Spread Footings in Sand: Load Settlement Curve Approach

A study of the assumptions involved in the ultimate bearing capacity equation indicates the shortcomings of that equation and load test data confirm these shortcomings. A new approach using a normalized load settlement curve is proposed to alleviate these shortcomings and to obtain the complete load settlement curve for a footing in sand. The normalization consists of plotting the mean footing pressure divided by a measure of the soil strength within the depth of influence of the footing versus the settlement divided by the footing width. It is shown that the normalized load settlement curve for a footing is independent of footing size and embedment. It is proposed to obtain the normalized curve point-by-point from a soil test. Because the deformation of the soil observed under full-scale footings during loading indicates a barreling effect similar to the soil deformation around a pressuremeter probe, the preboring pressuremeter curve is used to obtain the footing curve. The new method consists of transforming the preboring pressuremeter curve point-by-point into the footing load settlement curve. Load tests and numerical simulations are used to propose a method for a rectangular footing near a slope subjected to an eccentric and inclined load. The new method gives the complete load settlement curve for the footing and alleviates the problems identified with the bearing capacity equation.     

Experimental and Theoretical Studies for the Behavior of Strip Footing on Oil-Contaminated Sand

This paper presents the results of a series of plain-strain model tests carried out on both clean sand and oil-contaminated sand loaded with a rigid strip footing. The objectives of this study are to determine the influence of oil-contaminated sand on the bearing capacity characteristics and the settlement of the footing. Contaminated sand layers were prepared by mixing the sand with an oil content of 0–5% with respect to dry soil to match the field conditions. The investigations are carried out by varying the depth and the length of the contaminated sand layer and the type of oil contamination. A plain-strain elastoplastic theoretical model with an interface gap element between footing and the soil is carried out to verify the test results of the model. It is shown that the load-settlement behavior and ultimate bearing capacity of the footing can be drastically reduced by oil contamination. The bearing capacity is decreased and the settlement of the footing is increased with increasing the depth and the length of the contaminated sand layer. The agreement between observed and computed results is found to be reasonably good in terms of load-settlement behavior and effect of oil contamination on the bearing capacity ratio. A comparison between the model results and the prototype scale (B = 1.0?m) results are also studied.     

Reliability-Based Analysis of Strip Footings Using Response Surface Methodology

A reliability-based analysis of a strip foundation subjected to a central vertical load is presented. Both the ultimate and the serviceability limit states are considered. Two deterministic models based on numerical simulations are used. The first one computes the ultimate bearing capacity of the foundation and the second one calculates the footing displacement due to an applied load. The response surface methodology is utilized for the assessment of the Hasofer–Lind reliability indexes. Only the soil shear strength parameters are considered as random variables while studying the ultimate limit state. Also, the randomness of only the soil elastic properties is taken into account in the serviceability limit state. The assumption of uncorrelated variables was found to be conservative in comparison to the one of negatively correlated variables. The failure probability of the ultimate limit state was highly influenced by the variability of the angle of internal friction. However, for the serviceability limit state, the accurate determination of the uncertainties of the Young's modulus was found to be very important in obtaining reliable probabilistic results. Finally, the computation of the system failure probability involving both ultimate and serviceability limit states was presented and discussed.     

Influence of Nonassociativity on the Bearing Capacity of a Strip Footing

This paper examines the ultimate bearing capacity of a strip footing located at the surface of a homogeneous soil. The approach adopted involves a numerical solution of the equations governing elastic-plastic soils with a nonassociative flow rule and makes use of the finite-difference code FLAC. This code is utilized to obtain the three bearing capacity factors for a wide range of values of the friction angle for four different values of the angle of dilation. The values of the bearing capacity factors obtained from the numerical approach are then compared with results derived from classical solutions modified to incorporate the nonassociative plastic flow of soil.     

Seismic Bearing Capacity of Shallow Strip Footings Embedded in Slope

The seismic bearing capacity factors for shallow strip footings embedded in sloping ground with general c-? soil are found out by using the limit equilibrium method. The seismic forces are considered as pseudostatic forces acting both on the footing and on the soil below the footing. A composite failure surface involving planar and logspiral is considered in the analysis. A new methodology to establish minimum bearing capacity factors has been adopted by numerical iteration technique to determine the critical focus of the logspiral. Three different types of failure surfaces are considered depending on the embedment depth and ground inclinations. The seismic bearing capacity factors with respect to cohesion, surcharge and unit weight components viz. Ncd, Nqd, and Nγd, respectively, are found out separately for various values of soil friction angles and seismic acceleration coefficients both in the horizontal and vertical directions, ground inclinations, and embedment depths. Results of the present study are reported in tabular form. The effect of parametric variation on seismic bearing capacity factors has been studied. Comparisons of the proposed method with available theories in the seismic case are also presented.     

Scale Effects of Shallow Foundation Bearing Capacity on Granular Material

Scale effects of shallow foundation bearing capacity on granular materials were investigated to further evaluate the trend of decreasing bearing capacity factor, Nγ, with increasing footing width, B, observed by other researchers. Model-scale square and circular footing tests ranging in width from 0.025 to 0.914?m were performed on two compacted sands at three relative densities. Results of the model-scale footing tests show that the bearing capacity factor, Nγ, is dependent on the absolute width of the footing for both square and circular footings. Although this phenomenon is well known, the current study used a large range of footing sizes tested on well-graded sands to show that the previously reported modifications to the bearing capacity factor, Nγ, using grain-size and reference footing width do not sufficiently account for the scale effect seen in the test results from this study. It also shows that behavior of most model-scale footing tests cannot be directly correlated to the behavior of full-scale tests because of differences in mean stresses experienced beneath footings of varying sizes. The relationship of the initial testing conditions (i.e., void ratio) of the sand beds and mean stress experienced beneath the footing (correlated to footing size) to the critical state line controls footing behavior and, therefore, model-scale tests must be performed at a lower density than a corresponding prototype footing in order to correctly predict behavior. Small footings were shown to have low mean stresses but high Nγ values, which indicates high operative friction angles and may be related to the curvature of the Mohr–Coulomb failure envelope.     

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.     

Three-Dimensional Large Deformation FE Analysis of Square Footings in Two-Layered Clays

In strong over soft two-layered clays, there is a potential for the footing to experience a punch-through failure, where the footing penetrates a large distance at a short time after the initial peak resistance is reached. Three-dimensional (3D) large deformation finite-element analyses using 3D RITSS method were conducted to simulate the penetration responses of square footings in strong over soft clays. The effects of surface soil heave and soil layer interface deformation during footing penetration were studied in weightless soils. Fitted equations were proposed to express the footing capacity response against the penetration depth. Based on the fitted equations, formulas to calculate footing peak bearing factor and the corresponding penetration depth were developed. The peak footing capacity factor and the corresponding penetration depth increases with the increasing of soil layer strength ratio, relative top soil layer thickness and soil weight factor, thus the potential of punch-through failure was reduced accordingly. It was also found that the soil weight effect can be a simple surcharge based on the formula developed in the weightless soil. Design charts for the peak footing capacity factor and the corresponding penetration depth were developed.     

Undrained Bearing Capacity of Strip Footings on Slopes

The undrained bearing capacity of foundations on or near slopes is commonly calculated using empirical equations or from design charts which have been produced based on limit equilibrium or upper bound plasticity calculations. Many of the available methods do not take account of important parameters that affect the undrained bearing capacity factor, such as the distance of the footing from the slope, the slope height, or the soil properties. This paper presents finite element analyses of strip footings on or near undrained soil slopes performed in order to investigate the influence of the various parameters that affect undrained bearing capacity. The results of the analyses are compared to available methods. It is found that while some of these methods compare well with the finite element results for certain combinations of geometrical parameters and soil properties, they cannot produce sufficiently accurate results as they either do not take account of all of the affecting parameters or are generally not conservative. Based on the finite element results, design charts, equations, and a design procedure are proposed for the calculation of the undrained bearing capacity factor Nc as a function of the undrained shear strength and the bulk unit weight of the soil, the footing width, the distance of the footing from the slope, the slope angle and the slope height.     

Deformation Patterns of Reinforced Foundation Sand at Failure

While the stability of foundation soils has been written about extensively, the ultimate loads on reinforced soils is a subject studied to a much lesser degree. There is convincing experimental evidence in the literature that metal strips or layers of geosynthetic reinforcement can significantly increase the failure loads on foundation soils. Laboratory tests were performed to investigate the kinematics of the collapse of sand reinforced with a layer of flexible reinforcement. Sequential images of the deformation field under a model footing were digitally recorded. A correlation-based motion detection technique was used to arrive at an incremental displacement field under a strip footing model. Color-coded displacements are presented graphically. The mechanism retains some of the characteristic features of a classical bearing capacity pattern of failure, but the reinforcement modifies that mechanism to some extent. The strips of geotextile used as model reinforcement give rise to the formation of shear bands in a narrow layer adjacent to the geosynthetic. Reinforcement restrains the horizontal displacement of the soil and alters the collapse pattern. The mechanism of deformation identified in the tests will constitute a basis for limit analysis of reinforced foundation soils.     

Undrained Bearing Capacity of Square and Rectangular Footings

The uniaxial vertical bearing capacity of square and rectangular footings resting on homogeneous undrained clay is investigated with finite element analyses, using both Tresca and von Mises soil models. Results are compared with predictions from conventional bearing capacity theory and available analytical and numerical solutions. By calibrating the finite element results against known exact solutions, best estimates of bearing capacity for rough-based rectangular footings are derived, with the shape factor fitted by a simple quadratic function of the footing aspect ratio. For a square footing, the bearing capacity is approximately 5% lower than that based on Skempton’s shape factor of 1.2.     

Axial Compression of Footings in Cohesionless Soils. II: Bearing Capacity

An extensive database of full-scale field load tests was used to examine the bearing capacity for footings in cohesionless soils. Each load test curve was evaluated consistently to determine the interpreted failure load (i.e., bearing capacity) using the L1-L2 method. This test value then was compared with the theoretical bearing capacity, computed primarily using the basic Vesi? model. The comparisons show that, for footing widths B>1?m, the field results agree very well with the Vesi? predictions. However, for B<1?m, the results indicated a relationship between B and the predicted-to-measured bearing capacity ratio. Accordingly, a simple modification was made to the bearing capacity equation, and the resulting predictions are very good.     

Bearing Capacity of Shallow Foundations on Sand: A Relative Density Approach

An accurate prediction of bearing capacity of shallow foundations on granular soils has been historically complicated by effects due to scale of the foundation. These effects are due to the nonlinear strength behavior of the granular soil and the phenomenon of progressive failure. The former can be conveniently accounted for by strength-dilatancy relationships. It is proposed that the effect of progressive failure on ultimate bearing capacity can be described in terms of the relative dilatancy index inherent in strength-dilatancy relationships. A design approach to bearing capacity based on these considerations is presented. The approach is calibrated using bearing capacity results from studies spanning the past 20 years. The solution is shown to work well for the sands examined and is useful in that the proposed process by which strength parameters are determined reduces, or may eliminate, the need for laboratory or in situ shear testing, while increasing the accuracy of the predictions made when compared to conventional methods.     

Scale Effect of Strip and Circular Footings Resting on Dense Sand

This paper presents the results of a research program of strip and circular footings resting on dry dense sand. The scale effect on the bearing capacity and the shape factor s;gg of the footings is investigated numerically and experimentally. The footings are analyzed using the method of characteristics. A wedge failure mechanism has been adopted. Triaxial compression tests conducted under confining pressures up to 2,500 kPa show that the friction angle of dense sand decreases with stress level. The stress-dependent friction angle of soil is adopted in the characteristics analysis. The numerical results indicate that the bearing capacity increases exponentially with footing size. With increasing footing size, the bearing capacity factor N;gg is reduced, while the shape factor s;gg is increased. Centrifuge tests of strip and circular footings with dimensions up to the equivalent of 7 m have been conducted. The experimental work verified the numerical analysis through the consistency of results.     

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.     

平面K型圆钢管搭接节点滞回性能的有限元分析

节点作为结构的关键部位,其静力承载力及滞回性能的研究具有重要的现实意义。本文采用ANSYS有限元分析计算,探讨了平面K型圆钢管搭接节点的受力性能、破坏模式、滞回性能下极限承载力以及搭接率、内隐蔽部分焊接与否、节点处集中荷载和各几何参数对节点承载力性能的影响。     

Reliability-Based Analysis and Design of Strip Footings against Bearing Capacity Failure

This paper presents a reliability-based approach for the analysis and design of a shallow strip footing subjected to a vertical load with or without pseudostatic seismic loading. Only the punching failure mode of the ultimate limit state is studied. The deterministic models are based on the upper-bound method of the limit analysis theory. The random variables used are the soil shear strength parameters and the horizontal seismic coefficient. The Hasofer-Lind reliability index and the failure probability are determined. A sensitivity analysis is also performed. The influence of the applied footing load on the reliability index and the corresponding design point is presented and discussed. It was shown that the negative correlation between the soil shear strength parameters highly increases the reliability of the foundation and that the failure probability is highly influenced by the coefficient of variation of the angle of internal friction of the soil and the horizontal seismic coefficient. For design, an iterative procedure is performed to determine the breadth of the footing for a target failure probability.     

Simple Formulas for the Response of Shallow Foundations on Compressible Sands

The engineering design of shallow foundations on sand is almost universally based on one of the variants of the classical bearing capacity formula. However, this formula is suitable only where the sand exhibits dilative behavior and a clear rupture mechanism forms at failure. The main challenge then is choosing a suitable friction angle, taking into account the soil density and the high stresses beneath the footing. When other conditions apply, in particular when the footing is large or founded on compressible materials, alternative approaches need more focus on soil compressibility. Two simple semianalytical formulas are proposed and explored in this paper: (1) an analysis using a one-dimensional (1D) compression equation; and (2) an analysis using the concept of “bearing modulus.” It is argued that the bearing modulus approach may be used for conditions that reflect moderate design parameters (i.e., moderate foundation size and sand compressibility), but for very large foundations or highly compressible soils the 1D compression method is found more suitable. It is shown that the bearing modulus analysis can be approached in terms of the compression response of the soil, suggesting a possible route to link the bearing modulus directly to the compression model parameters of the soil.     

Numerical Study of the Effect of Foundation Size for a Wide Range of Sands

This paper presents a numerical investigation of the effect of foundation size on the response of shallow circular foundations on siliceous and calcareous sands. The study is based on the predictive capabilities of the MIT-S1 soil model for simulating both the compression and shear behaviors of natural sands over a wide range of densities, K0 values and confining pressures. The paper highlights the variations in the deformation mechanisms for the siliceous and calcareous sands cases. The assessment of the bearing capacity factor, Nγ, is examined, showing a dramatic decrease in the values with increasing foundation size for the case of footings on calcareous sands, eventually converging to a terminal Nγ value. At this stage the sand resistance is insensitive to variations in initial density and foundation size because the sand tends to loose its initial characteristics due to grain crushing, leading the material rapidly toward ultimate conditions. In the silicious sand case, it is found that, eventually, for extremely large footing diameters, the deformation mechanism progresses toward a punching shear mechanism, rather than the classical rapture pattern accompanied by surface heave as employed in current bearing capacity equations. A dimensional transition between the failure mechanisms can clearly be defined, referred to as a “critical size” in the Nγ–D relationship.