Circular Footings Research Articles

Numerical study of ring and circular foundations resting on fibre-reinforced soil

ABSTRACT A numerical study has been carried out for ring and circular footings resting on unreinforced and fibre-reinforced layered sand beds. The sand bed consists of two layers. The top layer of sand has been reinforced with randomly distributed fibres (by weight) up to different depths. The underlying sand layer has been kept unreinforced throughout the study. The effect of footing type, fibre percentage, thickness of fibre reinforced sand, and different combinations of relative densities of top fibre-reinforced and underlying unreinforced sand has been studied in this paper. Results obtained from numerical study have been compared with the experimental results and are found to be in good agreement with each other. Furthermore, the same numerical model has been utilized to study the scale effects of the model geometry. Moreover, empirical expressions (using regression technique) have also been developed to assist the practising engineers in designing ring and circular footings resting on fibre-reinforced sand.

Parametric study from laboratory tests on twin circular footings on geocell-reinforced sand

Bearing capacity (BC) test results are presented for bounded and unbounded twin circular footings on unreinforced and geocell-reinforced (GCR) sand. Analysis of the results demonstrate material, scale and size effects on the BC for a given combination in materials (sand-GCR), footing (single-twin) and the problem geometric dimensions. The significance of these combinations on BC and settlements is used to arrive at suitably modified BC factors for design that could be generalized. Plots given relative to reference cases for which BC design solutions are available provide correction factors to modify classical BC equations. Values of the BC and BC factors represent the lumped effect of all or separate problem variables including scale and any experimental limitations. Compared with previous works, these results give deeper critical depths for twin footings on unreinforced and GCR sand and BC higher than 4 times the reference case.

An Experimental and Numerical Study on the Bearing Capacity of Circular and Ring Footings on Rehabilitated Sand Slopes with Geogrid

This paper presents the results of a series of small-scale model tests and numerical analyses conducted on circular and ring model footings located near geogrid reinforced sand slopes. Layers of geogrid were applied as reinforcement. For numerical analyses Finite Element Method (FEM) was used. The effects of reinforcement depth, size, number of layers, and the horizontal distance between reinforcement and the slope surface were experimentally inspected. Moreover, the effects of other parameters such as slope angle, the distance of the footing from the slope crest (for circular footings) and the ratio of inner to outer diameters (for ring fittings) were also numerically inspected. The results of numerical analyses were compared with the laboratory test results and found to be in fair agreement. Optimum bearing capacity values were found for some studied parameters. The results indicate that if the reinforcement layers are implemented correctly, the bearing capacity of circular and ring footings over slopes would significantly increase.

A compliant guyed system for deep-sea installations of offshore wind turbines: Concept, design insights and dynamic performance

The paper explores the potential of a cost-efficient and easy-to-install foundation scheme for Mega-Turbines in seismic regions. The envisioned system comprises a compliant tower, tethered to the ground with an array of four pretensioned cables moored to the seabed by suction anchors. To facilitate installation, a single pinned connection is implemented at the tower base, which is founded on a circular shallow footing. Compared to conventional solutions, the studied scheme offers the necessary support without resource to massive and difficult to construct foundations. By eliminating the moment transfer at the tower foundation, its design requirements are substantially reduced. The efficacy of the proposed solution is demonstrated by investigating the performance of the NOWITECH 10 MW reference turbine installed at 50 m water depth, in the seismically active region of North-Western Adriatic. The entire soil–foundation–structure system is modelled in 3D, employing the finite element method. After confirming the acceptable performance of the guyed system against ULS and SLS conditions (even when allowing 3P mechanical vibrations to resonate with the oscillation of the turbine tower), its seismic response is evaluated. Under seismic loading, the guyed system is shown to be resilient, sustaining the seismically–induced loading with controlled displacements at the cable connection point, protecting the tower from excessive distress and undesirable inelastic deformations. The anchoring is also shown to have acceptable performance, with the maximum attained tension being much lower than the pullout capacity of the suction caisson; the seismically induced deformations are negligible. Finally, the seismic performance of the taut mooring lines is also shown to be satisfactory. Although a condition of “complete slack” may arise momentarily at the lee-ward cable, structural stability is not compromised.

Bearing capacity of foundation on rock mass depending on footing shape and interface roughness

The aim of this paper was to study the influence of the footing shape and the effect of the roughness of the foundation base on the bearing capacity of shallow foundations on rock masses. For this purpose the finite difference method was used to analyze the bearing capacity of various types and states of rock masses under the assumption of Hoek-Brown failure criterion, for both plane strain and axisymmetric model, and considering smooth and rough interface. The results were analyzed based on a sensitivity study of four varying parameters: foundation width, rock material constant (mo), uniaxial compressive strength and geological strength index. Knowing how each parameter influences the bearing capacity depending on the footing shape (circular vs strip footing) and the footing base interface roughness (smooth vs rough), two correlation factors were developed to estimate the percentage increase of the ultimate bearing capacity as a function of the footing shape and the roughness of the footing base interface.

Three-dimensional lower bound finite element limit analysis of an anisotropic undrained strength criterion using second-order cone programming

This paper describes a formulation of second-order cone programming for three-dimensional lower bound finite element limit analysis considering a cross-anisotropic undrained strength criterion. A three-dimensional generalized yield criterion accounting for the cross-anisotropic undrained strength of clay is proposed and requires four input shear strengths in triaxial compression and extension, direct simple shear, and pressuremeter tests. The proposed formulation is verified through the predictions of various compressions of anisotropic soil blocks while the importance of undrained strength anisotropy is demonstrated by analyses of undrained bearing capacity of strip, circular and square footings on anisotropic clays.

Scale model to measure stress under circular footings resting on sand

ABSTRACT This paper presents the results of a series of load tests carried out with a foundation model supported by sand. The aim of this study is to measure the stresses in the soil that occur when applying loads with a circular foundation model. Sand was placed in a circular tank of 60 cm in diameter and 45 cm in height. Diaphragm load cells were used to measure the stresses. It was used to determine the effect of the relative density in the vertical distribution of stresses in the sand. The stresses measured with the load cells were compared with those estimated with the Boussinesq’s method and were validated using a finite element model. The results showed that the inclusion of cells in the soil produced an alteration in the stress–settlement behaviour of circular footing resting on sand. Boussinesq’s method presented an acceptable approximation to the stresses measured with the load cells.

Bearing capacity of circular skirted footing on clay soil

Footing foundation has been worldwide used in resisting light to medium load of structures. Footing’s design has to consider the bearing capacity and the settlement of soil below. This research focuses on the investigation of the effect of skirt on circular footing to improve the footing performance in resisting vertical load on clay soil. There are nine samples of circular footing tested in vertical load system in laboratory in the diameter of 75 mm, 100 mm and 150 mm with length of skirt 100 mm and 150 mm on clay by keeping the similar water content and compaction method. The results show that the skirt effectively reduces the foundation settlement on clay which is observed on similar load 1 kN. The observations on L/D ratio on similar diameter also show that the higher L/D ratio the smaller settlement. On the observations of settlement 3 mm with similar diameter show that the longer the skirt the higher load retained by footing.

An experimental test study on ring footing resting on clay bed reinforced by stone column

Stone columns are used as a ground improvement technique, and they not only enhance the bearing capacity and reduce the settlement, but also serve as a primary function of reinforcement and drainage. Wrapping the stone columns with geosynthetic materials makes ordinary stone column (OSC) stronger and stiffer by enhancing its performance. Ring footings are more often provided for structures such as storage tanks and bridge piers. Stone column is generally used with square, rectangular and circular footings. The idea of using ring footing with encased stone column is very popular nowadays. By using geosynthetic-encased stone column (GESC) with combination of ring footing, more increase in bearing capacity and reduction in settlement are achieved as compared to OSC. Based on the experimental results, pressure–settlement response of the stone column-reinforced clay was studied. This paper also presents the subgrade modulus aspect of geosynthetic-encased stone column-reinforced clay bed The aim of this paper is to study the effect of different parameters such as the number of columns, length of column, diameter of column and the effect of encasement provided on OSC and GESC on bearing capacity and on subgrade modulus. The variation of bearing capacity ratio and settlement are also reported for different parameters. The experimental data were further used for regression analysis to fit the equation for bearing capacity of the improved soft clay bed. Thus, it was concluded that with the increase in the number of columns, length and diameter of column, bearing capacity and subgrade modulus of reinforced clay have increased.

Numerical Modelling of Stone Column Installation Effects on Performance of Circular Footing

In this paper, numerical analyses using Plaxis 2D code in axisymmetric model are carried out to evaluate the influence of stone column installation effects on the loading–settlement performance of circular footing supported by a small group of columns. First, the column installation inducing lateral expansion is modelled using large displacements as the undrained expansion of a cylindrical cavity. The focus is made on the evaluation of the installation effects in terms of stiffness and effective vertical, radial and circumferential stresses immediately after column installation and after consolidation. The results show that the dissipation of excess pore pressure, due to column installation, leads to more improvement in the effective radial than circumferential stresses in the vicinity of the column which induce to a significant increase in effective mean stress as well as the surrounding soil stiffness. Then, numerical investigations are performed on column group supporting a rigid circular footing to evaluate the influence of each improvement installation effect by producing the loading–settlement response. The results show more improvement of settlement is obtained when considering both effective horizontal stresses and soil stiffness improvements due to column installation and the improvement is more pronounced for high footing loading. Moreover, the columns bulging are mainly controlled by the effective horizontal stresses.

Estimating the bearing capacity of single reinforced granular fill overlying clay

This paper develops an empirical design approach for estimating the footing pressure and settlement behavior of a circular footing on a geogrid reinforced granular fill overlying a weak clay soil by regression analysis. A power model has been developed with a high coefficient of determination R2 with 0.959, according to the 398 training data obtained from in-situ tests. The empirical formulation has been evaluated for the validity of the regression model with 220 data which were not used in the derivation of the formulation and the mean absolute percentage error values have been demonstrated that the predictions were obtained with less than 10% error, on average. Additionally, the validity of the developed formulation has been confirmed with different plate load test results from literature, with an acceptable convergence.

Coupled effective stress analysis of insertion problems in geotechnics with the Particle Finite Element Method

This paper describes a computational framework for the numerical analysis of quasi-static soil-structure insertion problems in water saturated media. The Particle Finite Element Method is used to solve the linear momentum and mass balance equations at large strains. Solid-fluid interaction is described by a simplified Biot formulation using pore pressure and skeleton displacements as basic field variables. The robustness and accuracy of the proposal is numerically demonstrated presenting results from two benchmark examples. The first one addresses the consolidation of a circular footing on a poroelastic soil. The second one is a parametric analysis of the cone penetration test (CPTu) in a material described by a Cam-clay hyperelastic model, in which the influence of permeability and contact roughness on test results is assessed.

Prediction of the Effect of Using Stone Column in Clayey Soil on the Behavior of Circular Footing by ANN Model

Shallow foundations are usually used for structures with light to moderate loads where the soil underneath can carry them. In some cases, soil strength and/or other properties are not adequate and require improvement using one of the ground improvement techniques. Stone column is one of the common improvement techniques in which a column of stone is installed vertically in clayey soils. Stone columns are usually used to increase soil strength and to accelerate soil consolidation by acting as vertical drains. Many researches have been done to estimate the behavior of the improved soil. However, none of them considered the effect of stone column geometry on the behavior of the circular footing. In this research, finite element models have been conducted to evaluate the behavior of a circular footing with different stone column configurations. Moreover, an Artificial Neural Network (ANN) model has been generated for predicting these effects. The results showed a reduction in the bending moment, the settlement, and the vertical stresses with the increment of the stone column length, while both the horizontal stress and the shear force were increased. ANN model showed a good relationship between the predicted and the calculated results.

Upper-Bound Finite-Element Limit Analysis of Axisymmetric Problems for Mohr-Coulomb Materials Using Semidefinite Programming

An upper-bound formulation for performing finite-element limit analysis by using semidefinite programming (SDP) for an axisymmetric stability problem involving the Mohr-Coulomb yield criterion has been presented. The SDP technique has an advantage in that it can deal with the yield criterion directly in its native form in terms of principal stresses and strains without any smoothing of the parent yield surface. The associated flow rule and plastic power dissipation are expressed entirely in terms of principal plastic strain rates. Nodal velocities and element plastic strain rates were framed as basic governing variables without involving stresses. The solution was obtained by using the SDP solver MOSEK in MATLAB. The problem of finding the bearing capacity of a circular footing was dealt with by choosing a planar domain that was discretized with (1)three-noded constant strain finite elements and (2)six-noded linear strain finite elements. The results were obtained with and without the provision of the velocity discontinuities, and were compared with those reported in literature. It was learned that quite accurate solutions can be obtained with the application of six-noded linear strain triangular elements and using velocity discontinuities along all the elements' interfaces.

Response of circular footing on dry dense sand to impact load with different embedment depths

Machine foundations with impact loads are common powerful sources of industrial vibrations. These foundations are generally transferring vertical dynamic loads to the soil and generate ground vibrations which may harmfully affect the surrounding structures or buildings. Dynamic effects range from severe trouble of working conditions for some sensitive instruments or devices to visible structural damage. This work includes an experimental study on the behavior of dry dense sand under the action of a single impulsive load. The objective of this research is to predict the dry sand response under impact loads. Emphasis will be made on attenuation of waves induced by impact loads through the soil. The research also includes studying the effect of footing embedment, and footing area on the soil behavior and its dynamic response. Different falling masses from different heights were conducted using the falling weight deflectometer (FWD) to provide the single pulse energy. The responses of different soils were evaluated at different locations (vertically below the impact plate and horizontally away from it). These responses include; displacements, velocities, and accelerations that are developed due to the impact acting at top and different depths within the soil using the falling weight deflectometer (FWD) and accelerometers (ARH-500A Waterproof, and Low capacity Acceleration Transducer) that are embedded in the soil in addition to soil pressure gauges. It was concluded that increasing the footing embedment depth results in increase in the amplitude of the force-time history by about 10-30% due to increase in the degree of confinement. This is accompanied by a decrease in the displacement response of the soil by about 40- 50% due to increase in the overburden pressure when the embedment depth increased which leads to increasing the stiffness of sandy soil. There is also increase in the natural frequency of the soil-foundation system by about 20-45%. For surface foundation, the foundation is free to oscillate in vertical, horizontal and rocking modes. But, when embedding a footing, the surrounding soil restricts oscillation due to confinement which leads to increasing the natural frequency. Moreover, the soil density increases with depth because of compaction, which makes the soil behave as a solid medium. Increasing the footing embedment depth results in an increase in the damping ratio by about 50-150% due to the increase of soil density as D/B increases, hence the soil tends to behave as a solid medium which activates both viscous and strain damping.

Experimental Behavior of Circular Foundations on Oil Contaminated Sand

This paper studies the behavior of circular footings placed on the gasoil and kerosene-contaminated soil. The ultimate objective of this study is to determine the effect that oil contamination has on the sand bearing capacity. The contaminated sand layers were mixed with different levels of between 1 and 4 percent of gasoil and kerosene contamination. The influence of the contamination depth and type of contamination was examined in this study. Laboratory tests were conducted on small scale models and performed in load-controlled manner. The results showed that the contamination can influence the load-settlement curves and lead to a reduction in its load-bearing capacity. An increase in the depth and percentage of contamination decreased the bearing capacity. Some formulas have been provided in which by knowing the depth and percentage of contamination one can predict the third bearing capacity factor of a circular foundation

Axisymmetric alternating direction explicit scheme for efficient coupled simulation of hydro-mechanical interaction in geotechnical engineering—Application to circular footing and deep tunnel in saturated ground

Explicit solution techniques have been widely used in geotechnical engineering for simulating the coupled hydro-mechanical (H-M) interaction of fluid flow and deformation induced by structures built above and under saturated ground, i.e. circular footing and deep tunnel. However, the technique is only conditionally stable and requires small time steps, portending its inefficiency for simulating large-scale H-M problems. To improve its efficiency, the unconditionally stable alternating direction explicit (ADE) scheme could be used to solve the flow problem. The standard ADE scheme, however, is only moderately accurate and is restricted to uniform grids and plane strain flow conditions. This paper aims to remove these drawbacks by developing a novel high-order ADE scheme capable of solving flow problems in non-uniform grids and under axisymmetric conditions. The new scheme is derived by performing a fourth-order finite difference (FD) approximation to the spatial derivatives of the axisymmetric fluid–diffusion equation in a non-uniform grid configuration. The implicit Crank-Nicolson technique is then applied to the resulting approximation, and the subsequent equation is split into two alternating direction sweeps, giving rise to a new axisymmetric ADE scheme. The pore pressure solutions from the new scheme are then sequentially coupled with an existing geomechanical simulator in the computer code fast Lagrangian analysis of continua (FLAC). This coupling procedure is called the sequentially-explicit coupling technique based on the fourth-order axisymmetric ADE scheme or SEA-4-AXI. Application of SEA-4-AXI for solving axisymmetric consolidation of a circular footing and of advancing tunnel in deep saturated ground shows that SEA-4-AXI reduces computer runtime up to 42%–50% that of FLAC's basic scheme without numerical instability. In addition, it produces high numerical accuracy of the H-M solutions with average percentage difference of only 0.5%–1.8%.

Eccentrical behavior of square and circular footings resting on geogrid-reinforced sand

A simple approach to describe the centrically and eccentrically ultimate bearing capacity of circular and square footings resting on geogrid-reinforced sand is developed in this paper. To establish and evaluate this approach, a series experimental test for circular footing and square footing were considered as shallow foundation models. The proposed approach for eccentrical loading in unreinforced and reinforced conditions has been validated with Meyerhof’s Effective Width Concept, laboratory model tests, numerical analyses data and field tests on actual full scale reported in the literature review. It was revealed that the new method provides reasonable agreement of the ultimate bearing capacity. Also, the results show ultimate bearing capacity of circular footing decreases less with increment of load eccentricity in comparison of square footing in reinforced condition. Improvement Index investigated that reinforcement layers increased the ultimate bearing capacity in both loadings and their contributions increased with increasing the load eccentricity.

The use of skirts to improve the performance of a footing in sand

This paper investigates the use of skirts to improve the bearing capacity and to reduce the settlement of a circular footing resting on dune sand. The skirts are fixed to the perimeter of the footings. A series of tests were conducted on model footings in a large tank and the footings were instrumented to measure normal stresses and settlement. The test results indicate that the skirts increase the bearing capacity and reduce the settlement of the footing. The improvement in the bearing capacity is up to about 470% for a surface footing with skirt of a depth of 1.25B. The skirts also reduced the settlement of the footings to as small as 17% of the original settlement of a surface footing without skirts. A modified bearing equation was proposed for circular footings with skirts. The proposed equation agrees quite well with published experimental results.

Bearing capacity on sand overlying clay: An analytical model for predicting post peak behaviour

New analytical models have recently been presented for evaluating the peak bearing capacity of circular footings penetrating sand-over-clay and the subsequent capacity once embedded in the underlying clay. However, in lieu of any analytical model, current methods of analysis use an inaccurate linear interpolation for the bearing capacity between the peak and the clay surface. This paper proposes an analytical model for calculating the bearing capacity of circular footings after the peak failure in sand-over-clay soils and before the footing enters the clay. Based on observations from visualisation experiments conducted in a geotechnical centrifuge, and consistent with the silo analysis approach used in predicting the peak capacity, the failure mechanism is a vertical frustum of sand progressively being forced into the underlying clay. Analysis of the capability of the new model to retrospectively simulate a database of 66 geotechnical centrifuge tests is provided. Motivation for improved prediction methods comes from the offshore mobile jack-up industry where concerns remain over the punch-through of large 20 m diameter spudcan footings in sand-over-clay. Accurate prediction of not just the peak bearing capacity but the subsequent load-displacement behaviour is required in order to assess the effectiveness of operational methods used to mitigate punch-through incidents.