3471
Characterization of Model Uncertainty in Immediate Settlement Calculations for
Spread Footings on Clays
Caractérisation de l'incertitude des modèles de calculs du tassement immédiat de semelles
reposant sur des sols argileux
Strahler A.W., Stuedlein A.W.
Oregon State University
ABSTRACT: Immediate settlement calculations for spread footings supported by clay soils are generally based on displacement
influence factors derived from elastic stress fields and soil stiffness estimated from triaxial compression strength tests or correlations
to various measureable characteristics such as plasticity, strength, or stress history. As a consequence of the linear elastic design
models, curvature in load-displacement behaviour cannot be characterized unless the stiffness degradation of the subgrade is explicitly
incorporated. This paper uses a load test database of spread footings on clay to evaluate the accuracy of an elasticity-based immediate
settlement estimation method, which was shown to significantly reduce in accuracy with increasing magnitudes of displacement and
exhibit significant variability. A method to predict immediate settlements using a non-linear constitutive model set within an elastic
stress field is presented, and is shown to capture the general non-linear shape of footing load tests and maintain its accuracy over a
broad range in displacements with similar uncertainty to that of the elasticity-based method. Recommendations are made to estimate
an appropriate initial stiffness for use with non-linear and linear elastic models based on back-calculated undrained soil modulus.
RÉSUMÉ: Les modèles acceptés de prévision du tassement immédiat des semelles de fondation reposant sur les sols argileux sont
généralement basés sur des facteurs d'influence de déplacement calculé à partir de champs de contraintes élastiques en conjonction
avec la rigidité du sol estimée à partir d’essais triaxiaux, ou de corrélations avec des paramètres mesurables comme l’indice de
plasticité, la résistance au cisaillement non drainé, et la contrainte de préconsolidation. En raison de l'utilisation de modèle élastique
linéaire, la non-linéarité de la relation charge-déplacement ne peut pas être caractérisée sauf si la dégradation de la rigidité du sol de
fondation est incorporée explicitement dans le modèle. Cet article utilise une base de données d’essais de chargement de semelles sur
des sols argileux afin d’évaluer la précision d'une méthode d'estimation du tassement immédiat en élasticité. La performance de cette
méthode en termes de précision se dégrade sérieusement avec l'augmentation du déplacement. Elle est aussi caractérisée par une
grande variabilité. Dans cet article, une méthode de prévision des tassements immédiats à l'aide d'un modèle de comportement non
linéaire en champ de contrainte élastique est présentée. On montre qu'elle reproduit la forme générale non linéaire des essais de
chargement de semelles de fondation et qu'elle présente une bonne précision sur un grand intervalle de déplacements avec une
incertitude similaire à celle de la méthode basée sur l'élasticité. Des recommandations ont été faites pour estimer le module initial
utilisé avec les modèles élastiques non linéaires et linéaires qui sont fonction des modules de sols non drainés obtenus par retro-
calculs.
KEYWORDS: elastic settlement, settlement, shallow foundations, clay soils, undrained loading.
1 INTRODUCTION
Spread footings are used throughout the world as viable
foundation support systems for structures. They are typically
constructed of reinforced concrete, can assume any shape, and
generally meet the following criteria (Vesic, 1973; Das, 2011):
1. The depth of footing embedment,
D
f
, lies between the
ground surface and up to four times the footing width,
B
, below
the adjacent grade, and
2. Additional support, such as driven piles or drilled shafts,
are not located beneath the footing.
Designers must evaluate two conditions to ensure that the
foundation will perform adequately (Perloff and Baron, 1976):
safety against overall bearing failure in the supporting soil, and
displacements leading to unsatistfactory structural performance
must not occur. The first condition is often considered the most
critical limit state; however, immediate settlement can lead to a
serviceability limit state and must be included in design.
Generally accepted methods for estimating immediate
settlement of spread footings require the use of linear elastic
models to simulate soil behavior; this approach does not capture
the true non-linear behavior of soil. This study presents a
statistical evaluation of a commonly used elasticity-based
method and soil stiffness correlation using a load test database.
Then, a simple non-linear model capturing observed load-
displacement curvature in footing load tests is presented and its
accuracy is characterized. The undrained initial elastic modulus
is back-calculated using the load test database, and is found to
vary as a function of overconsolidation ratio.
2 IMMEDIATE SETTLEMENT OF SHALLOW
FOUNDATIONS ON CLAY
2.1
Elasticity-based design methodology
Carrier and Christian (1978) found that stress distributions
developed from finite element analyses (FEA) used in
conjunction with embedment factors proposed by Burland
(1970) produced the most reasonable values of displacement
assuming an undrained Poisson’s ratio,
ν
s
, equal to 0.5 for clay.
Mayne and Poulos (1999) modified Burland’s work and
developed an improved distortion settlement estimation
approach for circular foundations that accounts for variations in
Poisson’s ratio, soil modulus, foundation rigidity, and
embedment effects. The resulting expression for immediate
settlement can be constructed as (Mayne and Poulos 1999):
2
1
app eq E F G
i
s
s
q B I I I
E
(1)
where
q
app
= applied bearing stress,
B
eq
= equivalent diameter of
the footing,
I
E
,
I
F
,
I
G
are displacement influence factors that
control the magnitude of displacement (described below), and
E
s
is the Young’s modulus of the soil.
The stresses below a spread footing, and therefore the
immediate settlement, are affected by the amount of footing
embedment. Burland’s embedment influence factor,
I
E
, is used
to modify the stress distribution for embedment effects.
