Rectangular Foundations Research Articles

Three Dimensional Bearing Capacity Analysis of a Foundation Near a Slope

This paper deals with the evaluation of the bearing capacity of a rectangular shallow foundation located near a slope or an excavation, by means of the yield design theory. Taking into account the true three dimensional nature of the problem, two types of failure mechanisms are selected, resulting in optimal upper bound estimates for the ultimate load bearing capacity of the foundation obtained through the implementation of the kinematic approach from outside. A computational tool is thus developed based on this approach, making it possible, for instance, to provide a quantitative assessment of the bearing capacity reduction due to the slope proximity. Such theoretical estimates are finally compared with experimental values obtained on full scale and centrifuge-reduced scale models.

Soil inertia effects on the bearing capacity of rectangular foundations on cohesive soils

Two kinematic mechanisms are presented, which provide an upper bound of the ultimate bearing capacity of shallow rectangular foundations resting on cohesive soil, modeled by the Tresca strength criterion. The soil-foundation interface is described by the same criterion. The foundation is subjected to an inclined/eccentric load. The horizontal component of the body force in the soil is also taken into account to discuss the effects of the soil inertia on the bearing capacity. A multi-dimensional minimization algorithm allows one to find the geometric parameters corresponding to the best upper bound solutions for different load conditions. The shape effects are discussed and the solutions are compared both with previous theoretical upper bound solutions and with experimentally based formulas, in use in engineering geotechnical practice. Finally, the detrimental effects of the soil inertia on the ultimate bearing capacity of the foundation are analysed, as a function of the shape ratio and the design safety factor.

TRANSFER FUNCTIONS FOR RIGID RECTANGULAR FOUNDATIONS

Closed-form expressions and comprehensive numerical solutions are presented for the transfer functions of surface-supported, rigid, rectangular foundations excited by horizontally polarized, incoherent shear waves for which the motions are parallel to one of the foundation sides. The free-field ground motion is specified stochastically in terms of a local power spectral density function and an orthotropic incoherence function which decays exponentially with the square of the excitation frequency and the separation distance. The response quantities examined include the lateral and torsional components of the foundation motion. Displayed graphically, the results elucidate the effects and relative importance of the numerous parameters involved. For vertically incident incoherent wave fields, the lateral transfer function of a rectangular foundation is related to that of a judiciously selected square foundation, and the interrelationship of the results is examined.

Shape optimization of a dynamically loaded machine foundation coupled to a semi-infinite inelastic medium

A numerical model of the shape optimization of a rectangular machine foundation embedded in soil when subjected to external dynamic forces and moments is presented. A sequential programming method with move limits is used to obtain the minimum weight (mass) of the block. Numerical examples are given to illustrate the application of the model which takes 3-D dynamic soil-foundation interaction into account.

Effects of Rectangular Foundation Geometry on Local Pier Scour

A method for predicting the effect of rectangular foundation geometry on local scour around bridge piers is presented using existing scour equations and considering the mechanisms of local scour. Normalized scour depths predicted from the method are compared to normalized scour data collected by others and data collected by the writers in a laboratory study. The data and the method show the effect of the rectangular foundations through the entire range of possible pier to foundation width ratios and through the entire range of foundation elevations. The effect of an upstream foundation extension also is examined. The study reveals that considerable reduction in the scour depth may be observed if the foundation is located at or below the streambed. The method can be used to evaluate the potential for scour around existing piers. Problems associated with relying on foundations to reduce scour depths are presented. Recommendations for the use of the method are made and future research is suggested.

Infinite boundary elements for the analysis of halfspace problems

This paper describes an efficient infinite element approach for the boundary element analysis of half-space problems. A decay function for stress analysis is then developed based on the theoretical displacement attenuation away from the source of loading. Efficient order-adaptive criteria are derived for numerical integration of the integrals over the infinite boundary elements and illustrative results for rectangular foundations demonstrate the potential of the formulation.

Dynamics of a rectangular foundation contacting a viscoelastic layered medium

1. The models realized permit calculating the dynamics of structures in a wide range of variation of the properties of the base and structure.

Consistent infinitesimal finite-element cell method: in-plane motion

To calculate the unit-impulse response matrix of an unbounded medium for use in a time-domain analysis of medium-structure interaction, the consistent infinitesimal finite-element cell method is developed. Its derivation is based on the finite-element formulation and on similarity. The limit of the cell width is performed analytically yielding a rigorous representation in the radial direction. The discretization is only performed on the structure-medium interface. Explicit expressions of the coefficient matrices for the in-plane motion of anisotropic material are specified, which depend only on the geometry of the structure-medium interface and the material properties of the unbounded medium. For each time step a linear system of equations is solved. The calculated unit-impulse response matrix is symmetric. In contrast to the boundary-element formulation, no fundamental solution is necessary and equilibrium and compatibility on the layer interfaces extending from the structure-medium interface to infinity, if present, are incorporated automatically. Excellent accuracy is achieved for an inhomogeneous semi-infinite wedge and a rectangular foundation embedded in an inhomogeneous half-plane.

Unit-impulse response matrix of unbounded medium by infinitesimal finite-element cell method

To calculate the unit-impulse response matrix of the unbounded medium, the infinitesimal finite-element cell method based solely on the finite-element formulation and working exclusively in the time domain is developed. A formulation can be derived for acceleration, velocity and displacement unit-impulse response matrices. Starting from the acceleration unit-impulse impulse response matrix those of the velocity and displacement are constructed. The algorithm to determine the acceleration unit-impulse response matrix and its application are simpler than the other two alternatives. As in the cloning algorithm, the approach is based on similarity of the unbounded media corresponding to the interior and exterior boundaries of the infinitesimal finite-element cell. The derivation is performed exclusively in the time domain. At each time station a linear system of equations is solved. The consistent-boundary method to analyse a layered medium in the frequency domain and the viscous-dashpot boundary method are special cases of the infinitesimal finite-element cell method. The error is governed by the finite-element discretization in the circumferential direction, as the width of the finite-element cell in the radial direction is infinitesimal. The infinitesimal finite-element cell method is thus “exact in the finite-element sense”. The method leads to highly accurate results for a vast class of problems, ranging from a one-dimensional spherical cavity to a rectangular foundation embedded in a half-plane.

Field verification of a theoretical model to predict the dynamic response of a soft clay deposit

A 40-m thick clay deposit was subjected to sinusoidal excitations using a foundation block and an eccentric mass type vibrator. The response of the foundation block and the surrounding soil was measured using geophones inside the soil and on the surface. The phase shift between the excitation signal and the response signal, the accelerations of the foundation block and the particle velocities in the soil are compared with those obtained from a frequency-dependent numerical model based on the exact analytical solution for the boundary value problem of a rectangular foundation resting on a linear elastic halfspace.

Dynamic‐stiffness matrix in time domain of unbounded medium by infinitesimal finite element cell method

AbstractTo calculate the dynamic‐stiffness matrix in the time domain (unit‐impulse response functions) of the unbounded medium, the infinitesimal finite element cell method based solely on the finite element formulation and working exclusively in the time domain is developed. As in the cloning algorithm, the approach is based on similarity of the unbounded media corresponding to the interior and exterior boundaries of the infinitesimal finite element cell. The derivation can be performed exclusively in the time domain, or alternatively in the frequency domain. At each time station a linear system of equations is solved. The consistent‐boundary method to analyse a layered medium in the frequency domain and the viscous‐dashpot boundary method are special cases of the infinitesimal finite element cell method. The error is governed by the finite element discretization in the circumferential direction, as the width of the finite‐element cell in the radial direction is infinitesimal. The infinitesimal finite element cell method is thus ‘exact in the finite‐element sense’. This method leads to highly accurate results for a vast class of problems, ranging from a one‐dimensional spherical cavity to a rectangular foundation embedded in a half‐plane.

Analysis of flexible rectangular raft foundations under dynamic loading

This study deals with the analysis of the vertical response of flexible rectangular raft foundations subjected to vibratory load. The raft is assumed to be supported on a Winkler medium. The finite element method with eight-noded isoparametric plate bending elements of rectangular shape is used for the analysis. The Newmark integration method is applied to solve the dynamic equilibrium equations. Different types of foundation soils, namely sand, soft clay and peat, are considered. The subgrade modulus of these soils is determined in the laboratory. Dynamic response curves for four aluminium plates are obtained both by analytical methods and experimental investigations and the results are compared. The agreement is quite good in respect of the qualitative nature of the curves and reasonable in respect of quantitative values.

Ultimate bearing capacity of rectangular foundations on geogrid-reinforced sand. Technical note: Omar M T; Das, B M; Yen, S C; Puri, V K; Cook, E E Geotech Test JV16, N2, June 1993, P246–252

Ultimate bearing capacity of rectangular foundations on geogrid-reinforced sand. Technical note: Omar M T; Das, B M; Yen, S C; Puri, V K; Cook, E E Geotech Test JV16, N2, June 1993, P246–252

Insight on 2D‐ versus 3D‐modelling of surface foundations via strength‐of‐materials solutions for soil dynamics

AbstractTo simplify the analysis, three‐dimensional soil–structure interaction problems are often modelled by considering a two‐dimensional slice without changing the material properties of the soil. This procedure, although convenient, is of questionable validity because two‐dimensional modelling inherently overestimates the radiation damping for translational and rocking motions. To make matters worse, two‐dimensional modelling always entails an underestimation of the dynamic‐spring coefficient for the translational motions. The damping ratio of the two‐dimensional case, which is proportional to the ratio of the damping coefficient to the spring coefficient, will thus be even larger. Thus, reliance upon a two‐dimensional analysis based on an equivalent slice of a strip foundation may result in a dangerously non‐conservative design.Valuable insights into the essence of radiation damping and the difference between two‐dimensional and three‐dimensional models may be obtained via approximate strength‐of‐materials solutions based on cone–wedge models and travel‐time considerations. By examining the decay of the waves along the axes of the cone–wedge models, the essence of radiation damping can be grasped. The heuristic concept of more spreading of waves in three dimensions than in two is misleading. Indeed, just the opposite is true: The less the amplitude spreads and diminishes with distance, the greater is the radiation damping.Because the damping ratio is grossly overestimated, two‐dimensional modelling of a three‐dimensional case cannot be recommended for actual engineering applications. It is more feasible to take the opposite approach and idealize slender soil–structure interaction problems with a radially symmetric model.As an alternative, when defining the equivalent slice of the two‐dimensional strip foundation, the impedance of the soil can be changed to achieve a much better agreement of the high‐frequency limits of the damping coefficients. In the low‐frequency range this modified two‐dimensional model also overestimates radiation damping, although to a lesser extent.As a by‐product, the dimensions of the equivalent slice of a two‐dimensional strip foundation are discussed; and equations for the aspect ratios determining the opening angles of the corresponding wedges are derived. Also addressed is the quite separate but related topic of the transition from square to slender rectangular foundations.

Minimum‐Weight Design of Machine Foundation under Vertical Load

In this paper a numerical model for the minimum‐weight design of a rectangular machine foundation under a harmonic vertical load is presented. The analysis of the dynamics of foundation‐soil interaction is based on frequency‐dependent dynamic properties of a semi‐infinite supporting medium and includes the shape of the foundation plan, the embedment of the foundation into the soil, and hysteretic material damping of the soil. Dimensions of the concrete block are assumed as design variables. Constraints are placed on resonant frequency, vertical displacement amplitude, stresses in the soil and dimensions of the foundation concrete block. A sequential programming method with variable move limits is used to obtain the optimal solution, which is affected by inertia properties of the machine‐foundation‐soil system, damping from dynamic soil‐foundation interaction and local soil conditions. Numerical examples are given to demonstrate the applications of the proposed approach.

Ultimate Bearing Capacity of Rectangular Foundations on Geogrid-Reinforced Sand

Abstract Model test results for the ultimate bearing capacity of rectangular surface foundations supported by geogrid-reinforced sand are presented. The tests were conducted using one type of sand at one relative density of compaction with only one type of geogrid. The length-to-width ratios of the model foundations were varied as 1, 2, 3, and ∞. Based on the model test results, the maximum required depths of reinforcement and the sizes of the geogrid layers to obtain maximum-bearing-capacity ratios have been presented.

Effects of the depth of the embedment on the system response during building-soil interaction

The effects of the depth of the embedment on the system response, under plane-strain conditions, have been studied for buildings supported by rigid circular foundations embedded into a homogeneous, isotropic and elastic half-space. The building has been represented by an equivalent single degree-of-freedom oscillator with a rotational spring and viscous damping. A linear analysis and the substructure approach have been used to calculate the system response. The wave passage effects have also been included. Results are shown for incident plane SV-waves. The system damping ratio and the system frequency have been measured directly from the transfer-function of the relative building response. The system damping ratio has been measured by the width of the peak response, normalized by the system frequency. The results have show that, during soil-structure interaction, deeper foundation act ‘stiffer’, and reduce less the system frequency, relative to the fixed-base frequency. The relative response, for the two-dimensional model, is smaller when the depth of the foundation is smaller. Except for heavy and tall buildings, the system damping ratio is smaller when the foundation is deeper. The results of this study have been compared with the results for three-dimensional rectangular prismatic foundations and for hemispherical foundations.

複合体理論を適用しモデル化した沖積層地盤の動力学特性に関する研究 : (その1)長方形基礎の上下加振ground complianceの特徴

複合体理論を適用しモデル化した沖積層地盤の動力学特性に関する研究 : (その1)長方形基礎の上下加振ground complianceの特徴

Analysis of Foundation-Elastic Halfspace Interaction Using a Mixed-Variational Approach

Flexural behavior of thin square or rectangular raft foundations resting in smoot hcontact with an isotropic elastic halfspace is examined using a mixed-variational approach. The deflected shape and the flexural moments of the foundation are assumed as even functions of the spatial coordinates x and y and a number of unknown constants. The contact stress distribution at the foundation-halfspace interface is expressed as a direct function 1 of the assumed deflected shape of the foundation. Numerical results are obtained for deflection, flexural moments and contact stress at the interface for different foundation frigidities. Comparison of results with the finite element solutions shows a good agreement for various relative rigidities. The proposed method is computationally efficient and can be used effectively to predict deflections and flexural moments of raft foundations.

Inertial soil-foundation interaction by a direct time domain BEM

A direct time domain BEM formulation of the general inertial SSI problem is presented. The dynamic response of a rigid massive foundation resting on the surface of a linear elastic, homogeneous, isotropic half-space and subjected to externally applied forces is computed for illustration purposes. Results for rectangular and circular foundations are presented assuming, i) complete bond with the half-space, and ii) relaxed boundary conditions. Comparison studies with frequency domain or simplified time domain analyses confirm the results of this study.