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.     

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.     

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.     

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.     

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.     

Reappraisal of Size Effect of Bearing Capacity from Plastic Solution

A simplified method for estimating the ultimate bearing capacity of surface footings on sand is described with special attention to the dependency of the angle of internal friction of sand on confining stress. An extended slip line method is developed, in which the dependency of the angle of internal friction on the confining stress is formulated from results of conventional triaxial compression tests for various sands. Based on results from a comprehensive series of calculations employing the extended slip line method, the writers reappraise size effects on bearing capacity and investigate the relationship between strength parameters of sand and size effects on bearing capacity. A modified formula and several diagrams that provide a simple estimation method are proposed to consider size effects on bearing capacity. A comparison between estimations using the formula and ultimate bearing capacities measured from several series of centrifuge tests demonstrates the practicability of the proposed method for both strip and circular footings.     

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.     

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.     

Plate Load Tests on Cemented Soil Layers Overlaying Weaker Soil

This paper addresses the interpretation of plate load tests bearing on double-layered systems formed by an artificially cemented compacted top soil layer (three different top layers have been studied) overlaying a compressible residual soil stratum. Applied pressure-settlement behavior is observed for tests carried out using circular steel plates ranging from 0.30 to 0.60 m diameter on top of 0.15 to 0.60-m-thick artificially cemented layers. The paper also stresses the need to express test results in terms of normalized pressure and settlement—i.e., as pressure normalized by pressure at 3% settlement (p/p3%) versus settlement-to-diameter (δ/D) ratio. In the range of H/D (where H = thickness of the treated layer and D = diameter of the foundation) studied, up to 2.0, the final failure modes observed in the field tests always involved punching through the top layer. In addition, the progressive failure processes in the compacted top layer always initiated by tensile fissures in the bottom of the layer. However, depending on the H/D ratio, the tensile cracking started in different positions. The footing bearing capacity analytical solution for layered cohesive-frictional soils appears to be quite adequate up to a H/D value of about 1.0. Finally, for a given project, combining Vésic’s solution with results from one plate-loading test, it is possible (knowing of the demonstrated normalization of p/p3%-δ/D, where the pressure-relative settlement curves for different H/D ratios produce a single curve for all values of H/D) to estimate the pressure-settlement curves for footings of different sizes on different thicknesses of a cemented upper layer.     

Dynamic Response of Footings Resting on a Sand Layer of Finite Thickness

Dynamic response of foundations depends on several factors, namely, size and shape of the foundations, depth of embedment, soil profile and properties, frequency of loading, and mode of vibration. An attempt was made in this Technical Note to investigate the dynamic behavior of foundations resting on a sand layer underlain by a rigid layer. Model block vibration tests were carried out in a pit of size 2.0?m×2.0?m×1.9?m using a concrete footing of size 0.4?m×0.4?m×0.1?m and a vertically acting rotating-mass type mechanical oscillator. Using locally available river sand, a sand layer of six different thicknesses was prepared, and, for each thickness, tests were carried out for two different static weights and three different dynamic loadings. It was observed that the resonant frequency decreases with an increase in layer thickness and it nearly equals that of the half-space when the thickness of the layer is more than three times the width of the footing. It was also observed that the radiation damping of the sand layer was affected by the presence of a rigid layer at bottom. Inclusion of rigid layer causes a 9.8% reduction with respect to homogeneous sand condition even for a sand layer of thickness four times the width of the footing.     

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.     

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.     

Load Testing of a Closed-Ended Pipe Pile Driven in Multilayered Soil

Piles are often driven in multilayered soil profiles. The accurate prediction of the ultimate bearing capacity of piles driven in mixed soil is more challenging than that of piles driven in either clay or sand because the mechanical behavior of these soils is better known. In order to study the behavior of closed-ended pipe piles driven into multilayered soil profiles, fully instrumented static and dynamic axial load tests were performed on three piles. One of these piles was tested dynamically and statically. A second pile served as reaction pile in the static load test and was tested dynamically. A third pile was tested dynamically. The base of each pile was embedded slightly in a very dense nonplastic silt layer overlying a clay layer. In this paper, results of these pile load tests are presented, and the lessons learned from the interpretation of the test data are discussed. A comparison is made of the ultimate base and limit shaft resistances measured in the pile load tests with corresponding values predicted from in situ test-based and soil property-based design methods.     

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.     

Undrained Stability of Footings on Slopes

Solutions for the ultimate bearing capacity of footings on purely cohesive slopes are obtained by applying finite element upper and lower bound methods. In a footing-on-slope system, the ultimate bearing capacity of the footing may be governed by either foundation failure or global slope failure. The combination of these two factors makes the problem difficult to solve using traditional methods. The importance of a dimensionless strength ratio in determining the footing capacity is broadly discussed, and design charts are presented for a wide range of parameters. In addition, the effect of footing roughness and surface surcharge are briefly quantified.     

Assessment of the Axial Load Response of an H Pile Driven in Multilayered Soil

Most of the current design methods for driven piles were developed for closed-ended pipe piles driven in either pure clay or clean sand. These methods are sometimes used for H piles as well, even though the axial load response of H piles is different from that of pipe piles. Furthermore, in reality, soil profiles often consist of multiple layers of soils that may contain sand, clay, silt or a mixture of these three particle sizes. Therefore, accurate prediction of the ultimate bearing capacity of H piles driven in a mixed soil is very challenging. In addition, although results of well documented load tests on pipe piles are available, the literature contains limited information on the design of H piles. Most of the current design methods for driven piles do not provide specific recommendations for H piles. In order to evaluate the static load response of an H pile, fully instrumented axial load tests were performed on an H pile (HP?310×110) driven into a multilayered soil profile consisting of soils composed of various amounts of clay, silt and sand. The base of the H pile was embedded in a very dense nonplastic silt layer overlying a clay layer. This paper presents the results of the laboratory tests performed to characterize the soil profile and of the pile load tests. It also compares the measured pile resistances with those predicted with soil property- and in situ test-based methods.     

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.     

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.     

Analysis of Load Tests on Piles Driven through Calcareous Desert Sands

The ultimate bearing capacity of short, precast concrete piles driven into calcareous sands was examined by pile-load tests carried out at two sites in Kuwait. The piles had a 0.3 m × 0.3 m square cross section and extended to a maximum depth of 12 m. They were driven through a loose-to-compact calcareous surface sand layer underlain by a competent dense-to-very-dense siliceous cemented sand deposit. The pile tips and part of the pile shafts were embedded in the lower layer. The base resistance and shaft friction were calculated using the Meyerhof method for a layered soil profile. The method employs the standard penetration test N values. The results indicate that a great portion of the pile capacity is due to base resistance. The skin friction mobilized is small and consists of two components corresponding to the two layers penetrated along the pile shafts. The calculated pile capacities were very close to the measured values. The unit skin friction is not constant along the pile shafts.     

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.