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Bounding solutions for the pressuremeter modulus using variational principles in elasticity
Author(s) -
Dormieux L.
Publication year - 1992
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.1610160502
Subject(s) - shear modulus , bounding overwatch , anisotropy , mathematics , plane stress , upper and lower bounds , bulk modulus , young's modulus , modulus , elastic modulus , geotechnical engineering , mathematical analysis , finite element method , mechanics , materials science , geometry , geology , physics , composite material , thermodynamics , computer science , quantum mechanics , artificial intelligence
It is classically assumed that the pressuremeter modulus (determined from the initial slope of the pressuremeter expansion curve) can be used as an estimate for the soil's shear modulus, provided disturbance effects can be neglected. This approximation is only rigorous in the plane‐strain case and requires that the height of the cell be large in comparison with its diameter. The present paper allows to quantify the error that results from this approximation as a function of the height over diameter ratio. The analysis is based on an application of the variational principles of elasticity. It is shown that the static and the kinematic approaches lead, respectively, to a lower‐ and an upper‐bound estimate of the pressuremeter modulus expressed in terms of the soil's elastic coefficients. The calculations are completely carried out in the case of an infinite cavity subjected to a pressure on a finite length. It is shown that the plane‐strain approximation overestimates the shear modulus. Based on the kinematic approach, a method is developed to derive the shear modulus from the pressuremeter modulus which accounts for the finite slenderness of the cell. This method can be extended to more complex geometries and material properties, including soil heterogeneity and anisotropy.