Surface Footings Research Articles

Bearing capacity of surface footings by finite elements

A finite element elasto-viscoplastic solution is presented for a general bearing capacity problem of strip and circular surface footings. A Mohr-Coulomb yield criterion has been assumed for the soil behaviour. Both associated and non-associated flow rules have been incorporated and the footing behaviour is studied in detail. Contributing bearing capacity factors of the conventional solution have been assessed and superposition errors are indicated. Results have been compared with existing solutions and presented graphically.

Cone Models for Embedded Foundation

The dynamic analysis of surface footings may be performed approximately, but quite accurately, by idealizing the soil as a truncated cone instead of an elastic half‐space. In this paper, cone models are extended to represent embedded foundations. To this end, a double‐cone model is introduced to represent a disk in the interior of a homogeneous full space. Symmetry considerations applied to a pair of double cones enable the simulation of a free surface midway between the two disks. By using a stack of such disk pairs, an embedded foundation is modeled. The subsequent calculation is conducted by conventional matrix methods familiar from elementary finite element analysis. The accuracy of both frequency‐domain and time‐domain formulations is just as good as for surface footings. This is confirmed by comparing the dynamic‐stiffness coefficients for cone models with rigorous solutions. In addition, cone models enable simple determination of the effective foundation input motion imposed by earthquakes upon structures with embedded foundations.

On the Bearing Capacity of Surface Footings on Sand Under General Planar Loads

ABSTRACT Estimation of the bearing capacity of a shallow footing subjected to both inclined and eccentric loads is usually based on well-known limit-equilibrium solutions which apply linear superposition to a problem that is highly non-linear. This paper concerns an alternative approach using “interaction diagrams” to relate the different loading components at failure. Such curves define a region inside which all allowable load combinations must lie. They can be obtained experimentally as the failure envelope of a series of load tests. A comprehensive experimental programme, using a new three-dimensional, small-scale physical model, has been carried out at the University of Padua to determine the form of such diagrams for a very dense sand. The experimental rig as well as the test programme—in which the loading path was the only variable parameter—is briefly described. Failure conditions in all three loading component planes are analysed and very simple expressions are found to interpret the experimental data in an acceptable way. In the H-M/B plane, where the sign of the eccentricity is important in relation to the direction of the horizontal load, a new, interesting geometrical form of failure envelope has been revealed. All the planar interaction diagrams investigated appear to be load-path independent and therefore provide a rational way of studying the load capacity of such footings.

Alternatives to the iambic-trochaic law

This article seeks to develop alternatives to recent theories (Hayes 1985, 1987, 1991; McCarthy and Prince 1986, 1990; Prince 1991) that explain quantitative asymmetries between iambic and trochaic systems on the basis of a rhythmiciambic-trochaic law. The theory proposed here derives such asymmetries from two different rhythmic factors: moraic prominence-relations internal to heavy syllables, and avoidance of clash and lapse in sequences of moras. Firstly, it argues for a distinction between parsing feet and surface feet. Parsing feet draw from a symmetric foot inventory, based on two parameters:stressable element (mora vs. syllable), andheadedness (iambic vs. trochaic). That is, the basic foot inventory is no longer governed by the iambic-trochaic law. Secondly, parsing feet are mapped into surface feet by rules that impose quantitative changes, or by stray adjunction, induced by strict prosodic layering. Thirdly, a rhythmic sub-theory defines filters that rule out clashes and lapses in sequences of moras or syllables, depending on the type of stressable element. It explains iambic-trochaic asymmetries with respect to lengthening and shortening, and an asymmetry with respect to directionality of iambic parsing. Evidence will be presented from Tubatulabal, Yidiny, Araucanian, Chugach Alutiiq Yupik, Cayuga, Latin, and English.

Reactive hot-pressing studies of high density oxide-carbide composite ceramics

A number of brittle-brittle composites have been synthesized by reactive hot pressing. By using one inert phase and a phase formed in situ from metal hydride and a solid nonmetal, it was possible to produce microcomposites in which the reacting phase formed a continuous matrix, and isolated the grains of the inert phase. Densification rates for the reactively hot-pressed materials were appreciably higher than for the conventionally hot-pressed materials with the same nominal composition. Composites formed by Al 2O 3TiC, Al 2O 3TiB 2 and B 4CTiB 2 exhibited high Rockwell A hardness. Reactively hot-pressed Al 2O 3TiC composite was tested on inconel 718 and exhibited performance better or equivalent to the commercially available Al 2O 3TiC tool. B 4CTiB 2 tested on titanium 6–4 alloy exhibited higher uniform flank wear at short cutting times than a commercial WC 6% Co cutting tool (Carboloy grade 883). However, it continued cutting to the end of the 3-min test, while the carbide tool was limited to 2 min of cutting due to gross deformation. The volume of the tool material worn showed linear dependence on cutting times at all cutting speeds higher than 200 surface feet per minute (sfm). At those speeds, the dominant wear mechanism appeared to be chemical interaction with the workpiece, while at 200 sfm, microfracturing became more prominent.

Mechanica and Physical Properties of Microwave Sintered Si3N4

ABSTRACTMicrowave energy at 2.45 GHz has been used to sinter silicon nitride in times of between 30 and 120 minutes to form a dense product with an average grain size of 0.35 μm and substantially improved uniformity of properties over all commercial silicon nitrides and sialons investigated.A comparison between microwave and conventionally sintered parts of the same density showed the average mechanical properties to be the same for both sintering techniques, but revealed an improvement in the uniformity of mechanical properties of the microwave sintered products.Silicon nitride components with 5% Al2O3 and 5% Y2O3 as sintering aids, has been sintered to a density of approximately 97% of theoretical. Hipping of these components at 1800 °C for 60 minutes, resulted in the complete removal of residual porosity. Dense components were evaluated in machining tests against commercial ceramic cutting tools. The results show a reduction in wear rate of batter than 10% for microwave sintered Sl3N4 in turning and milling operations on cast iron at a cutting speed of 2000 surface feet per minute.

Free Vibration of Embedded Foundations: Theory versus Experiment

Comprehensive experimental results of 54 free-vibration tests on model footings embedded at various depths in moist dense sand and having circular, square, and rectangular base shapes were reported by Erden and Stokoe in 1974 and 1985. The results for vertical and coupled swaying-rocking oscillations are used in this paper to verify the homogeneous-half-space solutions given in a companion paper published by Gazetas in 1991 in the form of algebraic formulas and graphs for dynamic stiffnesses and damping factors. Particular attention is accorded to selecting appropriate values of the effective S-wave velocity, using either Erden’s original measurements and recommendations of 1974 or the measured response of the corresponding surface footings. It is demonstrated beyond significant doubt that: (1) The lower value of shear modulus around the footing sides and slippage at the footing side-soil interface may have contributed to not more than 25% of the shortfall in the experimental values; and (2) boundary wave reflections, primarily at the vertical interface between the sand and the high-damping soft boundary layer, are responsible for at least 75% of the observed discrepancies, having essentially eliminated the contribution to radiation damping from the swaying component of motion.

Response of circular footings and anchor plates in non‐homogeneous elastic soils

AbstractThe axisymmetric elastic response of circular footings and anchor plates in a linearly non‐homogeneous elastic soil is analysed. It is assumed that footings/anchors are flexible and subjected to axisymmetric vertical loads. The response of the footing/anchor is modelled by using the classical Poisson–Kirchhoff thin plate theory. A variational technique is used to analyse the interaction problem. A representation for the contact stress is established by using a fundamental solution corresponding to a unit vertical pressure acting over an annular region in the interior of the non‐homogeneous soil. The fundamental solution can be derived by using rigorous analytical procedures. The influence of the footing flexibility and the degree of soil non‐homogeneity on the displacements, bending moments and contact stresses of a surface footing is examined over a wide range of governing parameters. In the case of anchor plates the influence of depth of embedment, degree of soil non‐homogeneity and anchor flexibility on the anchor displacement is investigated.

High-speed machining of cast iron with BZN compacts

Polycrystalline cubic boron nitride (PCBN) cutting tools, as represented by BZN compacts, can be used to mill highly pearlitic cast iron at very high speeds. This is indicated by a uniform flank wear (UFW) of only 0.18 mm (0.007 in) after 36 min at 66.5 m s −1 (13 100 surface feet per minute (sfm)). A single test was carried out at 93.0 m s −1 (18 300 sfm) but the onset of chatter precluded more than two passes across the workplace. BZN compacts outperformed an SiAlON tool (Kyon 3000) at the three speeds (14.9, 29.9 and 50.0 m s −1; 2932, 5890 and 9817 sfm) for which comparisons were made. The arithmetic average (AA) surface roughness of BZN-compact-machined cast iron was less than half that of SiAlON-machined cast iron. In no case was the roughness of the BZN-compact-machined surface greater than 0.74 μm (29 μin) and it was only 0.48 μm (19 μin) after the test at 93.0 m s −1 (18 300 sfm). BZN compact wear in milling ferritic cast iron was much greater than that in milling highly pearlitic cast iron; a flank wear of 0.13 mm (0.005 in) occurred after 0.5 min on the former at 29.9 m s −1 (5890 sfm). For comparison, the BZN compact wear was only 0.071 mm (0.0028 in) after milling the more pearlitic material for 14.5 min at the same speed. The greater BZN compact wear in machining ferritic cast iron may be due to (1) greater workpiece ductility, (2) higher temperature at the cutting interface, (3) greater diffusion of boron from the CBN into the ferrite, or combinations of all three.

Vertical and horizontal deformation of an inhomogeneous elastic half‐space

AbstractVertical and horizontal deformations of surface footings have been studied for an inhomogeneous elastic half‐space in which the shear modulus increases with an arbitrary power of depth, n, and Poisson's ratio is constant. A general solution for displacements has been obtained first for point loads applied in vertical and horizontal directions. These are then used in obtaining closed‐form solutions for displacements of uniformly loaded circular and rectangular footings. Finally, a numerical method is described that can be used to analyse a rigid footing of an arbitrary shape, and results for rigid rectangular footings are given.

Strength Anisotropy and Shear Band Direction in Plane Strain Tests of Sand

ABSTRACT Strength anisotropy and shear band direction at failure and their relationship for sands were studied experimentally. Using reconstituted specimens of air-pluviated Toyoura sand, plane strain compression (PSC) tests, torsional shear tests and a bearing capacity test with a strip surface footing were performed. Also PSC tests were performed using undisturbed specimens of sand taken from layers in the field, formed by secondary deposition under water. For both types of sands, a significant degree of strength anisotropy was observed. For Toyoura sand, shear band(s) did not appear at a unique angle. That is, in the PSC tests on specimens deposited from the direction, the bedding plane direction differs largely from the zero-extension direction. In this case, shear bands tended to appear in the direction of the maximum stress obliquity plane. This type of shear band appeared also in a model ground loaded with a smooth footing. On the other hand, in the simple shear tests on specimens deposited vertically, the bedding plane direction coincides with the zero-extension direction (i.e, the horizontal direction). In this case, shear bands tended to appear in the the zero-extension direction. In the other cases, shear bands appeared at intermediate directions. The paper discusses also the point that many of the apparent contradictions concerning the shear band direction reported in the literature may be explained, at least partly, by taking into account the relative direction of bedding plane in each case.

Interaction functions of a rigid strip bonded to saturated elastic half-space

A comprehensive analytical solution is developed to generate the interaction functions of a rigid permeable strip in contact with a saturated porous elastic half-space. Linear hysteretic damping characteristics of the medium are included in the formulation. The mixed boundary-value problem of a welded (and smooth) surface footing is reduced to a set of coupled Fredholm integral equations of the first kind and a numerical solution is provided. Frequency-dependent interaction functions (stiffnesses and radiation damping coefficients) of a medium modelling a saturated dense sand are computed and exhibited graphically to reveal the influence of pore water, permeability effects and hysteretic damping characteristics of the medium. In the horizontal mode of response and without hysteretic damping, the pore water causes the effective stiffness to increase by 50–100% while it has negligible influence on the damping coefficient. With 5% hysteretic damping, the horizontal stillness changes sign and character and there is an increase of about 25% in its magnitude compared to the corresponding dry case. For the vertical and rocking modes of response, the impact of pore water on the interaction functions (both stiffnesses and damping coefficients) is much more pronounced. Without hysteretic damping, there are changes in sign in the stiffnesses of the medium, and the magnitudes of the interaction functions, relative to the corresponding dry case, could be as large as several folds, especially for the higher values of the dimensionless frequency. At 5% damping, the effective stiffnesses are increased by about 25–50% while the damping coefficients almost double. Concerning the influence of types of contact, the interaction functions are practically identical for smooth and welded contacts over the frequency range of interest. The results are useful in determining the response of surface structures to seismic excitation, in particular, where the ground water is at a level to impact such response.

Stress characteristics for bearing capacity in sand using a critical state model

A new stress characteristic solution has been developed for two-dimensional strip footings on the surface of a sand layer. The analysis uses sand properties defined by a critical state model. This analysis takes account of different stress levels, different placement densities, the sand compressibility, and the transition from strain softening to strain hardening behavior that accompanies increased stresses. The results show linear relationships between log (Nγ) and log (footing breadth) that depend on the details of the sand model used. The results have been compared with available summaries of laboratory- and field-scale results. Although the critical state models for the sands used in the experimental studies cannot be fully developed from published information, nevertheless the trend of the results is encouraging. Additional information on validations of the critical state sand model is needed. Key words: surface footings, stability, capacity coefficients, self-weight, plasticity, stress characteristics, critical state.

On Shear Instability in Machining a Nickel-Iron Base Superalloy

The deformation in chips produced in machining a nickel-iron base superalloy (Inconel 718), at various speeds up to 213.5 m/min [700 surface feet per minute (SFPM)] has been investigated. In addition to slip, considerable twinning in the chips is observed at all speeds. Up to a cutting speed of about 30.5 m/min (100 SFPM), the chips formed are essentially continuous and ribbon-like, although deformation in the chip is inhomogeneous. At cutting speeds above 61 m/min (200 SFPM), shear-localized chips form. The longitudinal midsections of the chips show gross inhomogeneous deformation with shear localization between any two segments, and relatively low deformation within any individual segment. With an increase in speed the extent of contact between segments decreases rapidly, until a speed is reached where the individual segments become completely detached. The speed at which this occurs for other difficult-to-machine materials, such as AISI 4340, was found in an earlier study, to depend upon the metallurgical condition of the material and its hardness. Based on this study, the mechanism of chip formation when machining Inconel 718 is very similar to that reported earlier for machining both titanium alloys and hardened AISI 4340 steels at higher speeds. While the hcp crystal structure of titanium alloys in addition to titanium’s poor thermal properties (kρc) is believed to be partly responsible for the intense shear localization in that material, results with Inconel 718 (fcc) and AISI 4340 steel (bcc) indicate that the effect of structure on shear localization is not yet well understood.

Thermoregulation in Newly Hatched Chicks

Chicks from seven early-feathering populations were used in a series of experiments to detail the course of thermoregulation in newly hatched chicks. Lines HN and LN were composed of White Plymouth Rock chickens that had been selected 24 generations for high and low 8-week body weight, respectively. Reciprocal crosses of those lines (HL and LH) and an F2 produced from HL as well as lines originating from HN and LN with the sex-linked dwarf allele (dw), HD and LD, respectively, were also used. Surface (foot pad) temperature, core (rectal) temperature, and body weight were obtained on female and male chicks at 2, 4, 6, 8, 11, 14, 17, 20, and 23 days in all populations and at 105 days of age in HN and LN lines. Although LN and LD chicks generally had lower surface temperatures than those from the other lines from 11 to 23 days of age, surface temperatures of HN and LN birds were not different at 105 days. No significant differences due to the dwarf allele were found in surface temperatures, but there was a consistent tendency for dwarfs to be cooler than normals in the high lines and warmer than normals in the low lines. The LN chicks had lower core temperatures through 23 days of age than the other populations measured, but the narrow range of core temperatures in all populations precluded a definitive analysis to reveal mode(s) of inheritance. Surface-to-core temperature ratios were also lower in LD and particularly LN chicks through 23 days of age, although no difference between HN and LN birds occurred in this trait at 105 days of age.

Bearing capacity of three closely-spaced footings on sand

Closely–spaced footings may be encountered on cohesionless soils in the form of grillage foundations and railway ties. Close spacing is known to permit higher loads than can be carried by similar isolated footings. This effect is due to interference between failure zones in the sand, and may increase the capacity by 150% when ø = 35° and the centreline separation of the footings is approximately twice the footing width B. The method of stress characteristics has been used to calculate the theoretical bearing capacity of a series of parallel footings, and these have been compared with laboratory tests on three parallel surface footings at various spacings on two different sands. The testing programme also investigated the effects of footing roughness and load distribution. When interference occurs, pre-failure settlements become larger, and post-failure behaviour more ductile. The theoretical solutions show similar trends to the model tests, but suggest that interference stops at rather smaller spacings. Des semelles rapprochées se rencontrent parfois dans le cas de fondations à grillage ou de traverses de chemin de fer sur des sols pulvérulents. On sait qu'un tel écartement permet des charges plus importants que celles qui peuvent etre supportées par des semelles semblables isolées. Cet effet est dû à l'interférence entre les zones de rupture dans le sable et il peut augmenter la force portante de 150% lorsque ø = 35° et la distance entre les centres des semelles est approximativement deux fois leur largeur B. La méthode des caractéristiques de contrainte a été employée pour calculer la portance théorique d'une série de semelles parallèles. Les résultats one été comparés avec ceux obtenus à partir de plusieurs essais faits en laboratoire sur trois semelles superficielles d'écartements variable sur deux sables différents. Les effects de la rugosité des semelles et de la distribution des charges one été etudiés aussi au cours du programme d'essais. Lorsque l'interférence a lieu les tassements précedant la rupture s'accroissent, et le comportement suivant la rupture devient plus ductile. Les solutions théoriques montrent des tendances similaires à celles trouvées dans les essais sur modèles, tandis qu'elles suggérent que l'interférence cesse è des écartements un peu plus faible.

Influence factors for settlement estimates of footings on finite layers

The estimation of the settlements of surface footings on finite layers is examined for values of Poisson's ratio ranging from 0 to 0.5. Influence factors based on Steinbrenner's approximate method were evaluated and were found to be in good agreement with influence factors obtained by a more rigorous and difficult evaluation by Giroud. This study confirms the findings by Christian and Carrier that the Janbu, Bjerrum, and Kjaernsli chart for the estimation of elastic settlements (v = 0.5) is incorrect. Keywords: elasticity, footings, settlement analysis.

Uncertainty in Bearing Capacity of Sands

Bearing capacity predictions for surface footings on sand based on modifications of Terzaghi's superposition method are partly empirical and partly theoretical. Based on currently available data for surface footings on sand, these predictions are compared with statistical analyses. For small uncertainty in soil properties, coefficients of variation of bearing capacity for cohesionless soil without surcharge range from 20% to 30%. As uncertainty in soil properties is introduced, uncertainty in bearing capacity rises rapidly. Quantified expressions of uncertainty are derived and illustrated by example. These analyses are used to identify sources of uncertainty.

Acoustically absorbent truck tire splash guard

An acoustically absorbent truck tire splash guard is mounted behind the tire for absorbing noise generated by the tire. The splash guard includes a face panel which is impervious to damage by particulate matter thrown thereagainst by the tire. The face panel overlies and is juxtaposed with an acoustical foam panel of one to two inches to thickness which is effective to absorb the higher tire noise frequencies, for example, above 1,000 Hz. An array of volume resonators of the Helmholtz type is provided behind the acoustical foam panel. The volume resonators are defined by a resonator panel having a latticework which defines a plurality of cavities. The front of the resonator cavities are closed by a resonator face panel which is juxtaposed with the resonator panel and the acoustical foam panel. Openings are provided in the resonator face panel and communicate with the adjacent resonator cavities. The number or size of the openings in the resonator face panel is varied to tune the resonators over a range of frequencies such as 400, 600, and 800 Hz. so that the array gives nearly uniform noise absorption over the range of noise frequencies which are encountered over a range of vehicle speeds. A back panel is juxtaposed with the back of the volume resonator panel to form the bottom of the resonator cavities and is relatively massive, for example, greater than three pounds per square foot of surface so that it acts as an effective barrier to sound which is not absorbed by the acoustical foam panel or the volume resonators.

Bearing capacity of eccentrically loaded surface footings on sand. Technical note : Das, B M Soils Found, V21, N1, March 1981, P115–119

Bearing capacity of eccentrically loaded surface footings on sand. Technical note : Das, B M Soils Found, V21, N1, March 1981, P115–119