Circular Footings Research Articles

Scale effect of rectangular and square footing of shallow foundation resting on cohesive soil

This experimental research work was performed to evaluate settlement and bearing capacity in cohesive soil. The predominant objective of this study is to develop the existing state of the knowledge about the present simulation processes to estimate its settlement and load carrying capacity. From the past literature study, the semi-empirical procedures were studied to estimate the settlement and bearing capacity parameters. The investigation was done into three parts, based on the past literature studies. The index and laboratory experimental investigations were done in the first stage. In the second part, the experimental procedure was elaborated to determine the settlement and load carrying capacity of small-scale model tests on cohesive soil. This research works presents, the effect of small-scale laboratory tests on the load carrying and settlement of model footings. The experiments were carried out with three types of model footing such as square, rectangular, and circular shapes were chosen to study the scale effect. For the circular footing, the diameters of 30, 40, and 50 mm sizes of plates were used and for square and rectangular model footings dimensions were used as 30mm×30 mm, 40mm ×40 mm, and 50mm ×50 mm and 50mm ×33 mm, 40mm ×28 mm, and 30mm ×20 mm respectively. A steel tank of size 330×220×300 mm was fabricated and used for conducting model tests. The width of the plates ranged from 50mm to 100mm for modeling plane strain and axisymmetric problems and care taken to avoid the wall friction when the load is applied. The size effects on settlement and bearing capacity was studied under different moisture conditions such as optimum moisture and plastic limit of the soil.

Axisymmetric adaptive lower bound limit analysis for Mohr-Coulomb materials using Semidefinite programming

A lower bound (LB) axisymmetric limit analysis formulation is presented for Mohr-Coulomb materials using finite elements and semidefinite programming (SDP). The details of the application of SDP to the axisymmetric LB finite element method for Mohr-Coulomb materials are described in this paper. Through the use of the SDP, the axisymmetric Mohr-Coulomb yield criterion can be directly applied in its native form in terms of principal stresses without any smoothing of the parent yield surface, and no assumption needs to be made about σθ. A node-stress-based adaptive mesh algorithm is also introduced into the proposed method to obtain an accurate high-accuracy LB solution. The proposed method is then applied to estimate the collapse load of circular footings and the stability of an unlined vertical circular excavation. The results are also compared with those reported in the literature; the results obtained from the proposed method are accurate and can provide failure patterns with greater clarity.

Small Scale Experiments to Assess the Bearing Capacity of Footings on the Sloped Surface

Construction of civil engineering structures on or next to a slope requires special attention to meet the bearing capacity requirements of soils. In this paper, to address such a challenge, we present laboratory-scale model tests to investigate the effect of footing shape on the sloped surface. The model comprised of a well stiffened mild steel box with three sides fixed and one side open. We considered both with and without reinforcement to assess the effectiveness of reinforcement on the sloped surface. Also, we used three types of footing (i.e., square, rectangular, and circular) to measure the footing shape effects. We considered three different slope angles to evaluate the impact of the sloped face corresponding to the applied load and the reinforcement application. We obtained that the maximum load carrying capacity in the square footing was higher than the rectangular and the circular footing for both the reinforced and the unreinforced soil. With the increase of geo-reinforcement in all three footing shapes and three sloped angles, the load carrying capacity increased. We also noticed a limiting condition in geo-reinforcement placement effectiveness. And we found that with the increase of slope, the load bearing capacity decreased. For a steep slope, the geo-reinforcement placement and the footing shape selection is crucial in achieving the external load sustainability, which we addressed herein.

Loose Ash Fills Reinforced With the High Confined Encased Stone Columns: Experimental and Numerical Investigation

The use of industrial waste (ash) in large-scale earthworks for civil engineering applications such as construction of highway embankments, the rise of ash dykes, the filling low-lying areas, fillings of buildings, solves the problem of waste disposal besides in addition to the conservation of the natural soils. It is has a low density, low consolidation, lower potential for bearing and higher settlement. To use these areas for construction purposes, it is necessary to reinforce them at deeper depths. The present study uses highly confined stone columns to investigate the strengthening of ash fills. A total of six cases are investigated, including slope reinforced with an encased stone column. Model tests were conducted with pond ash at 40% relative density with a circular footing on untreated and treated ash fills. The enhanced cases include ordinary stone columns,vertically encased columns with geotextile, vertically encased columns with geogrid, highly confined vertically encased columns with both geotextile and geogrids (HC-1) and highly encased columns with both vertical encased geotextile and horizontal geogrid (HC-2) layers. The parametric study includes an examination of load-settlement behavior, load-carrying ratio, settlement reduction ratio, and stiffness factor, modulus of subgrade reaction and post-failure behavior of slopes reinforced with encased stone columns. In all cases, the high confined encased system yields better results. In each case, the stone column failure pattern of was observed at a distance range of 1–3 times the stone column diameter. Post-failure behavior indicates that for steep slopes where massive slip failures are expected, highly confined encased stone columns can be useful. Results are validated by the numerical modelling analysis of Plaxis.

Behavior of Eccentrically Inclined Loaded Ring Footings Resting on Granular Soil

For civil engineers, the determination of ring footing bearing capacity subject to the combination of inclined and eccentric loading is a great topic of interest. In this paper, a novel approach is proposed to predict the behavior of ring footing subject to combinations of inclined and eccentric loading using the failure envelope approach, which can explain shallow footings behavior. Load eccentricity, inclination angle, and diameter ratio for ring footings are the most effective parameters on the failure envelope. In this regard, a series of experiments were conducted to investigate the behavior of ring footing subject to a possible form of eccentrically inclined loading. Three values of diameter ratio were considered, including n = 0.2, 0.4, and 0.6, along with a circular footing (n = 0). According to the test results, the conical 3D failure envelope and its equation were developed for each type of footing model. With constant vertical load the failure envelopes show that when the eccentricity is increased, the possible inclination angle is decreased. Also, by increasing the vertical loading, the possible eccentricity and inclination angle is decreased. Based on the observations, and obtained failure envelopes for different diameter ratios, when a ring footing is subject to combined eccentric inclined loading, n=0.4 is optimum. In the following, by using the failure envelope, the concepts of critical eccentricity and critical inclination angle were defined in a way that is suitable for studying the stability of ring footings in the V-H-M/B space.

Model studies of bearing capacity of rectangular foundation subjected to eccentric and inclined loads

This study presents the behaviour of eccentrically inclined loaded rectangular foundation on unreinforced and geogrid reinforced sand carried out experimentally, theoretically and numerically. In the past, several works have been done relating to the estimate of the ultimate bearing capacity (UBC) of shallow foundations supported by geogrid reinforced sand. These researches are limited to strip, square and circular footings. It is found that the less attention was given to determine the UBC of the shallow rectangular foundation under eccentric and inclined load with different depth of embedment $${D}_{\rm f}$$ . Hence, the present study is based on the behaviour of eccentrically inclined loaded rectangular (surface and embedded) foundation on the unreinforced and geogrid reinforced sand bed. To determine the load–settlement behaviour and compare it with experimental observation, equally theoretical and numerical analysis (PLAXIS 3D) has also been conducted.

Behaviour of circular footings confined by rigid base and geocell reinforcement

Soil in nature may exist in a stratified state. A possible condition is the case of a rigid layer underlying a weak sand stratum. In this instance, the bearing capacity of a shallow footing is affected by the lower rigid boundary. The treatment of thin soil layer by geocell reinforcement to raise the load carrying capacity of single shallow footing has been limited in the literature. Accordingly, rigid base and geocell reinforcement are investigated separately and in combination to study their influence on the behaviour and BC of shallow circular footings in dry sand bed. To capture that effect, different size rigid circular footings were tested on a bed in fully instrumented small- and large-scale laboratory installations. The ratio of sand layer thickness to footing diameter was changed considering optimum dimension and embedment depth for geocell mattress. The extensive laboratory part involved monitoring subgrade deformations, soil-geocell stresses and strains revealing the appropriate models for failure mechanisms in the presence of such confinements. Large increase in bearing capacity up to 225% and significant settlement reduction up to 66% are measured for the combined case. Base confinement less than three times the footing diameter in combination with the geocell mattress resulted in favourable higher design performance factors. New equations are proposed to estimate these factors for design and to extend classical formulations for footings strengthened by combined geocell-base confinement. A design performance factor is dependent on footing diameter, sand relative density and the ratio of layer thickness to footing diameter. As this ratio increases, this design factor decreases reaching a constant value at the critical depth.

Structural analysis and design of irregular shaped footings subjected to eccentric loading

AbstractThis article presents a simplified analytical model for designing irregular shaped reinforced concrete (RC) footings supporting square column and subjected to eccentric loading, that is, axial load P and biaxial moments, Mx in (x‐x) axis and My in (y‐y) axis, respectively. In this study, four design variations of footing sections are considered, namely, square, triangular, circular, and trapezoidal. Seven different footings (F‐1 to F‐7), each with a different loading condition, are used to analyze and design each of the selected irregular footings with the goal of getting the optimum footing section. The required reinforcing area of steel (As) is obtained using the SDM method in each selected footing which is then compared using finite element software (SAFE). The percentage difference of area of steel (As) for simplified method with the finite element software ranges within 1% to 13%. Moreover, the concrete volume results show that the circular and triangular footings prove to be the most economical footings followed by square and trapezoidal shaped footing sections. However, the results show that triangular shaped footings under heavy loads require a larger steel area (As) as in footing F‐7, which is not economical for heavy loads.

The effect of skirt footings for road settlement on peat soil

The construction of peat soils is a big challenge in the construction world coupled with the very special nature of peat soil. Road construction on peat soil is a major obstacle because the deformation that occurs on the road is so large. Skirt footings are one of the shallow foundations commonly used for building offshore oil refineries. With the principle of making soil that has a low bearing capacity into a single unit to be able to withstand the burden on it. Skirt footings are placed under the embankment with a parallel position stretching to the width of the road plan. Among the skirt, footings are connected with steel straps so that during the loading process the skirt footings decrease can be controlled. The purpose of this research is to make skirt footings a shallow foundation under a road built on peat soil. Tests were also carried out on two models of shallow foundation to determine the effect produced by skirt footings on the soil. The other two types of shallow foundation models are un-skirted footings and mini piles. Comparison of the results of tests between skirt footings with un-skirted footings, it can be concluded that skirts under circular footings act as a buffer against the effective stress of the soil. While from the comparison of test results between skirt footings with mini piles, it can be concluded that circular footings play a role in reducing the effect of the differential settlement on the soil. The results of this study are that skirt footing can withstand differential settlement patterns and able to increase road stability.

Bearing Capacity and Stiffness of Embedded Circular Footings on Stiff-Over-Soft Clay

AbstractThis technical note presents results from a series of undrained load tests performed at model scale on circular embedded footings founded in a two-layered stratigraphy, comprising uniform s...

Assessment of Changes in Shear Strength Parameters for Soils below Circular Machine Foundation

This paper focuses on the response of circular machine foundation resting on different soils (sand and clay) through studying the variation of soil shear strength parameters and strain with the number of cycles. The objective of the current study is to explore the results related to the parameters of the dynamic load (number of loading cycles and frequency of load) related to the circular footing of a machine on the dynamic shear strength parameters (for sand soil (ϕ˚dyn) and for clay soil (Cudyn)) in addition to the amplitude strain foundation. A special setup was designed and manufactured to simulate the vertical vibration of a circular machine foundation. A steel circular machine foundation with a diameter of 150 mm was used to represent the footing. A total of 6 cases were examined to take into account the effects of different parameters including different frequencies (0.5, 1, and 2 Hz); state of sand (medium and dense) which corresponded to relative densities of (50 and 80%), while the state of clay (medium and stiff) corresponded to undrained shear strengths (50 and 70 kPa). All tests were carried out under load amplitude of 2.5 kN. It was found that the rate of increase in shear strength parameters for the soil under a circular machine foundation decreases remarkably when increasing the frequency for both types of soil under the footing. While little change in the shear strength parameters, or even no change was observed under the effect of other locations. Moreover, the amplitude strain decreased when increasing the frequency for both types of soil.

Numerical Analyses of the Optimum Length for Stone Column Reinforced Foundation

The paper presents 3D numerical simulations that investigate the settlement performance for small groups of stone columns under a rigid circular footing. Particular consideration is given to the effects of stone column installation and load level on the optimum length of the stone columns. The results show that taking into account the installation effect by increasing the lateral earth pressure coefficient of the soil reduces the deformation of the columns and the surrounding soil. This leads not only to a reduction in the settlement of the footing but also to a reduction in the optimum length of the stone columns. This optimum length of columns is not constant, it increases with the increase in the load applied to the footing. However, overestimating the installation effect has a negligible consequence on the footing settlement and the optimum length of columns. In addition, the study shows that, for loads exceeding the working load levels of unreinforced soil, the optimum length of the columns is controlled by the extent of the total shear strains beneath the footing evolving with the applied load.

Use of a bounding surface model in predicting element tests and capacity in boundary value problems

The paper examines the merit of a bounding surface plasticity model at both element and system level. The governing equations are based essentially on the parent bounding surface plasticity model reported by Dafalias and Manzari in 2004 with some simple yet practical changes to enable realistic predictions for monotonic loading along different load paths. This is achieved by scaling the influence of the state parameter based on a normalised measure of anisotropy, thus leading to suitable change in dilatancy and plastic modulus for different loading directions. The paper presents a simple optimisation technique for calibrating the model parameters, providing an objective approach to reduce the uncertainties in parameter determination that leads to good agreement with responses measured in drained and undrained triaxial tests. The model has also been implemented for the boundary value problem of a buried circular plate anchor and a surface circular footing. Comparisons of the simulated responses with those measured in centrifuge tests demonstrate the potential of the model, whilst also pointing to the challenges in capturing the global response at all strain levels, even for rather simple boundary value problems.

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).

Experimental study on the behavior of eccentrically loaded circular footing model resting on reinforced sand

In this study, an experimental investigation has been conducted on a circular footing model subjected to eccentric load resting on the geonet-reinforced sand. To this end, five series of tests were carried out in order to evaluate the effect of reinforcement dimension and eccentricity on the bearing capacity, settlement, and rotation of the footing. Results show that the bearing capacity ratio (BCR) is in direct relationship with eccentricity and the impact of soil reinforcement at low settlements is much more significant in the case of eccentric loading. Additionally, the bearing capacity interaction diagram and variation in the position of rotation line at different load levels for reinforced and unreinforced conditions are presented.

Elastic Settlement Analysis for Various Footing Cases Based on Strain Influence Areas

In the present paper, the strain influence area method is introduced, which, technically, is classified between the classical elastic theory and Schmertmann’s semi-empirical method for immediate settlement analysis, exploiting the advantages of both. Strain influence area values are given in chart form for the calculation of elastic settlement at various locations on the plan view of flexible circular and rectangular footings, embankment loadings as well as for circular rigid footings on sands and clays. Among the major advantages of the proposed method is the direct and convenient calculation of the water table correction factor through the same charts; as known when the water table rises into the influence zone, the soil stiffness reduces, thus, additional settlement is induced. Finally, a new correction factor related to the effect of footing load on the modulus of elasticity of sands is proposed, whilst the Terzaghi’s empirical formula giving the effect of footing shape on the modulus of elasticity of soils has been revisited. It is very interesting that this empirical correction seems to cancel out the adverse effect of the second dimension of footing on elastic settlement analysis.

Bearing capacity of a side-rounded suction caisson foundation under general loading in clay

Abstract A novel side-rounded suction caisson foundation is proposed in this study. Compared to a conventional circular shape in plan, it has a rectangular middle section inserted in between the two circular halves for increased moment capacity. This paper presents an investigation into the bearing performance of this novel foundation in clay under uniaxial and combined loading by means of an extensive finite element parametric analysis. It is found that by adopting a dimensionless equivalent embedment ratio and a dimensionless equivalent strength heterogeneity ratio, which account for the side-rounded shape of the proposed foundation, its design approach can be unified with an existing framework established for conventional skirted circular footings. The advantage of the proposed foundation and the application of the proposed design method is demonstrated through an example application.

PERFORMANCE OF SKIRTED CIRCULAR SHALLOW FOOTINGS RESTING ON SANDY SOIL UNDER INCLINED LOADS

Experimental tests were conducted to study the behavior of skirted foundations rested on dry medium sandy soil subjected to vertical and inclined loads. To achieve this goal, a small-scale physical model was designed and performed which contained an aluminum circular footing (100 mm) in diameter and (10 mm) in thickness and skirts with different heights, local medium poorly graded dry sand is placed in a steel soil container (2 mm) thick with internal dimensions (1000 mm x 1000 mm in cross section and 800 mm in height). The main objective of this study was to evaluate the response of skirt attached to the foundation at different skirt (L/D) ratios (0.0, 0.5, 1.0 and 1.5) and is subjected to point load at different angles of inclination (θ) (90 °, 80 °, 70 ° to 60 °) varying with the horizontal. In all tests, the relative density of sand was kept constant and equal to (60%). Four tests were conducted on a foundation without a skirt, for comparison reasons, and twelve tests were conducted on a skirt attached to foundation. The results showed that with decreasing the angle of inclination of load with the horizontal the load carrying capacity decreased due to increase the horizontal component of applied load which leads to increase the shear stresses under the foundation, however that effect decreases with increase the skirt height.

Circular Footing on Geocell-Reinforced Granular Residue from Precious Gem Processing over a Sand Bed

Circular Footing on Geocell-Reinforced Granular Residue from Precious Gem Processing over a Sand Bed

Practical Large-Deformation Finite-Element Method for 3D Geotechnical Problems Involving Free Surface Deformations

The remeshing and interpolation technique with small-strain (RITSS) finite-element method has been widely adopted to address a broad range of two-dimensional (2D) large deformation geotechnical problems. However, its three-dimensional (3D) applications remain extremely limited due to the requirement of user-defined coding and the challenges in accurate tracking of free surfaces. This paper introduces a recently developed 3D RITSS method to tackle geotechnical problems that involve free surface deformations with only minimal programming effort required. Both the automated mesh regeneration and the Lagrangian finite-element increments are realized using available commercial packages. The entire simulation can be controlled and executed with a single piece of Python script. The reliability of the proposed method was verified by three validation examples. A further application example modeling the reinstallation of a circular footing near an existing footprint is also presented to demonstrate the advantage of the proposed method in coping with dramatic seabed surface deformations and hence illustrates its potential application to 3D geotechnical problems.