PART 1 DEALS WITH THE DYNAMIC ASPECTS OF THE SUBJECT: MATHEMATICAL ANALYSIS OF SYSTEMS SUBJECTED TO INDEPENDENT VIBRATIONS BY MEANS OF MATHEMATICAL MODELS. THE ANALYTICAL SYSTEMS USED ARE NON-LINEAR SYSTEMS, HYDRODYNAMICS AND NUMERICAL METHODS. PART 2 EXAMINES SEISMIC MOVEMENTS, THE DYNAMIC BEHAVIOUR OF STRUCTURES AND THE BASIC CONCEPTS OF THE SEISMIC DESIGN OF STRUCTURES.

Fundamentals of earthquake engineering

Soils that exhibit nonassociated flow may, according to stability postulates by Drucker and by Hill, become unstable when exposed to certain stress paths inside the failure surface. Series of conventional triaxial tests on fully saturated and on partly saturated specimens were performed under drained and undrained conditions to study the regions of stable and unstable behavior. For specimens that compress and have degrees of saturation higher than critical, undrained conditions lead to effective stress paths directed within the region of potential instability, and instability was observed provided the yield surface opens up in the outward direction of the hydrostatic axis. Thus, instability occurs inside the failure surface. Instability is not synonymous with failure, although both may lead to catastrophic events. The location of the instability line is discussed. Examples of a shallow submarine slope and a nearly fully saturated steeper slope representing a tailings dam, which both should remain stable a...

Closure of "Static Instability and Liquefaction of Loose Fine Sandy Slopes"

During the last 30 years various researchers have proposed approximate techniques to estimate the uplift capacity of soil anchors. As the majority of past research has been experimentally based, much current design practice is based on empiricism. Somewhat surprisingly, very few numerical analyses have been performed to determine the ultimate pullout loads of anchors. This paper presents the results of a rigorous numerical study to estimate the ultimate pullout load for vertical and horizontal plate anchors in frictional soils. Rigorous bounds have been obtained using two numerical procedures that are based on finite element formulations of the upper and lower bound theorems of limit analysis. For comparison purposes, numerical estimates of the break-out factor have also been obtained using the more conventional displacement finite element method. Results are presented in the familiar form of break-out factors based on various soil strength profiles and geometries and are compared with existing numerical ...

The ultimate pullout capacity of anchors in frictional soils

The magnitude of the passive earth pressure that resists the movement of a structure is controlled by the amount the structure moves and the direction in which it moves, strength and stiffness of the soil that resists its movement, friction or adhesion on the interface between the structure and soil, and shape of the structure. The Log Spiral Theory, corrected for 3D effects, provides an accurate means of computing ultimate passive pressures. A hyperbolic expression, together with estimated values of soil modulus and ultimate resistance, provides a means of estimating the relationship between structural movement and passive resistance. It is essential that the soil strength and stiffness used in making these estimates should be appropriate for the soil and the drainage conditions involved. The results of an undrained passive pressure load test in stiff sandy silt and a drained passive pressure load test in well-graded gravel are compared with passive pressures computed using the methods discussed. Reasonable agreement between the calculated and measured values shows that the Log Spiral Theory, corrected for 3D effects, and the hyperbolic load-deflection relationship provide an adequate means of estimating passive resistance for a wide range of conditions.

Passive earth pressures : Theories and tests

Numerical limit analysis solutions for the bearing capacity factor Nγ

By using an upper bound limit analysis in conjunction with finite elements and linear programming, the ultimate bearing capacity of two interfering rough strip footings, resting on a cohesionless medium, was computed. Along all the interfaces of the chosen triangular elements, velocity discontinuities were employed. The plastic strains were incorporated using an associated flow rule. For different clear spacing (S) between the two footings, the efficiency factor (ξγ) was determined, where ξγ is defined as the ratio of the failure load for a strip footing of given width in the presence of the other footing to that of a single isolated strip footing having the same width. The value of ξγ at S/B = 0 becomes equal to 2.0, and the maximum ξγ occurs at S/B =  Scr/B. For S/B⩽Scr/B, the ultimate failure load for a footing becomes almost half that of an isolated footing having width (2B + S), and the soil mass below and in between the two footings deforms mainly in the downward direction. In contrast, for S/B>Scr/B, ground heave was noticed along both the sides of the footing. As compared to the available theories, the analysis provides generally lower values of ξγ for S/B>Scr/B. Copyright © 2007 John Wiley & Sons, Ltd.

Bearing capacity of two interfering footings

By using the bender and extender elements tests, together with measurements of the travel times of shear (S) and primary (P) waves, the variation of Poisson ratio (nu) was determined for dry sands with respect to changes in relative densities and effective confining pressures (sigma(3)). The tests were performed for three different ranges of particle sizes. The magnitude of the Poisson ratio decreases invariably with an increase in both the relative density and the effective confining pressure. The effect of the confining pressure on the Poisson ratio was found to become relatively more significant for fine-grained sand as compared with the coarse-grained sand. For a given material, at a particular value of sigma(3), the magnitude of the Poisson ratio decreases, almost in a linear fashion, with an increase in the value of maximum shear modulus (G(max)). The two widely used correlations in literature, providing the relationships among G(max), void ratio (e) and effective confining pressure (sigma(3)), applicable for angular granular materials, were found to compare reasonably well with the present experimental data for the fine- and medium-grained sands. However, for the coarse-grained sand, these correlations tend to overestimate the values of G(max).

/pdf/effect-of-relative-density-and-confining-pressure-on-poisson-44a6qm9rms.pdf

Effect of relative density and confining pressure on Poisson ratio from bender and extender elements 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.

Interference of Two Closely Spaced Strip Footings on Sand Using Model Tests

Using a combination of a logarithmic spiral and a straight line as a failure surface, comprehensive charts have been developed to determine the passive earth pressure coefficients and the positions of the critical failure surface for positive as well as negative wall friction angles. Translational movement of the wall has been examined in detail, considering the soil as either an associated flow dilatant material or a non-dilatant material, to determine the kinematic admissibility of the limit equilibrium solutions.

Passive pressure coefficients, critical failure surface and its kinematic admissibility

By using the method of characteristics, the effect of footing-soil interface friction angle (delta) on the bearing capacity factor N-gamma was computed for a strip footing. The analysis was performed by employing a curved trapped wedge under the footing base; this wedge joins the footing base at a distance B-t from the footing edge. For a given footing width (B), the value of B-t increases continuously with a decrease in delta. For delta = 0, no trapped wedge exists below the footing base, that is, B-t/B = 0.5. On the contrary, with delta = phi, the point of emergence of the trapped wedge approaches toward the footing edge with an increase in phi. The magnitude of N-gamma increases substantially with an increase in delta/phi. The maximum depth of the plastic zone becomes higher for greater values of delta/phi. The results from the present analysis were found to compare well with those reported in the literature.

Jyant Kumar

Papers

Bearing capacity of two interfering footings

Effect of relative density and confining pressure on Poisson ratio from bender and extender elements tests

Interference of Two Closely Spaced Strip Footings on Sand Using Model Tests

Passive pressure coefficients, critical failure surface and its kinematic admissibility

The variation of N-gamma with footing roughness using the method of characteristics