Flexible Footings Research Articles

MSA-based seismic fragility analysis of RC structures considering soil nonlinearity effects and time histories compatible to uniform hazard spectra

In the present study, an updated ground motion simulation framework based on spectral compatible time histories is proposed for the evaluation of seismic performance of mid-rise reinforced concrete structures with multi-stripe analysis (MSA) based probabilistic seismic hazard analysis. The seismic fragility functions are generated for two numbers of three storied instrumented test buildings of which one is founded on individual flexible footings and other one is a base isolated building. The fragility analysis is carried out for different performance levels under a series of input ground motions (IGMs) by considering uncertainty in soil structure interaction and uncertainty in ground motion. IGMs are obtained from the uniform hazard response spectrum (UHRS) with different return period thus conserving the frequency content of input motion during the scaling of high intensity earthquakes. The UHRS compatible synthetic time histories are applied at rock level and amplified surface motion obtained from soil amplification studies considering soil nonlinearity are applied to the buildings supported on soil springs. Nonlinear time history analysis is performed by modelling hysteretic characteristic of columns using modified Takeda model. The fragility curves obtained from the proposed methodology are compared with that using simple scaling of accelerograms generally performed in literature. The proposed technique gives conservative result for structure with individual flexible footings while no marked differences are observed for base isolated structure.

Numerical Modeling of Rigid and Flexible Footings Constructed on Natural and Contaminated Soil Strata

In this article, a numerical model has been developed in order to examine the effect of rigid and flexible footings vertically loaded on the behavior of oil-contaminated soil layers by black oil with respect of natural soil strata characteristics. The analyses have included modeling the spread rigid and flexible footings founded on natural soil have been collected from south of Iraq, and contaminated specimens of 10% by weight. The thickness of the contaminated layer (D) has been gradually increased from 1.0 m to 4.0 m from footing base. Three footing width (B), 1.0m, 2.0m and 3.0 m have been simulated in the study. The finite element package PLAXIS 3D has been adopted to simulate the oil contamination problem and to relate the performance of a spread footing supported on natural soil and contaminated soil with different footing width (B) and thickness of contamination layer (D). The outcomes have found out that the vertical ground movement can be reduced by minimum thickness of soil contamination layer. The vertical ground movement has been reduced because of soil contamination when the contamination depth (D) is less than or equal footing width (B) with respect to vertical ground movement of natural soil in case of two types of footing. The behavior of rigid footing has showed more lessening in vertical ground movement as contamination layer thickness (D) 1.0m for all the footing widths.

Elastic Settlement Analysis of Rigid Rectangular Footings on Sands and Clays

In this paper an elastic settlement analysis method for rigid rectangular footings applicable to both clays and sands is proposed. The proposed method is based on the concept of equivalent shape, where any rectangular footing is suitably replaced by a footing of elliptical shape; the conditions of equal area and equal perimeter are satisfied simultaneously. The case of clay is differentiated from the case of sand using different contact pressure distribution, whilst, additionally, for the sands, the modulus of elasticity increases linearly with depth. The method can conveniently be calibrated against any set of settlement data obtained analytically, experimentally, or numerically; in this respect the authors used values which have been derived analytically from third parties. Among the most interesting findings is that sands produce “settlement x soil modulus/applied pressure” values approximately 10% greater than the respective ones corresponding to clays. Moreover, for large Poisson’s ratio (v) values, the settlement of rigid footings is closer to the settlement corresponding to the corner of the respective flexible footings. As v decreases, the derived settlement of the rigid footing approaches the settlement value corresponding to the characteristic point of the respective flexible footing. Finally, corrections for the net applied pressure, footing rigidity, and non-elastic response of soil under loading are also proposed.

Strain Influence Factor Charts for Settlement Evaluation of Spread Foundations based on the Stress–Strain Method

In this paper, the stress–strain method for the elastic settlement analysis of shallow foundations is revisited, offering a great number of strain influence factor charts covering the most common cases met in civil engineering practice. The calculation of settlement based on strain influence factors has the advantage of considering soil elastic moduli values rapidly varying with depth, such as those often obtained in practice using continuous probing tests, e.g., the Cone Penetration Test (CPT) and Standard Penetration Test (SPT). It also offers the advantage of the convenient calculation of the correction factor for future water table rise into the influence depth of footing. As is known, when the water table rises into the influence zone of footing, it reduces the soil stiffness and thus additional settlement is induced. The proposed strain influence factors refer to flexible circular footings (at distances 0, R/3, 2R/3 and R from the center; R is the radius of footing), rigid circular footings, flexible rectangular footings (at the center and corner), triangular embankment loading of width B and length L (L/B = 1, 2, 3, 4, 5 and 10) and trapezoidal embankment loading of infinite length and various widths. The strain influence factor values are given for Poisson’s ratio value of soil, ranging from 0 to 0.5 with 0.1 interval. The compatibility of the so-called “characteristic point” of flexible footings with the stress–strain method is also investigated; the settlement under this point is considered to be the same as the uniform settlement of the respective rigid footing. The analysis showed that, despite the effectiveness of the “characteristic point” concept in homogenous soils, the method in question is not suitable for non-homogenous soils, as it largely overestimates settlement at shallow depths (for z/B < 0.35) and underestimates it at greater depths (for z/B > 0.35; z is the depth below the footing and B is the footing width).

Bearing capacity of a flexible plastic plate for soil nailing

A large flexible bearing face plate for soil nailing made from reclaimed plastics has recently been developed to improve the construction performance and reduce the impact on the natural environment. This study aims to clarify the influence of bending stiffness and dimensions of the bearing plate on its deformation and bearing capacity characteristics. The authors conducted a series of fundamental laboratory bearing capacity tests on rigid and flexible model footings placed on dense sand to simulate and compare the mechanical behaviour of bearing plates installed on a slope surface. The reduction in the ultimate bearing capacity caused by footing flexibility was 10–20% under experimental conditions, which is small considering the extremely large difference (i.e. three to four orders of magnitude) in rigidity between the rigid and flexible footings. For practical application, the plastic bearing plate may not mobilise the required bearing pressure due to the reduction in subgrade reaction when an extremely large or thin bearing plate is used.

A transfer function method to predict building vibration and its application to railway defects

This work presents a simplified method to evaluate building shaking due to arbitrary base excitations, and an example application to railway problems. The model requires minimal computational effort and can be applied to a wide range of footing shapes, thus making it attractive for scoping-type analysis. It uses the soil excitation spectrum at the building footing location as it’s input, and computes the building response at any arbitrary location within it’s 3D structure. To show an application of the model versatility, it is used to compute building response due to a variety of singular railway defects (e.g. switches/crossings). It is however suitable for more general applications including railway problems without defects. The approach is novel because current railway scoping models do not use soil-structure transfer functions combined with free-field response to estimate building vibration by railway defects. First the soil-structure interaction approach is outlined for both rigid and flexible footings. Then it is validated by comparing results against a comprehensive fully-coupled 3D FEM-BEM model. Finally, it is used to analyse the effect of a variety of variables related to railway defects on building response. Local track defects are shown to have a strong influence on building vibrations. Further, vibration levels close to the threshold of human comfort are found in buildings close to the railway line. Overall the new approach allows for the computation of building vibrations accounting for soil-structure interaction, floor amplification and the measured/computed free-field response due to railway traffic using minimal computational effort.

Dynamic Winkler Foundation for vibration analyses of flexible footings

For the design of mitigation measures against railway traffic induced vibrations the interaction between the unbounded soil and the flexibility of the foundation must be taken into account. Common numerical schemes like Boundary Elements, Transmitting Boundaries, and Perfectly Matched Layer bear computational costs which render their application impractical. The concept of Dynamic Winkler Foundation (DWF) is a tempting alternative due to its simplicity, but it neglects certain important peculiarities of soil-structure interaction. Hence, the coefficients of the DWF must be carefully chosen, taking into account the properties of the foundation soil, as well as the properties of the structure. As part of an ongoing research we derive such coefficients and assess their suitability from analyses of a real-world building for which mitigation methods have been implemented.

Effect of Subsurface Conditions on the Behavior of Footing by Using PLAXIS Software

The purpose of this paper is to present the study on the effect of soil below the footing on the footing behavior. Also, it used two types of footings (Rigid and Flexible Footings). Footings are structural elements that transmit column or wall loads to the underlying soil below the structure. Footings are designed to transmit these loads to the soil without exceeding its safe bearing capacity, to prevent excessive settlement of the structure to a tolerable limit, to minimize differential settlement, and to prevent sliding and overturning. PLAXIS, finite element software package, was used to perform numerical modeling and analyses to evaluate the structural response and behavior of the square footing. The results show that the soil conditions below the footing may have a significant effect on the footing behavior such as vertical and horizontal displacements, stresses, and shear strains and should be considered during the design of footing.

Behaviour of weak soils reinforced with soil cement columns formed by the deep mixing method: Rigid and flexible footings

This paper presents a comparison of the failure behaviour of the Deep Mixing (DM) method under models of rigid and flexible foundations. A series of physical model tests at 1g were performed in this study consisting of unreinforced and fully and partially penetrated soil–cement columns. For the improvement case, the columns of 23.5mm diameter and lengths of 200 and 100mm were installed in the ground model with an improvement area ratio, ap, of 26.0%. The failure mechanism was measured using close range photogrammetry and Particle Image Velocimetry (PIV). For verification, the bearing capacity performance and failure mechanisms were then compared with the Ultimate Limit State numerical analysis and the existing analytical solution proposed by Boussida. The results show a good agreement between the bearing capacity value obtained from the experiment and the numerical software.

New Stabilized Finite Element Method Embedded with a Cap Model for the Analysis of Granular Materials

Standard displacement-based finite element formulations show a tendency to lock in the modeling of nearly incompressible materials. This overly stiff response often leads to an overestimation of the collapse load for the system. In this paper we present a stabilized mixed displacement-pressure finite element method that can effectively model the nearly incompressible materials in their elastic and inelastic range. The stabilized formulation is free of volumetric locking effects and allows equal low-order interpolation for both the displacement and the pressure fields. The formulation is integrated with a three-surface elastoplastic cap model for the simulation and analysis of granular materials. The good performance of the method is demonstrated via numerical examples of the hydrostatic compression test for concrete and the bearing capacity and limit load analyses of flexible footings.

Elastic settlement and rotation of rectangular footings on nonhomogeneous soil

Keywords: Elasticity ; footings ; foundations ; numerical modelling and analysis ; settlement ; soil ; structure interaction ; stiffness ... Show All

A flexible rectangular footing on aGibson soil: Required rigidity for full contact

The problem of a rectangular footing or a strip footing resting on a nonhomogeneous elastic half-space is studied in this paper. The medium is assumed to be isotropic with a shear modulus linearly increasing with depth G (z) = G 0+ mz and a constant Poisson's ratio equal to 1/3. An important feature of this model is that either the Winkler foundation or the elastic homogeneous half-space can be made special cases by letting G 0 or m equal zero, respectively some results are presented for these cases. In order to investigate the necessary conditions for a footing to be considered rigid, both rigid and flexible footings have been studied. Central concentrated (column) loading, in addition to the self-weight, is treated-being the most demanding in terms of the zero uplift requirement (under conditions of symmetry in the loading with respect to the plate geometry, imposed for reasons of mathematical feasibility). The contact is assumed to be tensionless. There are three important steps in this formulation. The fundamental solution of the nonhomogeneous half-space is separated into the fundamental solution of the homogeneous half-space and a function related to the nonhomogeneity of the half-space. The latter function is approximated by an analytically tractable expression. The contact region is discretized using an adaptive scheme that accounts for the possible edge and corner singularities. The latter scheme removes the burden of most of the numerical integration. A rigid strip footing and a rigid rectangular footing are treated first to ascertain the convergence of the solution procedure and to provide information requisite for the flexibility study. The title problem is transformed into the solution of three coupled two dimensional singular integral equations. The contact regions are found iteratively since the problem is nonlinear.

Vertical vibration tests on flexible footings : Moore, P J; Lim, S N Soil Dynamics and Liquefaction, Proc 4th International Conference on Soil Dynamics and Earthquake Engineering, Mexico City, 23–26 October 1989P303–315. Publ Southampton: Computational Mechanics Publications, 1989

Vertical vibration tests on flexible footings : Moore, P J; Lim, S N Soil Dynamics and Liquefaction, Proc 4th International Conference on Soil Dynamics and Earthquake Engineering, Mexico City, 23–26 October 1989P303–315. Publ Southampton: Computational Mechanics Publications, 1989

Nonlinear soil-structure interaction analysis using coupled finite-infinite elements

Soil-structure interaction analysis for a strip footing is presented using a coupled finite-infinite element formulation. Two-dimensional mapped infinite elements with 1/ r type of decay are used. The shape functions for mapped infinite elements with 1/√ r type of decay are also presented. In the interactive analysis of footing, non-linear stress-strain behaviour of the soil using the hyperbolic fit is taken into account. The results are presented for both rigid and flexible footings. It is found that the vertical stress distribution for a flexible footing matches very well with the Boussinesq solution. The infinite elements in combination with the conventional finite elements yield a very attractive coupled formulation in terms of far field physical representation, computer use and data preparation.

11. Flexible footings on model foundations—An application of the analogue computer to soil-vehicle Mechanics: L.I. Leviticus and R.M. Peart.J. agric. Engng Res.12 (2), 110–114 (1967)

11. Flexible footings on model foundations—An application of the analogue computer to soil-vehicle Mechanics: L.I. Leviticus and R.M. Peart.J. agric. Engng Res.12 (2), 110–114 (1967)

Flexible footings on model foundations–An application of the analogue computer to soil-vehicle mechanics

A method is presented which uses mechanistic models to solve soil-wheel interface problems. The advantages of using an analogue computer in this type of analysis are pointed out. An example of a Filonenko model loaded by a simple triangular distribution is worked out and the resulting curves on the X-Y plotter are shown for this case.