Rigid Footing Research Articles

Response of Circular Footings to Vertical Vibrations

In this paper, analog solutions are presented for the response of a circular footing resting on an elastic half-space with uniform and parabolic contact pressure distributions and subjected to frequency dependent and frequency independent excitations. In addition, an analog solution to a rigid circular footing subjected to frequency dependent excitation is also presented. The results have been compared with the rigorous solution of Sung and the agreement is found to be good.

Strip foundations on a cross-anisotropic soil layer subjected to dynamic loading

A rigorous semi-analytical formulation is presented to study the static and dynamic response of rigid strip footings supported on the surface of a horizontally layered soil deposit. Each layer is modelled as a homo- geneous cross-anisotropic medium with a vertical axis of material symmetry while the loading consists of har- monically time-varying horizontal or vertical forces and moments. The solution, based on an experimentally verified relationship among the anisotropic soil para- meters that uncouples the wave equations in closed- form, is exact in that it properly accounts for the true boundary conditions at the layer interfaces and the surface. Comprehensive parametric studies are presented in the form of normalized displacement-load or rota- tion-moment ratios as functions of dimensionless geo- metric and material parameters. Simple and sufficiently accurate formulas ofdirect practical applicability are also given for static displacements and resonant frequency factors. The results clearly demonstrate the significance of soil anisotropy in determining undrained static and dynamic response of foundations; soils with a large ratio of horizontal to vertical Young’s moduli experience smaller static displacements and quite different dynamic response characteristics from equivalent isotropic soil deposits. L'article présente une formulation semi-analytique rigoureuse pourétudier la réponse dynamique et statique de semelles Mantes rigide reposant à la surface de sédiments de sob a couches horizontales. Chaque couche est modélisée sous la forme d'un milieu homogéne de section anisotrope ayant un axe vertical de symétrie matérielle, tandis que la charge est constituée de forces et moments verticauxou horizontaux à variation harmonique dans le temps. La solution, basée sur une relation vérifiée expérmentalement entre les paramétres de sots anisotropes qui découple les équations d'onde de forme fermée, est exacte en ce qu'elle tient bien compte des conditions de hmite vraie aux interfaces des couches et à la surface. L'article presente des études paramétriques complétes sous la forme de rapports rotation-moment ou déplacement-charge normalisés en tant que fonctions de paramétres matériels et géomitriques adimensionnels. L'article prtsente également des formules simples et suffisamment precises ayant une application pratique directe pour des facteurs de fréquence de résonance et des déplacements statiques. Les résultats montrent bien I'importance que représente l'anisotropie des sols pour la détermination de la reponse dynamique et statique non drainée de fondations; dans le cas de sob dont le rapport desmodules d'élasticite de Young horizontal/vertical est important, les déplacements statiques sont moindres et les caractéristiques de résponse dynamique sont totalement differents de celles de sédiments de sols isotropiques équivalents.

Consolidation of Anelastic Porous Media

The transient response of saturated anelastic porous media is analyzed. The porous skeleton is modeled as a piecewise linear time-independent solid, and the fluid is assumed to behave macroscopically, like a perfect fluid. The coupled field equations are presented and solved numerically by the use of the finite element method. The numerical stability of the proposed time integration scheme is investigated. The use of the proposed formulation for solving boundary value problems is illustrated by applying it to analyze the one- and two-dimensional consolidation of a linear elastic porous medium. Good agreement between numerical and analytical results is obtained. Further, the formulation allows solutions to be obtained for cases in which large strains/deformations occur in the porous medium. Finally, the use of the proposed formulation is illustrated by applying it to analyze the time-dependent response of a rigid footing.

Stresses for an elastic half-space uniformly indented by a rigid rectangular footing. Short communication : Int J Num Anal Meth Geomech, V4, N3, July–Sept 1980, P277–284

Stresses for an elastic half-space uniformly indented by a rigid rectangular footing. Short communication : Int J Num Anal Meth Geomech, V4, N3, July–Sept 1980, P277–284

Stresses for an elastic half‐space uniformly indented by a rigid rectangular footing

International Journal for Numerical and Analytical Methods in GeomechanicsVolume 4, Issue 3 p. 277-284 Short Communications Stresses for an elastic half-space uniformly indented by a rigid rectangular footing S. J. Mullan, S. J. Mullan Carnegie-Mellon University, Pittsburgh, Pennsylvania, U.S.A.Search for more papers by this authorG. B. Sinclair, G. B. Sinclair Carnegie-Mellon University, Pittsburgh, Pennsylvania, U.S.A.Search for more papers by this authorP. W. Brothers, P. W. Brothers Department of Scientific and Industrial Research, Lower Hutt, New ZealandSearch for more papers by this author S. J. Mullan, S. J. Mullan Carnegie-Mellon University, Pittsburgh, Pennsylvania, U.S.A.Search for more papers by this authorG. B. Sinclair, G. B. Sinclair Carnegie-Mellon University, Pittsburgh, Pennsylvania, U.S.A.Search for more papers by this authorP. W. Brothers, P. W. Brothers Department of Scientific and Industrial Research, Lower Hutt, New ZealandSearch for more papers by this author First published: July/September 1980 https://doi.org/10.1002/nag.1610040306Citations: 6AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Citing Literature Volume4, Issue3July/September 1980Pages 277-284 RelatedInformation

Yield Line Analysis of Square Footings

The yield line theory has proved to be quite accurate in determining the strength of reinforced concrete slabs. It has also been found to be more accurate than other methods for analysis of square footings. However, computations by the yield line theory involve some effort. Thus, curves have been included here for determining yield moments in square footings subjected to axial loads assuming soil pressures to be uniform as well as parabolic. These are intended as a design aid. Effect of parabolic soil pressure distribution on footing size and yield moment has also been considered. Design moments can be easily determined on the basis of yield line theory by using moment curves for uniform as well as parabolic soil pressure distributions. It is evident that for n 1 (rigid footing on cohesionless soil) footing area increases and moment reduces. In the latte case these changes are smaller than the former. Also percentage change in moment is much smaller than the change in footing size. (Author)

Stress Transmission in Granular Media

An attempt is made to bring out the contribution of the material parameter E/G (E-Young's modulus, G- Shear modulus), by presenting graphically some of the pertaining numerical results as a supplement to earlier work (by the same author) using the model E/G greater than 1(1+mu) where mu-Poisson's ratio of the material in state. In the study of the stress distribution problems the effect of the material parameter E/G and of limited thickness of a compressive layer, d, have been examined. The results lead to the following conclusions: development of the onion-shaped pressure bulb depends on the E/G ratio but is only slightly affected by mu; the concentration of stresses around the loading area increases as the material parameter E/G increases. Increase in E/G value represents increase in looseness/softness of the medium; normal stresses on the axis depend on the thickness of the medium and d/a ratio (a-radius of the rigid circular footing) but are only slightly affected by the nature of the contact surface. Thus the E/G values are an effective measure of the state of the medium which influences the stress transmission in materials other than solids.

Elastic solutions for the design and analysis of rock-socketed piles

This paper gives elastic solutions for the following: (i) settlement of a shear socket; (ii) settlement reduction due to recessment of a shear socket in a shaft; (iii) settlement reduction of flexible or rigid footings due to recessment in a shaft; (iv) load distribution in a rock socket; and (v) settlement of a rock socket.This paper illustrates the use of these solutions in the design of socketed piles and in the back-analysis of field tests on rock sockets.

Dynamic Response of Pile Foundations in Torsion

A theory is presented which facilitates the evaluation of torsional stiffness and damping of piles embedded in horizontally layered soils. This theory employs the matrix stiffness method and is an extension of a continuum approach presented earlier by the writers. Response curves for piled footings may be calculated using the data presented in the figures for stiffness and damping. The theory is compared with field experiments. The results of the experiments show good agreement with theoretical predictions. Dynamic properties of piles are found to be very dependent on the variation of soil properties with depth and on soil material damping. The importance of soil material damping is also demonstrated for shallow rigid footings vibrating in the torsional as well as rocking modes.

Étude expérimentale de la capacité portante d'une couche compressible d'épaisseur limitée

In order to study the behaviour of a compressible layer resting on a rough rigid base, several loading tests were carried out on a large-scale model. For all the tests the compressible layer consists of dry sand with the following mean characteristics: density= 1·61 and σ = 38° (triaxial test). The load was applied to rigid footings of width B = 20, 35 and 50 cm. Several values of the ratio H/B, where H is the thickness of the compressible layer, are studied between 0·5 and 6·8. The shallow footing case is also investigated for B= 35 cm with Df/B = 0·25, 0·50 and 1·0, where Df is the depth of the footing. Special attention is paid to the influence of the parameter H/B on the bearing capacity and geometry of the failure. The experimental values obtained are compared with the theoretical and experimental results already published. Dans le but d'étudier le comportement d'une couche compressible d'épaisseur limitée par une base rigide rugueuse, de nombreux essais de chargement ont été réalisés dans un modèle de grandes dimensions. Le matériau formant la couche compressible est un sable sec de caractéristiques moyennes: densité = 1·61 et σ = 38° (essai triaxial) pour tous les essais. Les fondations utilisées sont des semelles rigides de largeur B = 20, 35 et 50 cm. Plusieurs valeurs du rapport H/B, où H représente l'épaisseur de la couche compressible, sont étudiées, variant entre 0·5 et 6·8. Le cas semienterré est traité pour B = 35 cm avec Df/B = 0·25, 0·50 et 1·0, Df étant la profondeur de la fondation. L'influence du paramètre H/B sur la géométrie de la rupture et la capacité portante est plus particulièrement étudiée. Les résultats obtenus sont comparés dans certains cas avec les résultats théoriques et expérimentaux déjà connus.

Three-Dimensional Consolidation of A Saturated Clay Under Model Footings

ABSTRACT Magnitudes and rates of settlements predicted by the one-dimensional theory seldom coincide with observed values. Of the many attempts made to improve the accuracy of theoretical predictions, Biot’s poroelastic three-dimensional theory stands out. This paper presents an attempt made to verify the validity of different theories experimentally. Two circular, one rectangular and one square rigid model footings resting on the surface of saturated clay beds were loaded to an intensity of 0.5 kg/cm2. Settlements in and outside the loaded region were recorded. The magnitudes and rates of settlements predicted from various theories were compared with observed values. While there were no significant errors in the magnitudes, rates predicted by the one-dimensional theory were found to be much lower than the observed values and those predicted from Biot’s theory were very close.

The effect of increasing strength with depth on the bearing capacity of clays : Davis, EH Booker, JR Authors reply to discussion of original paper, Geotechnique, V24, N3, 1974, 1T, 1R Geotechnique, V24, N4, Dec. 1974, P690

Solutions are obtained to the problem of bearing capacity of clay by means of the theory of plasticity. The bearing capacity of rigid strip footings is shown to depend markedly on the breadth, and to a small extent on the roughness of the underside of the footing. The analysis can also be applied to the stability of embankments on soft soils. The purpose of this paper is to investigate, by means of the theory of plasticity, the influence on bearing capacity of this type of inhomogeneity of strength.

The effect of increasing strength with depth on the bearing capacity of clays : 14F, 6R. GEOTECHNIQUE, V23, N4, DEC. 1973, P551–563

By means of the theory of plasticity, solutions are obtained to the problem of bearing capacity of clay (φ=0) which is inhomogeneous in the vertical direction only. It is shown that the rate of increase of cohesion with depth plays the same role as density plays in the bearing capacity of homogeneous cohesive-frictional soils. When considered in relation to reclamation of swampy areas by sand filling, the results suggest that only very flat slopes of the edge of the filling are possible without the creation of a mud wave. The bearing capacity of rigid strip footings is shown to depend markedly on the breadth, and to a small extent on the roughness of the underside of the footing. The analysis can also be applied to the stability of embankments on soft soils. Finally, comparison between the plasticity and slip circle solutions reveals very serious overestimates in the latter when inhomogeneity dominates. Au moyen de la theorie de la plasticite on trouve des solutions au probleme de portance de l'argile (φ=...

Dynamic behaviour of structures with embedded foundations

AbstractA study of the dynamics of building‐soil interaction is presented that includes embedding of the foundation and material damping. By considering buildings on rigid footings embedded into linear elastic soil with hysteretic damping, it is shown that the earthquake response of the building‐foundation model may be found from the response to modified excitation of equivalent one‐degree‐of‐freedom linear, viscously damped oscillators resting on rigid ground. For a single‐storey building approximate formulas are developed for the modified natural frequency and damping ratio.Results show that the natural frequency and damping in the system increase with embedding. Effective damping also increases with internal friction in the soil. Ignoring these two factors may underestimate considerably the effective natural frequency and damping in the system. In spite of additional sources of energy dissipation provided by the soil, damping in the equivalent oscillator may be greater or smaller than that corresponding to the superstructure alone, depending upon the system parameters.For lightly damped superstructures, the peak amplitude of the steady‐state overturning moment at the base of a building supported on flexible soil is significantly smaller than that corresponding to rigid ground. This result has practical implications for earthquake design.

The effect of increasing strength with depth on the bearing capacity of clays

By means of the theory of plasticity, solutions are obtained to the problem of bearing capacity of clay (φ=0) which is inhomogeneous in the vertical direction only. It is shown that the rate of increase of cohesion with depth plays the same role as density plays in the bearing capacity of homogeneous cohesive-frictional soils. When considered in relation to reclamation of swampy areas by sand filling, the results suggest that only very flat slopes of the edge of the filling are possible without the creation of a mud wave. The bearing capacity of rigid strip footings is shown to depend markedly on the breadth, and to a small extent on the roughness of the underside of the footing. The analysis can also be applied to the stability of embankments on soft soils. Finally, comparison between the plasticity and slip circle solutions reveals very serious overestimates in the latter when inhomogeneity dominates. Au moyen de la théorie de la plasticité on trouve des solutions au problème de portance de l'argile (φ= 0) non homogène dans le sens vertical seulement. On démontre que le taux d'accroissement de la cohésion avec la profondeur tient un rôle équivalent à celui de la densité pour la portance de sols homogènes cohérents et ayant du frottement. Si on les étudie en vue de l'utilisation des régions marécageuses par remblayage au sable, les résultats obtenus semblent suggérer que seules des pentes très plates en bordure du remblai sont acceptables pour éviter des vagues de boue. On montre que la portance de semelles filantes rigides dépend de façon notable de la largeur, et à un degré moindre de la rugosité de la semelle. On peut analyser de la même manière la stabilité des remblais sur sols mous. Enfin, la comparaison entre les solutions en plasticité et par cercles de glissement, révèle une surestimation très sérieuse de ces dernières lorsque l'hétérogénéité est importante.

Analog-discrete approach for the solution of a class of rigid-contact problems

This investigation consists in finding stresses and displacements produced by a rigid footing (or punch) at the plane boundary of a semi-infinite elastic solid. The proposed method is a combined application of electrical analog and finite-difference technique and can be applied to any arbitrary shape of rigid footing (or punch). The experimental setup is very simple and the numerical-analysis part is easily amenable to computer programming. The method has been exemplified by 3 cases: (1) rigid strip footing (or punch); (2) rigid circular footing (or punch); and (3) rigid square footing (or punch) on a three-dimensional semi-infinite solid. The results, wherever possible, have been compared with exact solutions and have been found to be in close agreement.

Stress state and displacements of a ponderable, nonlinearly deformable soil half-space under a circular rigid footing

Stress state and displacements of a ponderable, nonlinearly deformable soil half-space under a circular rigid footing

Contact Pressure of A Rigid Circular Foundation

A study of the distribution of contact stresses on a foundation-soil interface is presented based on experimental results from a rigid circular footing with smooth base and sides. The effects of magnitude of applied force, repeated loading and embedment are considered with the view of comparing the existing theories.