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 applying the lower bound finite element limit analysis in conjunction with non-linear optimisation, the bearing capacity factors, Nc, Nq and Nγ, due to the components of cohesion, surcharge and unit weight, respectively, have been estimated for a horizontal strip footing placed along a sloping ground surface. The variation of Nc, Nq and Nγ with changes in slope angle (β) for different soil friction angle (φ) have been computed for smooth as well as rough strip footings. The analysis reveals that along a sloping ground surface, in addition to Nγ, the factors Nc and Nq also vary considerably with changes in footing roughness. Compared to the smooth footing, the extent of the plastic zone around the footing becomes greater for the rough footing. The results obtained from the analysis are found to compare well with those previously reported in literature.

Bearing capacity of foundations on slopes

By using the method of characteristics, the bearing capacity factor Nγ was computed for a rough strip footing. The analysis was performed by considering a curved nonplastic wedge under the foundati...

Nγ for rough strip footing using the method of characteristics

By taking the failure surface as a combination of the arc of a logarithmic spiral and a straight line, passive earth pressure coefficients in the presence of horizontal pseudostatic earthquake body...

Seismic passive earth pressure coefficients for sands

The effect of horizontal earthquake body forces on the bearing capacity of foundations has been examined computationally in a rigorous manner by employing the method of stress characteristics. The bearing capacity factors N-c, N-q and N-y, due to the components of soil cohesion, ground surcharge pressure and soil unit weight respectively, have been plotted as a function of earthquake acceleration coefficient (a(h)) for different values of soil friction angle (phi). The inclusion of earthquake body forces causes a considerable reduction in the bearing capacity factors. The bearing capacity factors N-c and N-q are seen to be approximately of the same magnitude as those reported in the literature on the basis of different solution methods. However, the obtained values of N-y are found to be significantly smaller than the available results. The nature of the pressure distribution along the footing base and the geometry of the observed failure patterns vary with the consideration of earthquake body forces.

Seismic bearing capacity factors for spread foundations

The effect of interface friction angle $(\delta)$ between the footing and underlying soil mass on the bearing capacity factor $N_\gamma$ 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 leads to a continuous increase in $N_\gamma$. With $\delta=\phi$, the magnitude of $N_\gamma$ 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 $\delta$ and $\phi$. The obtained values of $N_\gamma$, for perfectly smooth and perfectly rough footings, compare quite favorably with those reported in literature. The study demonstrates that in the case when $\delta$ is smaller than $\phi$, the assumption of a perfectly rough footing will lead to an unsafe prediction of the ultimate bearing capacity.

Jyant Kumar

Papers

Bearing capacity of foundations on slopes

Nγ for rough strip footing using the method of characteristics

Seismic passive earth pressure coefficients for sands

Seismic bearing capacity factors for spread foundations

Effect of Footing Roughness on Bearing Capacity Factor $N_ \gamma$