—Work of non-ACI organizations

360R-4 ACI COMMITTEE REPORT
and magnitude and position of the loads. In most cases, the
effects of these factors can only be evaluated by making
simplifying assumptions with respect to material properties
and soil-structure interaction. The following sections briefly
review some of the theories that have been proposed for the
design of soil-supported concrete slabs.
1.4.2 Review of classical design theories—The design
methods for slabs-on-ground are based on theories originally
developed for airport and highway pavements. An early
attempt at a rational approach to design was made around
1920, when Westergaard (1926) proposed the so-called
“corner formula” for stresses. Although the observations in
the first road test with rigid pavements seemed to be in
agreement with the predictions of this formula, its use has
been limited.
Westergaard developed one of the first rigorous theories of
structural behavior of rigid pavement in the 1920s (Westergaard
1923, 1925, 1926). This theory considers a homogeneous,
isotropic, and elastic slab resting on an ideal subgrade that
exerts, at all points, a vertical reactive pressure proportional
to the deflection of the slab. This is known as a Winkler
subgrade (Winkler 1867). The subgrade acts as a linear
spring, with a proportionality constant k with units of pres-
sure (lb/in.
2
[kPa]) per unit deformation (in. [m]). The units
are commonly abbreviated as lb/in.
3
(kN/m
3
). This is the
constant now recognized as the coefficient (or modulus) of
subgrade reaction. Extensive investigations of structural
behavior of concrete pavement slabs performed in the 1930s
at the Arlington Virginia Experimental Farm and at the Iowa
State Engineering Experiment Station showed good agreement
between observed stresses and those computed by the
Westergaard theory, as long as the slab remained continuously
supported by the subgrade. Corrections were required only
for the Westergaard corner formula to account for the effects
of slab curling and loss of contact with the subgrade.
Although a proper choice of the modulus of subgrade
reaction was essential for good agreement with respect to
stresses, there remained much ambiguity in the methods for
experimental determination of that correction coefficient.
Also in the 1930s, considerable experimental information
was accumulated that showed that the behavior of many
subgrades may be close to that of an elastic and isotropic
solid. Two characteristic constants—the modulus of soil
deformation and Poisson’s ratio—are typically used to evaluate
the deformation response of such solids.
Based on the concept of the subgrade as an elastic and
isotropic solid, and assuming that the slab is of infinite extent
but of finite thickness, Burmister, in 1943, proposed the
layered-solid theory of structural behavior for rigid pavements
(Burmister 1943) and suggested that the design be based on
a criterion of limited deformation under load. The design
procedures for rigid pavements based on this theory,
however, were not sufficiently developed for use in engineering
practice. The lack of analogous solutions for slabs of finite
extent (edge and corner cases) was a particular deficiency.
Other approaches based on the assumption of a thin elastic
slab of infinite extent resting on an elastic, isotropic solid
have also been developed. The preceding theories are limited
to consideration of behavior in the linear range, where
deflections are proportional to applied loads. Lösberg
(Lösberg 1978; Pichaumani 1973) later proposed a strength
theory based on the yield-line concept for ground-supported
slabs, but the use of strength as a basis for the design of the
slab-on-ground is not common.
All existing theories can be grouped according to models
used to simulate the behavior of the slab and the subgrade.
Three different models are used for the slab:
• Elastic-isotropic solid;
• Thin elastic slab; and
• Thin elastic-plastic slab.
The two models used for the subgrade are:
• Elastic-isotropic solid; and
•
Winkler.
The Winkler subgrade models the soil as linear springs so
that the reaction is taken proportionally to the slab deflection.
Existing design theories are based on various combinations
of these models. The methods included in this guide are
generally graphical, plotted from computer-generated solutions
of selected models. Design theories need not be limited to
these combinations. While the elastic-isotropic model
provides closer prediction for the response of real soils, the use
of the Winkler model is almost universally used for design,
and a number of investigators have reported good agreement
between observed responses to the Winkler-based predictions.
1.4.3 Finite-element method—The classical differential
equation of a thin plate resting on an elastic subgrade is often
used to represent the slab-on-ground. Solving the governing
equations by conventional methods is feasible only for
simplified models where the slab and subgrade are assumed
to be continuous and homogeneous. In reality, however, a
slab-on-ground usually contains discontinuities, such as
joints and cracks, and the subgrade support may not be
uniform. Thus, the use of this approach is quite limited.
The finite-element method can be used to analyze slabs-
on-ground, particularly those with discontinuities. Various
models have been proposed to represent the slab (Spears and
Panarese 1983; Pichaumani 1973). Typically, these models
use combinations of various elements, such as elastic blocks,
rigid blocks, and torsion bars, to represent the slab. The
subgrade is usually modeled by linear springs (the Winkler
subgrade) placed under the nodal joints. While the finite-
element method offers good potential for complex problems,
graphical solutions and simplified design equations have
been traditionally used for design. The evolution of modern
computer software has made modeling with finite elements
more feasible in the design office setting.

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