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Settlement Uncertainty Analysis for Continuous Spread Footing on Elastic Soil

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Abstract

In conventional design, continuous spread footings are always designed on the basis of their transverse behavior, where the natural variability of soil properties and any uncertainties in the geometrical and mechanical properties of the structure are usually not considered. In order to reveal the effects of these uncertainties and the soil variability on the behavior of spread footings, the longitudinal direction needed to be studied. Numerous mechanical models, which describe the soil-structure interaction as a beam on elastic foundation, were developed. The common parameter between these models is the subgrade reaction coefficient which depends on numerous parameters. In this paper, the FOSM method was used, first on four semi-empirical models which give the subgrade reaction coefficient, and secondly on the analytical solution of a beam from Winkler’s hypothesis including different boundary conditions. Uncertainties in the subgrade reaction coefficient, differential settlement and bending moment were obtained for the following case: continuous wall footing in residential construction, where a low stiffness zone or shrinkage of clayey soil is possible. Results from a global uncertainty analysis demonstrated the major effects of uncertainties in soil modulus; Poisson’s ratio and width of the spread footing on the uncertainty of the subgrade reaction coefficient, and thus on uncertainties of the differential settlement and bending moment. Finally, it was shown that when the soil modulus and geometrical dimensions of the foundations are uncertain and where a zone of weak soil or shrinkage of clayey soils are present, the longitudinal behavior of continuous spread footings for residential construction should also be considered in their design.

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Abbreviations

k s :

Coefficient of subgrade reaction (or constant of proportionality of Winkler)

w(x):

Vertical displacement (settlement)

p(x):

Reactive pressure of the foundation

k 1 :

Second foundation parameter

E c I :

Constant bending stiffness of the beam (E c and I are respectively the Young’s modulus of concrete and the moment of inertia of the cross section of the foundation)

q(x):

Transversal continuous load

w 0(x):

Homogeneous solution of the differential equation of foundation

w q (x):

Particular solution of the differential equation of foundation

M(x):

Bending moment

V(x):

Shear force

E s :

Soil Young modulus

ν s :

Poisson’s ratio of soil

b :

Width of the foundation

h :

Height of the foundation

E c :

Young’s modulus of the concrete

µ :

Non-dimensional parameter

E PMT :

Ménard’s pressuremeter modulus

α :

Structural or rheological coefficient

B 0 :

Reference width of the foundation

λ c and λ d :

Form factors of the foundation geometry

f(x):

Studied function

\(\overline{x}\) :

Mean of the input variable

\(f^{'} (\overline{x} )\) :

First derivative of the studied function

\(V\left[ x \right]\) :

Variance of the input variable

\(V\left[ {f(x)} \right]\) :

Variance of the studied function

\(f^{''} (\overline{x} )\) :

Second derivative of function \(f(x)\)

\(\beta (1)\) and \(\beta (2)\) :

Are the coefficients of skewness and kurtosis, respectively

\(CV_{f(x)} (x_{i} )\) :

Coefficient of variation of \(f(x)\) for the i input variables (x i )

\(CV_{{x_{i} }}\) :

Coefficient of variation for the input variable i

\(\overline{x}_{i}\) :

Mean of the input variables i

\(\overline{f(x)}\) :

Mean of the function f(x)

n :

Number of variables

\(CV_{w}\) :

Coefficient of variation of the maximum deflection

max(w):

Value of the maximum deflection for a given value of k s and corresponding to a abscissa x max(w) considered as constant over the range of variation of k s

CV M :

Coefficient of variation of the maximum bending moment of the foundation

max(M):

Value of the maximum bending moment for a given value of k s and corresponding to a abscissa x max(M) considered as constant over the range of variation of k s

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Author notes

  1. S. Imanzadeh

    Present address: INSA de Rouen, LOFIMS, Av. de l’Université - BP 08, 76801, Saint-Étienne-du-Rouvray, France

Authors and Affiliations

  1. Université de Bordeaux, UMR 5295 -I2M- Département GCE, Av.des facultés, 33405, Talence Cedex, France

    S. Imanzadeh, A. Denis & A. Marache

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Correspondence to A. Marache.

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Imanzadeh, S., Denis, A. & Marache, A. Settlement Uncertainty Analysis for Continuous Spread Footing on Elastic Soil. Geotech Geol Eng 33, 105–122 (2015). https://doi.org/10.1007/s10706-014-9828-6

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