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.     

Deep Penetration of Strip and Circular Footings into Layered Clays

The bearing behavior of footings on layered soils has received significant attention from researchers, but most of the reported studies are limited to footings resting on the surface of the soil and are based on the assumption of small deformations. In this article, large deformation analyses, simulating the penetration of strip and circular footings into two‐layered clays, are described. The upper layer was assumed to be stronger than the lower layer. The importance of large deformation analysis for this problem is illustrated by comparing the small and large deformation predictions. The bearing behavior is discussed and the undrained bearing capacity factors are given for various cases involving different layer thicknesses and different ratios of the undrained shear strengths of the two clay layers. The development of the plastic zones and the effect of soil self‐weight on the bearing capacity are also discussed in the article.     

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.     

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.     

Closely Spaced Footings on Geogrid-Reinforced Sand

The results discussed in this paper are based on a total of 74 tests performed on closely spaced strip and square footings on geogrid-reinforced sand. The study was carried out to evaluate the effect of spacing between the footings, size of reinforcement, and continuous and discontinuous reinforcement layers on bearing capacity and tilt of closely spaced footings. The interference effects on bearing capacity and settlement of closely spaced square footings on reinforced sand were almost insignificant in comparison to those on isolated footings on reinforced sand; whereas a significant improvement in the tilt of adjacent square footings has been observed by providing continuous reinforcement layers in the foundation soil under the closely spaced footings. A considerable improvement in bearing capacity, settlement, and tilt of adjacent strip footings has been observed by providing continuous reinforcement layers in the foundation soil under the closely spaced strip footings.     

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.     

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.     

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.     

Behavior of Five Large Spread Footings in Sand

Five square spread footings ranging in size from 1 to 3 m were load tested up to 150 mm of settlement. They were all embedded 0.75 m into a medium dense, fairly uniform, silty silica sand. Load-settlement curves are presented, as well as creep curves relating settlement and time under a constant load. Since the soil mass was instrumented with telltales and inclinometers, vertical and horizontal movements in the soil mass were obtained as a function of depth and lateral extent. Conclusions are reached regarding how best to measure footing settlement, how to present load test results, new correlations for use in design, creep settlement, effect of cyclic loading and preloading on creep rate, zone of influence under the footing, mode of deformation of the soil mass, and volume change observations. Twelve settlement methods, six bearing capacity methods, and the WAK (wave activated stiffness) test are evaluated by comparing the predictions with the measurements. Many results of these large-scale instrumented tests confirm findings at small scale of previous researchers.     

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.     

Elastic Settlement under Eccentrically Loaded Rectangular Surface Footings on Sand Deposits

This paper presents the practical elastic settlement formulae for the eccentrically loaded surface footings resting upon an elastic mass. The presented closed-form solutions can be readily implemented into the practice allowing efficient and accurate prediction of elastic settlement under the rectangular footing which is subjected to the biaxial bending. The presented solutions are determined by evaluating the integration of strain expressions based on the Boussinesq stress equations. The common assumption of linear contact pressure in footing-soil interface is adopted for the solutions. The presented formulae are validated to be used for the settlement under any point of linear full-contact loading and their applicability to the current design process is demonstrated. The solutions are also developed for the theoretical cases where the location of incompressible soil layer is infinitely deep. The simplified influence factors are presented graphically and the numerical examples are provided for their practical use. In this respect, the paper represents a significant step forward in understanding of elastic settlement, rotation, and differential elastic settlement under eccentrically loaded footings.     

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.     

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.     

Behavior of Model Rafts Resting on Pile-Reinforced Sand

Piles in a pile raft are sometimes considered as settlement reducers, not load-carrying members. In design, one often tries to minimize the number of piles. This often results in a high axial stress in the piles that may deter their use due to the limits on pile stress in practice. An alternative is to consider the pile as reinforcement in the base soil, and not as a structural member. Serving as a soil stiffener, the pile can tolerate a lower safety margin against structural failure without violating building codes. Previous numerical studies on the use of disconnected piles as settlement reducers have shown the effectiveness of such piles. This study aims to verify experimentally the effectiveness of such piles through load tests of model rafts resting on pile-reinforced sand. By varying factors such as raft stiffness, pile length, pile arrangement, and pile number, results of the investigation indicate that structurally disconnected piles are effective in reducing the settlement and bending moments in the model rafts.     

Circular Elastic Plate Resting on Tensionless Pasternak Foundation

In this technical note, a thin circular plate resting on a two-parameter (Pasternak-type) foundation is studied under concentrated central and distributed loads. The governing equations of the plate are derived for static loading case considering the lift off (uplift) of the plate from the foundation. For the approximate solution, a Galerkin technique is adopted and the free vibration mode shapes of the completely free plate are chosen as the displacement functions. The technique yields a system of algebraic nonlinear equations, and its solution is accomplished by using an iterative method. The numerical results are obtained for evaluation of the behavior of the plate and then given comparatively in figures. Although in the case of a tensionless Winkler foundation, the lift off of the plate from the foundation takes place, when the displacement of plate is negative, while in case of the two-parameter foundation the lift off appears when the slopes of the foundation surface and that of the plate are not equal.     

Combination Effect of Si and P on Tertiary Scale Characteristic of Hot Rolled Strip

For high strength interstitial free(IF)steel containing P element,the salt and pepper(SP)defects exist on the strip surface and could not be eliminated effectively by optimizing the hot rolling process,such as temperature and cooling water.The combination effect of Si and P on the characteristic of tertiary scale has been studied comprehensively by scanning electron microscopy(SEM)and electron probe microanalysis(EPMA),and the concept is proposed firstly that Si and P are of combination effect which can be utilized to eliminate the SP defect.The results show that the SP defects were induced by the rolled-in scale during finish rolling.P can be enriched at the interface between substrate and tertiary scale,which is easy to decrease the adhesion of tertiary scale.However,Si enrichment at the interface between substrate and tertiary scale can increase the adhesion.The SP defects can be eliminated completely,which is attributed to the accompanying enrichment of Si and P.