Stresses in Foundation Soils Due to Vertical Subsurface Loading

Abstract

Synopsis Based on the work of R. D. Mindlin solutions have been obtained for the stresses created by vertical subsurface loading in a semi-infinite, homogeneous, isotropic, elastic medium obeying Hooke's law. The original Mindlin solution and two extensions of it have been considered and the results are presented in the form of dimensionless stress coefficients. For practical application the complex expressions for the vertical-stress coefficients have been evaluated by electronic computer and the results given in tabular form. Coefficients for the other stress components are presented for positions lying on the axis of loading. The results of the vertical-stress computations are compared with those resulting from using the Boussinesq expression as if it applied to subsurface loading. From the results it can be deduced that such a misuse of the Boussinesq equation may give rise to over-estimates of up to 180% for the range of parameters with which calculations have been performed. Des solutions baseés sur le travail de R. D. Mindlin ont été obtenues pour les contraintes crées par chargement vertical de sous-sol dans un milieusemiillimité homogène, isotropique, eĺastique conforme à la loi de Hooke. La solution originale de Mindlin et deux de ses corollaires ont été considérées et les résultats sont présentésous la forme de coefficients de contrainte sans dimension. Pour l'application pratique les expressions complexes des coefficients de contrainte verticale ont été évaluées par calculatrite électronique et lés résultats sont donnés sous forme tabulaire. Les coefficients pour les autres composants de contrainte sont présentés pour des positions prises sur l'axe de chargement. Les résultats des calculs de contrainte verticale sont comparés à ceux obtenus en utilisant l'expression Boussinesq comme si elle s'appliquait à un chargement de sous-sol. D'après les résultats on peut déduire qu'un tel mésusage de l'équation Boussinesq peut causer des surestimations atteignant 180% de la gamme des parametres avec lesquels les calculs ont été faits.

Stresses due to vertical subsurface loading for an inhomogeneous cross‐anisotropic half‐space

“…The numerical results are in good agreement with the Mindlin's [3] and Geddes's solutions [5] when the medium is homogeneous and isotropic (as seen in Figure 6 in the illustrative examples section), and with Wang's solutions [7] when the medium is homogeneous but cross-anisotropic (as seen in Figures 7-9 in the Illustrative Examples section).…”

“…where x is a singular point; a; b are the lower, upper limit, respectively; e is a tiny parameter with respect to the integral interval b À a: Thus, the stresses for an end-bearing pile in the inhomogeneous and cross-anisotropic halfspace, as seen in Figure 2, can be obtained by substituting Z by L in Equation (5). The numerical results are in good agreement with the Mindlin's [3] and Geddes's solutions [5] when the medium is homogeneous and isotropic (as seen in Figure 6 in the illustrative examples section), and with Wang's solutions [7] when the medium is homogeneous but cross-anisotropic (as seen in Figures 7-9 in the Illustrative Examples section).…”

Surface displacements due to batter piles driven in cross‐anisotropic media

“…Furthermore, since the assumptions inherent in the analyses, vertical surface displacements for compound forms of loading can be acquired by superposition. With results from the three types of loadings analysed a great deal of loadings can be treated [14]. For instance, in the case of a friction load varying linearly from a maximum at the ground surface to zero at the pile length L, the solution, u d z(oblique) , is obtained from the following relationship:…”

“…Normally, for a friction pile, load distributions around the pile shaft are due to the shear forces acting along the interface of the pile and the soil [13]. The loads practically could be considered as a uniformly or linearly varying distributed with depth from the surface to the pile length [13,14]. However, for an end-bearing pile, which relies primarily on the concentrated soil resistance at the tip of the pile, and the tip's resistance, could be modelled as a point load [11].…”

“…At present, only vertical stress solutions for batter piles subjected to an embedded point load, a uniform skin friction, and a linear variation of skin friction in an isotropic medium were proposed by Ramiah and Chickanagappa [13]. In their solutions, the extension of Geddes's solution [14] by an oblique co-ordinate system instead of the usual Cartesian one was utilized. Therefore, Mindlin's solution [17] was modified with respect to the new co-ordinate system, and closed-form expressions were derived for the three above-mentioned loading conditions.…”