Bearing Capacity of Strip Footings on Jointed Rock Masses

Bearing capacity solutions are presented for strip footings on jointed rock masses with one and two sets of discontinuities. The solutions employ a lower bound bearing capacity model coupled with a simple discontinuity strength model. The strength of the rock material and the discontinuities, and the number and orientation of the discontinuity sets, are evaluated explicitly. The results are presented as bearing capacity factor charts that illustrate the significant effects of the strength and discontinuity geometric parameters. The trends of the results agree well with those obtained from other models. The solution is straightforward, and it can be implemented manually or in any spreadsheet program.     

Bearing Capacity of Circular Footings

Numerical computations using FLAC are reported to evaluate the soil-bearing capacity for circular smooth and rough footings. The effect of nonassociativity of the soil is investigated. The results indicate a decrease in the bearing capacity-factors value when the soil displays high nonassociativity. The bearing capacity factors Nγ′ obtained from the computations are significantly lower than those reported by Bolton and Lau in 1993. The results compare favorably with experimental data reported by de Beer in 1970. The sources of possible inaccuracies in numerical simulations are discussed.     

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.     

Undrained Limit States of Shallow Foundations Acting in Consort

There is no established procedure for the calculation of bearing capacity of a shallow foundation system comprising cojoined footings. Ad hoc approaches are relied on and may simply involve summing the ultimate limit states of the individual footings as if they acted independently; neglecting additional capacity of the system available from the kinematic constraint provided by the structural connection between the footings. In this study, the undrained capacity under general loading of rigidly connected two-footing systems at various separations has been investigated with finite-element analyses. Results are presented in terms of ultimate limit states under pure vertical (V), horizontal (H), and moment (M) loading, and failure envelopes defining limiting load states under combined VH, VM, HM, and VHM loads. Kinematic failure mechanisms observed in the finite-element analyses are presented and in cases used to provide the basis for upper bound solutions.     

Undrained Bearing Capacity of Two-Strip Footings on Spatially Random Soil

A probabilistic study on the interference of two parallel rough rigid strip footings on a weightless soil with a randomly distributed undrained shear strength performed. The problem is studied using the random finite element method, where nonlinear finite element analysis is merged with random field theory within a Monte Carlo framework. The variability of undrained shear strength is characterized by a lognormal distribution and an exponentially decaying spatial correlation length. The estimated bearing capacity statistics of isolated and two footings cases are compared and the effect of footing interference discussed. Although interference between footings on frictionless materials is not very great, the effect is shown to be increased by soil variability and spatial correlation length.     

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.     

Capacity, Settlement, and Energy Dissipation of Shallow Footings Subjected to Rocking

The effectiveness of structural fuse mechanisms used to improve the performance of buildings during seismic loading depends on their capacity, ductility, energy dissipation, isolation, and self-centering characteristics. Although rocking shallow footings could also be designed to possess many of these desirable characteristics, current civil engineering practice often avoids nonlinear behavior of soil in design, due to the lack of confidence and knowledge about cyclic rocking. Several centrifuge experiments were conducted to study the rocking behavior of shallow footings, supported by sand and clay soil stratums, during slow lateral cyclic loading and dynamic shaking. The ratio of the footing area to the footing contact area required to support the applied vertical loads (A/Ac), related to the factor of safety with respect to vertical loading, is correlated with moment capacity, energy dissipation, and permanent settlement measured in centrifuge and 1 g model tests. Results show that a footing with large A/Ac ratio (about 10) possesses a moment capacity that is insensitive to soil properties, does not suffer large permanent settlements, has a self-centering characteristic associated with uplift and gap closure, and dissipates seismic energy that corresponds to about 20% damping ratio. Thus, there is promise to use rocking footings in place of, or in combination with, structural base isolation and energy dissipation devices to improve the performance of the structure during seismic loading.     

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.     

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.     

Inclination Factors for Seismic Bearing Capacity

The classic approach for static analysis and design for the effect of shear forces transmitted by shallow foundations is to modify the bearing capacity by introducing inclination factors to reduce the shear strength provided by cohesion, surcharge and self-weight in the standard bearing capacity equation. These static inclination factors are usually based on empirically derived relationships determined by laboratory and field tests. However, it is possible to derive them from limit analysis of a simple Coulomb-type mechanism and thereby extend the concept of inclination factors to the dynamic case giving values for seismic design.     

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.     

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.     

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.     

Computation of Bearing Capacity Factor Nγ?Terzaghi’s Mechanism

A procedure based on K?tter’s equation is developed for the evaluation of bearing capacity factor Nγ with Terzaghi’s mechanism. Application of K?tter’s equation makes the analysis statically determinate, in which the unique failure surface is identified using force equilibrium conditions. The computed Nγ values are found to be higher than Terzaghi’s value in the range 0.25–20%, with a diverging trend for higher values of angle of soil internal friction. A fairly good agreement is observed with other solutions which are based on finite difference coupled with associated flow rule, limit analysis, and limit equilibrium. Finally, the comparison with available experimental results vis-à-vis other solutions shows that, computed Nγ values are capable of making a reasonably good prediction.     

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 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.     

Theoretical Study of Strengthening for Increased Shear Bearing Capacity

In recent years, the use of carbon fiber reinforced polymer (CFRP) has been shown to be a competitive method for strengthening both the structural and economic performance of concrete. The method has been used for almost a decade, yet – most research undertaken has studied the flexural behavior of strengthened structures, while research on shear strengthening has been limited. The work presented in this paper focuses on CFRP shear strengthening of concrete beams. The theory presented addresses the limitations of the widely used truss model, and a refinement is suggested. A reduction factor to consider the nonuniform strain distribution over the cross section is proposed and strain limitations are prescribed for the principal strain in the concrete instead of the fiber strain, as in previous studies. The derived analytical model is compared to experimental data from tests. Fairly good agreement is found between results from tests and calculated values from theory with regard to both shear-bearing capacity and average fiber utilization.     

Experimental Investigation of the Reinstallation of Spudcan Footings Close to Existing Footprints

The large footprints that remain on the seabed after offshore mobile jack-up platforms have completed operations provide hazardous conditions for any future jack-up installation at that site. The slope of the footprint and varying soil strengths below the surface cause detrimental horizontal and moment loads to be induced on the spudcan during the preloading process where only vertical loads are expected. Experimental data from 12 tests investigating the reinstallation of a spudcan footing close to an existing footprint is presented in this paper. The experiments were carried out using a geotechnical drum centrifuge at a radial acceleration level equivalent to 250 times that of Earth’s gravity. The stiffness of the loading leg and model spudcan shape were scaled to ensure conditions of stress similitude between the model and prototype. In all of the experiments, an initial footprint was created. The spudcan was then offset and reinstalled with the combined vertical, horizontal, and moment loads on the spudcan recorded. The effects of reinstallation location, preloading levels, and change in leg stiffness were investigated. The worst location for reinstallation was found to be at an offset half a spudcan diameter from the initial spudcan installation. The horizontal and moment loads were also greater when a more extensive footprint was created by the initial spudcan being embedded deeper and with a higher preload. For the range of conditions tested, changing the leg stiffness did not affect the results.     

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.