• Proceedings of the Korean Geotechical Society Conference
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• 2004.03b
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• pp.565-573
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• 2004

This study is to present explicit analytical expressions for calculating bearing capacity factor $N_{\gamma}$, to provide results of the numerical computation instead of the graphical method. In this study, $N_{\gamma}$ is proposed in the critical failure surface on assumption that the center of log spiral in the radial shear zone can be located at the any points of around footing. The critical failure surface is one which yields minimum passive pressure $P_{\gamma}$ on the radial shear zone from the family of log spirals accoding to change of the center of log spiral. This study adoptes Terzaghi's bearing capacity principle(e.g., Prandtl's mechanism, limit equilibrium equation, superposition principle) but the soil wedge in an elastic zone makes angle $45^{\circ}+{\phi}/2$ with the horizontal and the location of the log spiral's center.

• Geomechanics and Engineering
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• v.1 no.3
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• pp.205-218
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• 2009

The bearing capacity factor $N_{\gamma}$ is computed for a rough conical footing placed over horizontal ground surface. The axisymmetric lower bound limit analysis formulation, in combination with finite elements and linear programming, proposed recently by the authors is used in this study. The variation of $N_{\gamma}$ with cone apex angle (${\beta}$), in a range of $30^{\circ}-180^{\circ}$, is obtained for different values of ${\phi}$; where ${\phi}$ is soil friction angle. For ${\phi}<30^{\circ}$, the magnitude of $N_{\gamma}$ is found to decrease continuously with an increase in ${\beta}$ from $30^{\circ}$ to $180^{\circ}$. On the other hand, for ${\phi}>30^{\circ}$, the minimum magnitude of $N_{\gamma}$ is found to occur generally between ${\beta}=120^{\circ}$ and ${\beta}=150^{\circ}$. In all the cases, it is noticed that the magnitude of $N_{\gamma}$ becomes maximum for ${\beta}=30^{\circ}$. For a given diameter of the cone, the area of the plastic zone reduces generally with an increase in ${\beta}$. The obtained values of $N_{\gamma}$ are found to compare quite well with those available in literature.

• Journal of the Korean Geotechnical Society
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• v.30 no.1
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• pp.49-63
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• 2014

Bearing capacity factor $N_{\gamma}$ and shape factor were studied for rigid strip and circular footings with a rough base on sand by numerical modelling considering the effect of dilation angle. The numerical model was developed with an explicit finite difference code. Loading procedures and interpretation methods were devised in order to shorten the running time while eliminating the exaggeration of the reaction caused by the explicit scheme. Using the Mohr-Coulomb plasticity model with associated (${\psi}={\phi}$) and nonassociated (${\psi}$ < ${\phi}$) flow-rules, the bearing capacity factor $N_{\gamma}$ was evaluated for various combinations of internal friction angles and dilation angles. Bearing capacity factor decreased as the dilation angle was reduced from the associated condition. An equation applicable to typical sands was proposed to evaluate the relative bearing capacity for the nonassociated condition compared to the associated condition on which most bearing capacity factor equations are based. The shape factor for the circular footing varied substantially when the plane-strain effect was taken into account for the strip footing. The numerical results of this study showed closer trends with the previous experimental results when the internal friction angle was increased for the strip footing. Discussions are made on the reason that previous equations for the shape factor give different results and recommendations are made for the appropriate design shape factor.

• Geomechanics and Engineering
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• v.5 no.4
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• pp.363-377
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• 2013

Any structure constructed on the earth is supported by the underlying soil. Foundation is an interfacing element between superstructure and the underlying soil that transmits the loads supported by the foundation including its self weight. Foundation design requires evaluation of safe bearing capacity along with both immediate and long term settlements. Weak and compressible soils are subjected to problems related to bearing capacity and settlement. The conventional method of design of footing requires sufficient safety against failure and the settlement must be kept within the allowable limit. These requirements are dependent on the bearing capacity of soil. Thus, the estimation of load carrying capacity of footing is the most important step in the design of foundation. A number of theoretical approaches, in-situ tests and laboratory model tests are available to find out the bearing capacity of footings. The reliability of any theory can be demonstrated by comparing it with the experimental results. Results from laboratory model tests on square footings resting on sand are presented in this paper. The variation of bearing capacity of sand below a model plate footing of square shape with variation in size, depth and the effect of permissible settlement are evaluated. A steel tank of size $900mm{\times}1200mm{\times}1000mm$ is used for conducting model tests. Bearing capacity factor $N_{\gamma}$ is evaluated and is compared with Terzaghi, Meyerhof, Hansen and Vesic's $N_{\gamma}$ values. From the experimental investigations it is found that, as the depth of sand cushion below the footing ($D_{sc}$) increases, ultimate bearing capacity and settlement values show an increasing trend up to a certain depth of sand cushion.

• Journal of the Korean Geosynthetics Society
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• v.9 no.1
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• pp.13-20
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• 2010

This paper describes the procedure to predict the entire load-displacement curve and the failure mechanism of shallow strip footing for real soil. The presented results show that it is possible to analyze the post peak behavior of shallow strip footing and to give a progressive failure mechanism clearly. Finite element computation of the bearing capacity factor $N_{\gamma}$ have been made for shallow strip footings with friction angles and dilation angle. It is shown that commonly used values of $N_{\gamma}$ which have generally been based on associated plasticity calculations are unconservative for real soil with non-associated plasticity and some smooth footing.

• Geomechanics and Engineering
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• v.15 no.6
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• pp.1193-1205
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• 2018

A footing located on slopes possess relatively lower bearing capacity as compared to the footing located on the level ground. The bearing capacity further reduces under seismic loading. The adverse effect of slope inclination and seismic loading on bearing capacity can be minimized by proving sufficient setback distance. Though few earlier studies considered setback distance in their analysis, the range of considered setback distance was very narrow. No study has explored the critical setback distance. An attempt has been made in the present study to comprehensively investigate the effect of setback distance on footing under seismic loading conditions. The pseudo-static method has been incorporated to study the influence of seismic loading. The rate of decrease in seismic bearing capacity with slope inclination become more evident with the increase in embedment depth of footing and angle of shearing resistance of soil. The increase in bearing capacity with setback distance relative to level ground reduces with slope inclination, soil density, embedment depth of footing and seismic acceleration. The critical value of setback distance is found to increase with slope inclination, embedment depth of footing and density of soil. The critical setback distance in seismic case is found to be more than those observed in the static case. The failure mechanisms of footing under seismic loading is presented in detail. The statistical analysis was also performed to develop three equations to predict the critical setback distance, seismic bearing capacity factor ($N_{{\gamma}qs}$) and change in seismic bearing capacity (BCR) with slope geometry, footing depth and seismic loading.