Effect of Footing Width on Bearing Capacity Factor Nγ for Smooth Strip Footings

By incorporating the variation of soil friction angle (?) with mean principal stress (σm), the effect of footing width (B) on bearing capacity factor Nγ was examined for a smooth strip footing placed on a granular medium without any surcharge pressure. The analysis was performed by means of a numerical lower bound limit analysis in conjunction with finite-elements and linear programming. An iterative computational procedure was framed to account for the dependency of ? on σm. Two well-defined ?–σm curves from literature associated with Hoston and Toyora sands, corresponding to relative density of 18 and 74.5%, respectively, were used. The magnitude of Nγ was obtained for different footing widths, covering almost the entire range of model and field footing sizes. It was noted that for B greater than about 0.4?m, it is possible to relate Nγ with B approximately in a linear fashion on a log–log scale. Further, it was seen that if an average value of ? along the footing–soil interface is obtained, it is possible to estimate a reasonable magnitude of Nγ for a given footing width provided the relationship between ? and σm is specified for the given material.     

Effect of Footing Roughness on Bearing Capacity Factor Nγ

The effect of interface friction angle (δ) between the footing and underlying soil mass on the bearing capacity factor Nγ was examined by using the upper bound limit analysis, finite elements, and linear programming. The analysis was carried out by employing velocity discontinuities along all the interfaces of the chosen triangular elements. The development of the plastic strains within elements was incorporated by using an associated flow rule. It was clearly noted that an increase in δ leads to a continuous increase in Nγ. With δ = ?, the magnitude of Nγ becomes almost the same as that for a perfectly rough foundation, that is, when no slippage takes place between the footing and underlying soil mass. The size of the plastic zones increases with increase in δ and ?. The obtained values of Nγ, for perfectly smooth and perfectly rough footings, compare quite favorably with those reported in literature. The study demonstrates that in the case when δ is smaller than ?, the assumption of a perfectly rough footing will lead to an unsafe prediction of the ultimate bearing capacity.     

Experimental and Numerical Study of Eccentrically Loaded Strip Footings Resting on Reinforced Sand

An experimental and numerical study of the behavior of an eccentrically loaded strip footing resting on geosynthetic-reinforced sand is presented. Particular attention was given to simulate footings constructed on unsymmetrical geogrid layers with eccentricity either direction of the footing. Several configurations of geogrid layers with different number, length, layer eccentricity along with the effect of the sand relative density, and the load eccentricity were investigated. A numerical study on a plane strain prototype footing was performed using finite element analysis. Test results indicate that the footing performance could be appreciably improved by the inclusion of layers of geogrid leading to an economic design of the footing. However, the efficiency of the sand-geogrid system is dependent on the load eccentricity ratio and reinforcement parameters. A close agreement between the experimental and numerical trend lines is observed. Based on the numerical and experimental results, critical values of the geogrid parameters for maximum reinforcing effect are established.     

Bearing Capacity of Rough Rigid Strip Footing on Cohesive Soil: Probabilistic Study

A probabilistic study on the bearing capacity of a rough rigid strip footing on a weightless cohesive soil is carried out to assess the influence of randomly distributed undrained shear strength. Nonlinear finite element analysis is merged with random field theory in conjunction with a Monte Carlo method. In a parametric study, the mean shear strength is held constant while the coefficient of variation and spatial correlation length of cohesion are varied systematically. The influence of the spatial variation of cohesion on the mean bearing capacity is discussed. The results are also presented in a probabilistic context to determine the probability of failure. A comparison between rough and smooth footing conditions is also made.     

Strain Influence Diagrams for Settlement Estimation of Both Isolated and Multiple Footings in Sand

Most of the existing methods for estimating settlements of footings in sand have been developed for either isolated square footings or for strip footings. The literature contains limited information on settlement analysis of rectangular footings, and, as a result, there is no way to accurately account for the effect of the footing length-to-width ratio on settlement. Additionally, no practical method exists for considering the interaction between neighboring footings in settlement estimates. In this paper, we use Schmertmann’s framework to propose a method of settlement estimation that takes full account of both the footing length-to-width ratio and the proximity of neighboring footings. Three-dimensional nonlinear finite element analyses were performed for various multiple footing configurations. Plate load tests were performed in sands using both a single plate and two plates separated by various distances. The numerical and experimental results indicate that the shape of the footing (expressed through its length-to-width ratio) and the proximity of neighboring footings affect two parameters of the strain influence diagram (which is the basis for the settlement estimation method): the depth to the peak influence factor Izp and the depth of the strain influence zone. We propose new strain influence diagrams for estimation of settlement under these more general conditions.     

Effects of Moment-to-Shear Ratio on Combined Cyclic Load-Displacement Behavior of Shallow Foundations from Centrifuge Experiments

Current design guidelines for shallow foundations supporting building and bridge structures discourage footing rocking or sliding during seismic loading. Recent research indicates that footing rocking has the potential to reduce ductility demands on structures by dissipating earthquake energy at the footing-soil interface. Concerns over cyclic and permanent displacements of the foundation during rocking and sliding along with the dependence of foundation capacity on uncertain soil properties hinder the use of footing rocking in practice. This paper presents the findings of a series of centrifuge experiments conducted on shear wall-footing structures supported by dry dense to medium dense sand foundations that are subjected to lateral cyclic loading. Two key parameters, static vertical factor of safety (FSV), and the applied normalized moment-to-shear ratio (M/(H?L)) at the footing-soil interface, along with other parameters, were varied systematically and the effects of these parameters on footing-soil system behavior are presented. As expected, the ratio of moment to the horizontal load affects the relative magnitude of rotational and sliding displacement of the footing. Results also show that, for a particular FSV, footings with a large moment to shear ratio dissipate considerably more energy through rocking and suffer less permanent settlement than footings with a low moment to shear ratio. The ratio of actual footing area (A) to the area required to support the vertical and shear loads (Ac), called the critical contact area ratio (A/Ac), is used to correlate results from tests with different moment to shear ratio. It is found that footings with similar A/Ac display similar relationships between cyclic moment-rotation and cumulative settlement, irrespective of the moment-to-shear ratio. It is suggested that shallow foundations with a sufficiently large A/Ac suffer small permanent settlements and have a well defined moment capacity; hence they may be used as effective energy dissipation devices that limit loads transmitted to the superstructure.     

Nonlinear Cone Penetration Test-Based Method for Predicting Footing Settlements on Sand

This paper presents centrifuge data from model footing tests on dry sand, where a high resolution optical displacement measurement technique was employed to record subsurface soil displacements beneath the centerline of loaded strip footings. These measurements allow derivation of vertical strain profiles, which are then used to estimate operational soil stiffness values. The stiffness values, which were assessed assuming a dependence on cone penetration test tip resistance and initial vertical effective stress level, are shown to degrade rapidly with increasing strain level. Despite such nonlinearity, the experimental strain data can be represented using an updated form of the well known Schmertmann strain influence profile. Settlements calculated using this profile are shown to be in agreement with subsurface settlements when appropriate soil stiffness values are employed.     

The inclination and shape factors for the bearing capacity of footings

In 1920, Prandtl published an analytical solution for the bearing capacity of a maximum strip load on a weightless infinite half-space. Prandtl subdivided the sliding soil component into three zones: two triangular zones on the edges and a wedge-shaped zone in between the triangular zones that has a logarithmic spiral form. The solution was extended by Reissner (1924) with a surrounding surcharge. Nowadays, a more extended version of Prandtl׳s formula exists for the bearing capacity. This extended formulation has an additional bearing capacity coefficient for the soil weight and additional correction factors for inclined loads and non-infinite strip loads. This extended version is known in some countries as “The equation of Meyerhof”, and in other countries as “The equation of Brinch Hansen”, because both men have separately published solutions for these additional correction factors. In this paper, we numerically solve the stresses in the wedge zone and derive the corresponding bearing capacity coefficients and inclination and shape factors. The inclination factors are also analytically solved.