
Mat foundations are typically more rigid and more portional to the deflection of the slab. This is known as
heavily reinforced than common slabs on grade. a Winkler subgrade. The subgrade is assumed to act as
1.2.7 ACI Committee 330-ACI Committee 330 moni- a linear spring, with a proportionality constant k with
tors developments and prepares recommendations on units of pressure (pounds per square inch) per unit de-
design, construction, and maintenance of concrete formation (in inches). The units are commonly abbrevi-
parking lots. While the principles and methods of design ated as pci. This is the constant now recognized as the
in this ACI 360 report are applicable to parking lot coefficient of subgrade reaction, more commonly called
pavements, the latter have unique considerations that are the modulus of soil reaction or modulus of subgrade
covered in ACI 330R, which includes design and con- reaction.
struction as well as discussions on material specifications, Extensive investigations of structural behavior of
durability, maintenance, and repair of parking lots. concrete pavement slabs performed in the 1930s at the
Arlington, Virginia Experimental Farm and at the Iowa
1.3-Work of non-ACI organizations State Engineering Experiment Station showed good a-
Numerous contributions to knowledge of slabs on greement between observed stresses and those computed
360R-4 ACI COMMITTEE REPORT
by the Westergaard theory as long as the slab remained closely the response of real soils.
continuously supported by the subgrade. Corrections 1.4.3 Finite element method-The classical differential
were required only for the Westergaard corner formula equation of a thin plate resting on an elastic subgrade is
to take care of the effects of the slab curling above the often used to represent the slab on grade. Solution of the
subgrade. However, although a proper choice of the governing equations by conventional methods is feasible
modulus of subgrade reaction was found to be essential only for simplified models, where the slab and the sub-
for good agreement with respect to stresses, there grade are assumed to be continuous and homogeneous.
remained much ambiguity in the methods for experi- However, a real slab on grade usually contains discon-
mental determination of that correction coefficient. tinuities, such as joints and cracks, and the subgrade
Also in the 193Os, considerable experimental infor- support may not be uniform. Thus, the use of this ap-
mation accumulated to indicate that the behavior of proach is quite limited.
many subgrades may be close to that of an elastic and The finite element method can be used to analyze
isotropic solid. Two characteristic constants, typically the slabs on grade in general, and particularly those with
modulus of soil deformation and Poisson’s ratio, are used discontinuities. Various models have been proposed to
to evaluate the deformation response of such solids. represent the Typically, these models use combi-
Based on the concept of the subgrade as an elastic nations of various elements, such as elastic blocks, rigid
and isotropic solid, and assuming that the slab is of in- blocks, and torsion bars to represent the slab. The sub-
finite extent but of finite thickness, Burmister in 1943 grade is usually modeled by linear springs (the Winkler
proposed the layered-solid theory of structural behavior subgrade) placed under the nodal joints. While the finite
for rigid He suggested that the design should element method offers good potential for complex prob-
be based on a criterion of limited deformation under lems, its use in typical designs has been limited. Micro-
load. However, the design procedures for rigid pavements computers may enhance its usage and that of other nu-
based on this theory were never developed enough for merical methods in the future.
use in engineering practice. The lack of analogous solu-
tions for slabs of finite extent (edge and corner cases) 1.5-Overview of subsequent chapters
was a particular deficiency. Other approaches based on Chapter 2 identifies types of slabs on grade and ap-
the assumption of a thin elastic slab of infinite extent propriate design methods. Chapter 3 discusses the role of
resting on an elastic, isotropic solid have been developed. the subgrade and outlines methods for physical determin-
All of the preceding theories are limited to consid- ation of the modulus of subgrade reaction and other
eration of behavior in the linear range, where deflections, needed properties. Chapter 4 presents a discussion of
by assumption, are proportional to applied loads. various loads. Chapters 5 through 9 provide information
berg later proposed a strength theory based on the on design methods and the related parameters needed to
yield-line concept for ground supported slabs, but the use complete the design. Design examples in the appendix
of strength as a basis for the design of the slab on grade illustrate application of selected design methods.
is not common.
All existing theories can be grouped according to
models used to simulate the behavior of the slab and the CHAPTER 2-SLAB TYPES AND
subgrade. Three different models are used for the slab: DESIGN METHODS
the elastic-isotropic solid
l the thin elastic slab 2.1-Introduction
l the thin elastic-plastic slab. This chapter identifies and briefly discusses the
Two models used for the subgrade are the elastic-iso- common types of slab-on-grade construction and the de-
tropic solid and the so-called Winkler subgrade. Existing sign methods appropriate for each (Table 2.1). The un-
design theories are based on various combinations of derlying theory, critical pressures, and construction
these models. The methods presented in this report are features intrinsic to each method are identified. Methods
generally graphical, plotted from computer-generated presented are those attributed to the Portland Cement
solutions of selected models. Design theories need not be Wire Reinforcement Institute,’ United
limited to these combinations. As more sophisticated an- States Army Corps of Engineers,” Post-Tensioning In-
alyses become available, other combinations may well stitute’” and ACI 223.
become more practical. As stated in the basic definition of Section 1.1, a slab
In developing a reliable theory for the design of slabs on grade is one whose total loading, uniformly distrib-
on grade, major attention should be devoted to modeling uted, would impart a pressure to the grade or soil that is
the subgrade. Most currently used theoretical design less than 50 percent of the allowable bearing capacity
methods for the rigid pavements use the Winkler model, thereof. There are, of course, exceptions such as where
and a number of investigators report good agreement be- the soil is highly compressible and allowable bearing
tween observed response of rigid pavements and the pre- pressures are extremely low. Such situations are covered
diction based on that model. At the same time, the elas- in literature of the Post-Tensioning Institute.
tic-isotropic solid model can, in general, predict more Slab on grade is an all-encompassing term that in-
DESIGN OF SLABS ON GRADE 360R-5
cludes slabs for both heavy and light industrial usage, cracking, nor does it add significantly to the load-carrying
commercial slabs, apartment slabs, single-family dwelling capacity of a Type B slab. Committee 360 believes that
slabs, and others. Although the term also includes park- the best way to obtain increased flexural strength is to
ing lot slabs and paving surfaces, these are not specific- increase the thickness of the slab.
ally covered in this report. 2.2.3 Type C, shrinkage-compensating concrete slabs-
The shrinkage compensating-concrete used in these slabs
2.2-Slab types is produced either with a separate admixture or with
The six types of construction for slabs on grade iden- ASTM C-845 Type K cement which contains the expan-
tified in Table 2.1 are: sive admixture. This concrete does shrink, but first it
expands an amount intended to be slightly greater than
a) Plain concrete slab its drying shrinkage. Distributed reinforcement for tem-
b) Slab reinforced for shrinkage and temperature perature and shrinkage equal to 0.15 to 0.20 percent of
only the cross-sectional area is used in the upper half of the
c) Shrinkage-compensating concrete with shrinkage slab to limit the initial slab expansion and to restrain the
reinforcement slab’s subsequent drying shrinkage.
d) Slab post-tensioned to offset shrinkage Reinforcement must be stiff enough that it can be
e) Slab post-tensioned and/or reinforced, with active positively positioned in the upper half of the slab. The
prestress slab must be isolated from fixed portions of the structure,
f) Slab reinforced for structural action such as columns and perimeter foundations, with a com-
pressible material that allows the slab to expand.
Slab thickness design methods appropriate for each Type C slabs are designed to remain uncracked due
type are also shown in Table 2.1. Slab Types A through to loads applied to the slab surface. Thickness design is
E are designed with the assumption that applied loadings the same as for Type A and B slabs, but joints can be
will not crack the slab. For Type F the designer antici- spaced farther apart than in those slabs. Design concepts
pates that the applied loadings may crack the slab. and details are explained in ACI 223.
2.2.1 Type A, plain concrete slab-The design of this 2.2.4 Type D, slabs post-tensioned to offset shrinkage-
slab involves determining its thickness as a plain concrete Post-tensioned slabs are normally made with
slab without reinforcement; however, it may have ASTM C 150 Type I or Type II cement, following thick-
strengthened joints. It is designed to remain uncracked ness design procedures like those for Types A, B, and C.
due to loads on the slab surface. Plain concrete slabs do As explained in literature of the Post-Tensioning Inst-
not contain any wire, wire fabric, plain or deformed bars, itute,” post-tensioning permits joint spacing at greater
post-tensioning, or any other type of reinforcement. The intervals than for Type A, B, and C slabs. However, spe-
cement normally used is portland cement Type I or II cial techniques and sequences of post-tensioning the ten-
(ASTM C-150). The effects of drying shrinkage and uni- dons are required.
form subgrade support on slab cracking are critical to the The effective coefficient of friction (explained in
performance of these plain concrete slabs. To reduce Chapter 6), is critical to design of Type D slabs. Joint
drying shrinkage cracks, the spacing of contraction and/or spacing and amount of post-tensioning force required to
construction joints is limited. recommends joint offset later shrinkage and still leave a minimum compres-
spacings from 2 to 3 ft for each inch of slab thickness. sive stress are explained in Chapter 8 and Reference 11.
2.2.2 Type B, slab reinforced for shrinkage and temper- 2.2.5 Type E, slabs post-tensioned and/or reinforced,
ature only-These slabs are normally constructed using with active prestress-Type E slabs are designed to be un-
ASTM C-150 Type I or Type II cement. Thickness design cracked slabs, following PTI using active
is the same as for plain concrete slabs, and the slab is prestress, which permits the use of thinner slabs. Rein-
assumed to remain uncracked due to loads placed on its forced with post-tensioning tendons and/or mild steel re-
surface. Shrinkage cracking is controlled by a nominal or inforcement, Type E slabs may incorporate monolithic
small amount of distributed reinforcement placed in the beams (sometimes called ribs) to increase rigiditiy of the
upper half of the slab, and therefore joint spacings can section.
be greater than for Type A slabs. The Type E slab may be designed to accept structural
Joint spacings can be computed using the subgrade loadings, such as edge loadings from a building super-
drag equation (Chapter 6) for a pre-selected amount of structure, as well as to resist the forces produced by the
steel for shrinkage and temperature control; however, the swelling or shrinking of unstable soils.
amount of reinforcement area or steel stress is usually 2.2.6 Type F, slabs reinforced for structural action-
computed from a predetermined joint spacing. Unlike the previously described slab types, the Type F
The primary purpose of the reinforcement in the slab is designed with the assumption that it is possible for
Type B slab is to hold tightly closed any cracks that may the slab to crack under loads a plied to its surface. Pre-
form between the joints. The reinforcement must be stiff viously cited design are only appropriate up
enough so that it can be accurately located in the top to the level of loading that causes the cracking stress of
half of the slab. Reinforcement does not prevent the the concrete to be reached. Beyond this cracking level,
360R-6 ACI COMMITTEE REPORT
Table 2.1-Slab types with design methods suitable for each
DESIGN METHODS
TYPE OF SLAB CONSTRUCTION
PCA WRI COE PTI ACI
223
Thickness selection
TYPE A, PLAIN CONCRETE,
no reinforcement Related details
Thickness selection
TYPE B, REINFORCED
for shrinkage and temperature Related details
TYPE C, SHRINKAGE-
COMPENSATING CONCRETE with
shrinkage reinforcement Related details
Thickness selection
TcrYacPkE coDn, trPoOlST-TENSIONED for ........................... ...................................................................................................................................................................................................................................................... .................................... .................. ...... Related details
TreYinPfEo rcEe,d , PwOiSthT a-TctEivNeS pIOreNstEreDs sand/or .................. ................. ............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. . TRheliactkende dsse tsaeillsection
Thickness selection
TYPE F, REINFORCED for
structural action Related details
conventional reinforced concrete design methods should method’
be used. l The Wire Reinforcement Institute (WRI)
Type F slabs are typically built with portland cement, method’
Types I or II, and are reinforced with conventional mild l The The United_ _States Army Corps of Engineers
steel in the form of deformed bars or substantial wire (COE)
fabric. One or two layers of reinforcement may be used; l The Post-Tensioning Institute (PTI) method”
however, the steel must be carefully positioned according l The shrinkage-compensating concrete method
to design requirements. Since cracking is anticipated, (ACI 223)
joint spacings, usually set for crack control, are not Structurally active reinforcement and fiber rein-
critical, but they must be set to accommodate the con- forcement are also used in slabs on grade, but separate
struction process. design methods for them are not presented here.
All five methods have been used successfully, and
2.3-Design and construction variables Committee 360 considers all of the methods to be ac-
Design and construction of slabs on grade involves ceptable. The common objective of all the methods is to
both technical and human factors. The technical factors minimize cracking and produce the required flatness and
include loadings, support system, joint types and spacings, serviceability (see ACI 302).
the design method, the slab type, the concrete mix, and The design engineer has many choices when planning
the construction process. Human factors involve the a slab on as outlined in Table 2.1. Each
workers’ abilities, feedback to evaluate the construction method includes recommendations for joint type and
process, and anticipated maintenance procedures to com- spacing. The modulus of subgrade support and friction
pensate for cracking, curling, shrinkage, and other con- between the slab and its supporting grade are the two
ditions. most important parameters that tie slab types and design
These and other factors should be considered in methods together. Multiple combinations of concepts and
planning a slab. It is important to consider not just one methods on one job are not uncommon. Committee 360
or two items, but to look judiciously at the full set of believes there is no single correct or incorrect decision,
interactive variables? but rather several combinations of slab type and design
method, each with its own critical features. Each will pro-
2.4-Design methods duce a successful slab on grade if these features are
2.4.1 Introduction-Five basic slab design methods are properly handled.
discussed in this report: 2.4.2 Portland Cement Association (PCA) method-
* The Portland Cement Association (PCA) This slab design method, attributed to the Portland
DESIGN OF SLABS ON GRADE 360R-7
Cement Association, is a thickness selection process: in is handled by placing loads in categories and by using a
chart form for wheel loading, rack, and post loading; and design index category. This index internally fixes the
in tables for uniform loading (see examples in Appendix value for wheel area, wheel spacing, axle loading and
Al). Reinforcement is not required and is frequently not other constants. The safety factor is also built into the
used. When used, it is placed in the slab for crack con- nomograph.
trol, temperature effects and, in the case of dowels, for Appendix A3 illustrates the method and Table A3.1
load transfer at joints. shows the index categories.
The design is based on a computerized solution by 2.4.5 Post- Tensioning Institute (PTI) method-The
and uses influence charts by Pickett and Post-Tensioning Institute for the analysis and
with the concept of equivalent single wheel loading cen- design of slabs with applied post-tensioning forces de-
trally located at the interior of the slab.’ The slab an- velops strength requirements in terms of moments and
alyzed has a radius of three times the radius of relative shears. While post-tensioning is the intended technique,
* deformed steel bars, welded wire fabric, or a combination
of tendons and reinforcing steel can also be used.
The design procedure is intended for slabs lightly
reinforced against shrinkage effects, for slabs reinforced
The effect of slab discontinuities beyond this limit is not and stiffened with ribs or beams, and for structural slabs.
included in the charts. PCA suggests that the slab be Slabs supported on unstable soils are also covered. In this
strengthened at the joints to account for lack of contin- situation, it is the supporting soil itself that may cause a
uity. This is commonly done by thickening at edges or by loading on the slab.
use of smooth dowels or tie bars. The PTI method is based on a number of soil param-
2.4.3 Wire Reinforcement Institute (WRI) method- eters and a number of structural parameters and their in-
This method presents design nomographs for slab thick- teraction. Some key parameters are climate, differential
ness determination’ based on solutions using a discrete soil movement, a moisture stability index (known as the
element computer model for the concrete slab as a con- Thornthwaite moisture index), slab length and width,
tinuum on a Winkler foundation? The slab is represent- beam spacings, applied loadings, and the depth and width
ed by rigid bars for slab flexure, by torsion bars for slab of the stiffening beams (also known as ribs). One section
twisting, and by elastic joints for plate bending. Contin- of the PTI manual presents an equation-based procedure
uous support is provided by elastic spring constants at all for calculation of stresses caused by concentrated load-
joints. Design variables are the modulus of elasticity of ings on the interior of the slab perimeter. It is based on
the concrete the modulus of subgrade reaction, diameter the theory of beams on elastic foundations.” Its use is
of the loaded area, the spacing of the wheels, the con- illustrated in Appendix A4.
crete’s modulus of rupture and the selected factor of 2.4.6 ACI Committee 223 shrinkage-compensating con-
safety. The WRI method provides solutions for wheel crete method (ACI 223)-This design method is unlike
loading and for uniform loading with a variable aisle the previous four in that it does not deal directly with the
width. There is an additional aisle solution by slab thickness required for loads placed on the surface of
The WRI approach graphically accounts for the relative the slab, which must be handled by one of the other
stiffness between grade support and concrete slab in the methods shown in Table 2.1. Rather, it deals with the
determination of moments in the slab. Only loadings on critical aspects of concrete mix expansion and shrinkage.
the interior of the slab are considered. (See examples in ACI 223 specifies the proper amount of reinforcement,
Appendix A2.) in the form of reinforcing steel, and its location within
2.4.4 Corps of Engineers (COE) method-The Corps the depth of the slab for specific values of anticipated
of Engineersmethod is based on Westergaard’s form- expansion and shrinkage. Requirements for expansion
ulae for edge stresses in the concrete slab. In this ap- joints are stated, as are joint spacings.
proach, the ability to support the load using both the
unloaded slab and the loaded slab at the edge or joint in 2.5-Fiber-reinforced concrete (FRC)
question is included. The joint transfer coefficient ac- The use of fiber reinforcement in slabs on grade is
counts for this action. The coefficient value used by the increasing. Fiber materials in use include steel, poly-
COE method is 0.75; thus the load support is reduced by propylene, polyester, and polyethylene. While the design
25 percent at the joint. The COE method uses a concrete concepts used for other material options are also used
modulus of elasticity of 4000 ksi, a Poisson’s ratio of 0.20, for FRC slabs on grade, the potential increases in com-
an impact factor of 25 percent, and a safety factor of posite material properties, such as flexural strength and
approximately 2. Variables in the nomographs are modu- flexural fatigue endurance, are taken into consideration.
lus of rupture, subgrade modulus, and the load. Loading References 20,21, and ACI 544.4R provide additional in-
formation.
The radius of relative stiffness in inches is found by taking the fourth root of
2.6-Conclusion
the results found by dividing the concrete plate stiffness by the subgrade modulus
There is no single design technique that the
k.
ACI COMMITTEE REPORT
committee recommends for all applications. Rather, there subgrade material. Various laboratory tests can be per-
are a number of identifiable construction concepts and a formed in order to identify the soil. Soil classification is
number of design methods. Each combination must be based primarily on grain size and the Atterberg limits as
selected based on the requirements of the specific indicated in Table 3.2.2.
application. The following tests and test methods are helpful in
proper classification of soil:
CHAPTER 3-SOIL SUPPORT 1. Sample preparation - ASTM D 421
SYSTEMS FOR SLABS ON GRADE 2. Moisture content - ASTM D 2216
3. Specific gravity - ASTM D 854
3.1 Introduction 4. Material larger than #4 Sieve - ASTM C 127
Design of the slab on grade involves the interaction 5. Liquid limits - ASTM D 4318
of the slab and the soil support system to resist moments 6. Plastic limit - ASTM D 4318
and shears induced by the applied loads. Therefore, the 7. Shrinkage limit - ASTM D 427
properties of both the concrete and the soil are im- 8. Sieve analysis - ASTM D 422
portant. This chapter discusses soil support of the slab on 9. Standard Proctor density - ASTM D 698
grade only, including: 10. Modified Proctor density - ASTM D 1557
l types and properties of soil
l site testing for modulus of subgrade reaction A more detailed listing of the ASTM standards is given
l range of values for the subgrade modulus in Chapter 10.
l how to compact and stabilize soils
Foundation design is an independent topic, not included 3.3-Modulus of subgrade reaction
in this document. 3.3.1 Introduction-Design methods listed in Chapter
The soil support system usually consists of a base, a 2, including Westergaard’s pioneering work, use the mod-
sub-base and a subgrade, as illustrated in Fig. 3.1. If the ulus of subgrade reaction to account for soil properties
existing soil has the required strength and properties to in design. The modulus, also called the modulus of soil
support the slab, the slab may be placed directly on the reaction, is a spring constant that depends on the kind of
existing subgrade. However, the existing grade is not soil, the degree of compaction, and the moisture content.
normally at the correct elevation or slope. Therefore, The general procedure for static non-repetitive plate load
some cut or fill is required with the best of site selec- tests outlined in ASTM D 1196 provides guidance in the
tions. field determination of the subgrade modulus. However,
it is not specifically oriented to the determination of
3.2-Soil classification and testing modulus of subgrade reaction using a 30 in. diameter
There are many standards by which soils are clas- plate for the test. Therefore, a brief description of the
sified. The Unified Soil Classification System is used in procedure is given in Sec. 3.3.2.
this document. Table 3.2.1 provides information on this 3.3.2 Procedure for the field test-Remove loose ma-
classification system and some important properties of terial from the surface of the grade or subgrade for an
each soil class. For complete details, see ASTM D 2487. area 3 to 4 feet in diameter. Place a thin layer of sand or
The nature of the soil must be identified in order to plaster of paris over this area to assure uniform bearing
determine its suitability as either a base, a subbase, or a under the load plates. Then place three 1-in.-thick steel
plates, 30,24, and 18 inches in diameter, stacked concen-
trically pyramid fashion on this surface. Rotate the plates
Load
I on the bearing surface to assure complete contact with
the subgrade.
Attach a minimum of three dial gages to 18-ft deflec-
Slab
tion beams spanning across the load plates. Position the
three dial gages on the top of the 30-in. plate, 120
degrees apart, to record the plate deflection. Generally,
a heavy piece of construction equipment can provide the
8000-lb load required for the test. Place a hydraulic jack
on the center of the load plates and apply a proof load
of approximately 700 to 800 lb to produce a deflection of
approximately 0.01 in. Maintain this load until the settle-
ment is stabilized; then release the load and reset the
dial gages to zero.
After this preparation, the test is performed by apply-
ing a series of loads and recording the settlement of the
Fig. 3. l-Soil system support terminology plates. Generally, three load increments are sufficient.
DESIGN OF SLABS ON GRADE 360R-9
Table 3.2.1-Unified soil classification system, from Reference 22
FIELD IDENTIFICATION PROCEDURES GROUP
(Excluding particles larger than 3 inches, and basing fractions on estimated weights) SYMBOL TYPICAL NAMES
Wide range in grain size and Well graded gravels, gravel-
CLEAN substantial amounts of all GW sand mixtures, little or no fines
GRAVELS intermediate particle sizes
GRAVELS (Little or no Predominantly one size or a Poorly graded gravels, gravel-
More than half of fines) range of sizes with some inter- GP sand mixtures, little or no fines
coarse fraction is mediate sizes missing
larger than No. 4 Non-plastic fines (for identifi- Silty gravels, poorly graded
sieve* GRAVELS WITH cation procedures see CL GM gravel-sand-silt mixtures
FINES below.)
COARSE (Appreciable Plastic fines (for i dentif ication Clayey gravels, poorly graded
GRAINED SOILS amount of fines) procedures see ML below) GC gravel-sand-clay mixtures
(More than half of
material is larger Wide range in grain sizes and Well graded sands, gravelly
than No. 200 substantial amounts of all SW sands, little or no fines
sieve*) CLEAN SANDS intermediate particle sizes
SANDS (little or no fines) Predominantly one size or a Poorly graded sands, gravelly
More than half of range of sizes with some in- SP sands, little or no fines
coarse fraction is termediate sizes missing
smaller than No. SANDS WITH Non-plastic fines (for identifi- Silty sands, poorly graded
4 sieve* FINES cation procedures see ML SM sand-silt mixtures
(appreciable below)
amount of fines) Plastic fines (for identification Clayey sands, poorly graded
procedures see CL below) SC sand-clay mixtures
Identification procedures on fraction smaller than no. 40 sieve
DRY
STRENGTH GROUP TYPICAL NAMES
(crushing SYMBOL
characteristics)
SILTS AND Inorganic silts and very fine
CLAYS, liquid None to slight Quick to slow ML sands, rock flour, silty or clayey
limit less than 50 fine sands with slight plasticity
FINE GRAINED Inorganic clays of low to medi-
SOILS (more than Medium to high um plasticity, gravelly clays,
half of material is CL sandy clays, silty clays, lean
smaller than No. clays
200 sieve*) Slight to Organic silts and organic-silt
medium OL clays of low plasticity
Slight to Inorganic silts, micaceous or
medium MH diatomaceous fine sandy or silty
SILTS AND soils, elastic silts
CLAYS, liquid High to Inorganic clays of high plasticity,
limit greater very high CH fat clays
than 50 Medium to Organic clays of medium to high
high OH plasticity
Readily identified by color, odor, spongy fell; frequently Peat and other highly organic
, , ,
HIGHLY ORGANIC SOILS by fibrous textures texture PT soils
* NOTES: All sive sizes here are US. standard. The No. 200 sieve is about the smallest particle visible to the naked eye. For visual cIassifications,the size
may be used as equivalent for the No.4 sieve size. BOUNDARY CLASSIFICATIONS: Soils possessingcharacteristicsof two groups are designated by combinations
of group symbols.
The load should be maintained until the rate of settle- modified modulus of subgrade reaction, based on a 12-
ment, an average recorded by dial gages is less than 0.001 in.-diameter plate test, can also be used to design slabs
in. per minute. The data should then be plotted on a on grade. The modified modulus test is less expensive to
load deflection graph and the modulus of subgrade re- perform, and the value for a given soil is twice that of
action k determined. The value of k is calculated as 10 the standard modulus.
divided by the deformation produced by a 10 psi load. (A 3.3.4 Influence of moisture content-The moisture
7070-lb load produces 10 psi on a 30-in. plate.) If the dial content of a fine-grained soil affects the modulus of
gages are not zeroed before the test is run, an adjustment subgrade reaction both at the time of testing and during
to the curve is required to make it intersect the origin as th.e service life of the slab. For example, if the field test
shown in Fig. 3.3.2. The calculation for k is also shown. for a modulus of subgrade reaction is performed on a
3.3.3 Modified modulus of subgrade reaction-A clay stratum with a liquid limit (LL) less than 50 and a
360R-10 ACI COMMITTEE REPORT
Table 3.2.2- Laboratory classification criteria for soils, from Reference 22
Group
Major Divisions Symbols Typical Names Laboratory Classification Criteria
Well-graded gravels, gravel-sand mix- greater than 4; - - between 1 and 3
tures, little of no fines x
Poorly graded gravels, gravel-sand mix-
Not meeting all gradation requirements for GW
turet, little or no fines
,
Silty gravels, gravel-sand-silt mixtures Atterberg limits below Above "A" line with P.I.
"A" line or P.I. less than 4 between 4 and 7 are border-
’
line cases requiring use Of
Clayey gravels, gravel-sand-clay mix- Atterberg limits below “A” dual symbols
tures line with P.I. greater than 7
Well-graded sands, gravelly sands, little =- greater than 6; = - between 1 and 3
or no fines
x
Poorly graded sands, gravelly sands, Not meeting all gradation requirements for SW
little or no fines
“ 0 %
Silty sands, sand-silt mixtures Atterberg limits above “A” Limits plotting in hatched
line or P.I. less than 4
zone with P.I. between 4
SC Clayey sands, sand-clay mixtures A ettbregr Atterberg limits above “A” arenqdu 7ir ianrge ubsoer deorfl indeu acl assyems-
line with P.I. greater than 7 bols
Inorganic silts and very fine sands,
ML rock flour, silty or clayey fine sands,
or clayey silts with slight plasticity
Plasticity Chart
Inorganic clays of low to medium
CL plasticity, gravelly clays, sandy clays, 60
8
silty clays, lean clays
. .
OL Organic silts and organic silty clays of 50
low plasticity
40
Inorganic silts, micaceous or diatoma-
30
MH ceous fine sandy or silty soils, elastic
silts
ii;;; CH Inorganic clays of high plasticity, fat 20
clays
c OH Organic clays of medium to high 1O
plasticity, organic silts
Liquid limit
Pt Peat and other highly organic soils
of GM and SM groups into subdivisions of d and u are for roads and airfields only. Subdivision is based on Atterberg limits; suffix d used when
L .L. is 28 or l ess and the P.I. is 6 or less; the suffix u used when L.L.is greater than 28.
example:
GW-GC, well-graded gravel-sand mixture with clay binder.
