The variation of N-gamma with footing roughness using the method of characteristics

By using the method of characteristics, the effect of footing-soil interface friction angle (delta) on the bearing capacity factor N-gamma was computed for a strip footing. The analysis was performed by employing a curved trapped wedge under the footing base; this wedge joins the footing base at a distance B-t from the footing edge. For a given footing width (B), the value of B-t increases continuously with a decrease in delta. For delta = 0, no trapped wedge exists below the footing base, that is, B-t/B = 0.5. On the contrary, with delta = phi, the point of emergence of the trapped wedge approaches toward the footing edge with an increase in phi. The magnitude of N-gamma increases substantially with an increase in delta/phi. The maximum depth of the plastic zone becomes higher for greater values of delta/phi. The results from the present analysis were found to compare well with those reported in the literature.

Semi-analytical finite element analysis of a strip footing on an elastic reinforced soil

A plane strain elastic interaction analysis of a strip footing resting on a reinforced soil bed has been made by using a combined analytical and finite element method (FEM). In this approach the stiffness matrix for the footing has been obtained using the FEM, For the reinforced soil bed (halfplane) the stiffness matrix has been obtained using an analytical solution. For the latter, the reinforced zone has been idealised as (i) an equivalent orthotropic infinite strip (composite approach) and (ii) a multilayered system (discrete approach). In the analysis, the interface between the strip footing and reinforced halfplane has been assumed as (i) frictionless and (ii) fully bonded. The contact pressure distribution and the settlement reduction have been given for different depths of footing and scheme of reinforcement in soil. The load-deformation behaviour of the reinforced soil obtained using the above modelling has been compared with some available analytical and model test results. The equivalent orthotropic approach proposed in this paper is easy to program and is shown to predict the reinforcing effects reasonably well.

Bearing capacity of circular footing on geocell-sand mattress overlying clay bed with void

The potential benefits of providing geocell reinforced sand mattress over clay subgrade with void have been investigated through a series of laboratory scale model tests. The parameters varied in the test programme include, thickness of unreinforced sand layer above clay bed, width and height of geocell mattress, relative density of the sand fill in the geocells, and influence of an additional layer of planar geogrid placed at the base of the geocell mattress. The test results indicate that substantial improvement in performance can be obtained with the provision of geocell mattress, of adequate size, over the clay subgrade with void. In order to have beneficial effect, the geocell mattress must spread beyond the void at least a distance equal to the diameter of the void. The influence of the void over the performance of the footing reduces for height of geocell mattress greater than 1.8 times the diameter of the footing. Better improvement in performance is obtained for geocells filled with dense soil. (C) 2008 Elsevier Ltd. All rights reserved.

Lower-bound collapse load Of square footing

Based on a radial moment field and the square yield criterion, a lower-bound collapse load is developed for a square footing subjected to a generalized contact pressure distribution. The current lower-bound collapse load compares well with the available upper-bound solutions.

Footing Response to Horizontal Vibration

For the prediction of response of footings subjected to horizontal vibration, different types of contact shear distributions and displacement conditions are to be considered. Solutions using elastic half-space theory are not available for all the cases of shear distribution and displacement conditions. In this paper, solutions are obtained for the cases in which solutions are not available and the relevant coefficients are presented in tables which could be used in the appropriate equations for the prediction of dynamic response. Spring constants are evaluated and tabulated for different displacement and shear distribution conditions.

Interaction analysis of strip footing resting on a non-homogeneous elastic medium

In this paper, a plane stress solution for the interaction analysis of strip footing resting on (i) a non-homogeneous elastic half-plane and (ii) a non-homogeneous elastic layer resting on a rigid stratum has been presented. The analysis has been done using a combined analytical and FEM method in which the discretization of the half-plane is not required and thereby minimizes the computational efforts considerably. The contact pressure distribution and the settlement profile for the selected cases of varying modulus half-plane, which has more relevance to foundation engineering, have been given. Experimental verification through a photoelastic method of stress analysis has been carried out for the case of footing on Gibson elastic half-plane, and the contact pressure distribution thus obtained has been compared with the theoretical results. Copyright (C) 1996 Elsevier Science Ltd

N-gamma for rough strip footing using the method of characteristics

By using the method of characteristics, the bearing capacity factor N-gamma was computed for a rough strip footing. The analysis was performed by considering a curved nonplastic wedge under the foundation base bounded by curved slip lines being tangential to the base of the footing at its either edge and inclined at an angle pi/4 - phi/2 with the vertical axis of symmetry. The existing theories in the literature for rough footings, which usually employ a triangular wedge below the footing base, were generally found to provide greater values of N-gamma as compared with the results obtained in this contribution.

Bearing capacity factors for a conical footing using lower- and upper-bound finite elements limit analysis

Bearing capacity factors, N-c, N-q, and N-gamma, for a conical footing are determined by using the lower and upper bound axisymmetric formulation of the limit analysis in combination with finite elements and optimization. These factors are obtained in a bound form for a wide range of the values of cone apex angle (beta) and phi with delta = 0, 0.5 phi, and phi. The bearing capacity factors for a perfectly rough (delta = phi) conical footing generally increase with a decrease in beta. On the contrary, for delta = 0 degrees, the factors N-c and N-q reduce gradually with a decrease in beta. For delta = 0 degrees, the factor N-gamma for phi >= 35 degrees becomes a minimum for beta approximate to 90 degrees. For delta = 0 degrees, N-gamma for phi <= 30 degrees, as in the case of delta = phi, generally reduces with an increase in beta. The failure and nodal velocity patterns are also examined. The results compare well with different numerical solutions and centrifuge tests' data available from the literature.

Evolution of electronic structure with dimensionality in divalent nickelates

We investigate the evolution of electronic structure with dimensionality (d) of Ni-O-Ni connectivity in divalent nickelates, NiO (3-d), La2NiO4, Pr2NiO4 (2-d), Y2BaNiO5 (1-d) and Lu2BaNi5 (0-d), by analyzing the valence band and the Ni 2p core-level photoemission spectra in conjunction with detailed many-body calculations including full multiplet interactions. Experimental results exhibit a reduction in the intensity of correlation-induced satellite features with decreasing dimensionality. The calculations based on the cluster model, but evaluating both Ni 3d and O 2p related photoemission processes on the same footing, provide a consistent description of both valence-band and core-level spectra in terms of various interaction strengths. While the correlation-induced satellite features in NiO is dominated by poorly screened d(8) states as described in the existing literature, we find that the satellite features in the nickelates with lower dimensional Ni-O-Ni connectivity are in fact dominated by the over-screened d(10)L(2) states. It is found that the changing electronic structure with the dimensionality is primarily driven by two factors: (i) a suppression of the nonlocal contribution to screening; and (ii) a systematic decrease of the charge-transfer energy Delta driven by changes in the Madelung potential. [S0163-1829(99)09619-8].

Interference of Two Closely Spaced Strip Footings on Sand Using Model Tests

By using small scale model tests, the interference effect on the ultimate bearing capacity of two closely spaced strip footings, placed on the surface of dry sand, was investigated. At any time, the footings were assumed to (1) carry exactly the same magnitude of load; and (2) settle to the same extent. No tilt of the footing was allowed. The effect of clear spacing (s) between two footings was explicitly studied. An interference of footings leads to a significant increase in their bearing capacity; the interference effect becomes even more substantial with an increase in the relative density of sand. The bearing capacity attains a peak magnitude at a certain (critical) spacing between two footings. The experimental observations presented in this technical note were similar to those given by different available theories. However, in a quantitative sense, the difference between the experiments and theories was seen to be still significant and it emphasizes the need of doing a further rigorous analysis in which the effect of stress level on the shear strength parameters of soil mass can be incorporated properly.

Partial Loss Of Support And Frame-Soil Interaction

An interaction analysis has been conducted to study the effects of a local loss of support beneath the beam footing of a two-bay plane frame. The results of the study indicate that the magnitude of increase in the bending moment and axial force in the structure due to the presence of a void are dependent, not only on the extent of support loss, but also on the relative stiffnesses between foundation beam and soil, and between superstructure and soil. The increase in bending moment even for a void span of 1/12 of the foundation beam length can become so significant as to exceed the safety provisions. The study shows that the effect of a void on the superstructure moments can be greatly minimized by a combination of rigid foundation and flexible superstructure.

Bearing capacity of square footings on geosynthetic reinforced sand

The results from laboratory model tests and numerical simulations on square footings resting on sand are presented. Bearing capacity of footings on geosynthetic reinforced sand is evaluated and the effect of various reinforcement parameters like the type and tensile strength of geosynthetic material, amount of reinforcement, layout and configuration of geosynthetic layers below the footing on the bearing capacity improvement of the footings is studied through systemati model studies. A steel tank of size 900 x 900 x 600 mm is used for conducting model tests. Four types of grids, namely strong biaxial geogrid, weak biaxial geogrid, uniaxial geogrid and a geonet, each with different tensile strength, are used in the tests. Geosynthetic reinforcement is provided in the form of planar layers, varying the depth of reinforced zone below the footing, number of geosynthetic layers within the reinforced zone and the width of geosynthetic layers in different tests. Influence of all these parameters on the bearing capacity improvement of square footing and its settlement is studied by comparing with the test on unreinforced sand. Results show that the effective depth of reinforcement is twice the width of the footing and optimum spacing of geosynthetic layers is half the width of the footing. It is observed that the layout and configuration of reinforcement play a vital role in bearing capacity improvement rather than the tensile strength of the geosynthetic material. Experimental observations are supported by the findings from numerical analyses.

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.

Effect of reinforcement form on the bearing capacity of square footings on sand

This paper presents the results of laboratory model loading tests and numerical studies carried out on square footings supported on geosynthetic reinforced sand beds. The relative performance of different forms of geosynthetic reinforcement (i.e. geocell, planar layers and randomly distributed mesh elements) in foundation beds is compared; using same quantity of reinforcement in each test. A biaxial geogrid and a geonet are used for reinforcing the sand beds. Geonet is used in two forms of reinforcement, viz. Planar layers and geocell, while the biaxial geogrid was used in three forms of reinforcement, viz. planar layers, geocell and randomly distributed mesh elements. Laboratory load tests on unreinforced and reinforced footings are simulated in a numerical model and the results are analyzed to understand the distribution of displacements and stresses below the footing better. Both the experimental and numerical studies demonstrated that the geocell is the most advantageous form of soil reinforcement technique of those investigated, provided there is no rupture of the material during loading. Geogrid used in the form of randomly distributed mesh elements is found to be inferior to the other two forms. Some significant observations on the difference in reinforcement mechanism for different forms of reinforcement are presented in this paper.

Bearing capacity of interfering multiple strip footings by using lower bound finite elements limit analysis

The ultimate bearing capacity of a number of multiple strip footings, identically spaced and equally loaded to failure at the same time,is computed by using the lower bound limit analysis in combination with finite elements. The efficiency factor due to the component of soil unit weight, is computed with respect to changes in the clear spacing (xi(gamma)) between the footings. It is noted that the failure load for a footing in the group becomes always greater than that of a single isolated footing. The values of xi(gamma) for the smooth footings are found to be always lower than the rough footings. The values ofxi(gamma) are found to increase continuously with a decrease in the spacing between footings. As compared to the available theoretical and experimental results reported in literature, the present analysis provides generally a little lower values of xi(gamma). (C) 2010 Elsevier Ltd. All rights reserved.