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 making use of limit analysis, an upper bound solution in a closed form for determining the ultimate pullout capacity of plate anchors buried in sandy slopes has been established. The anchor plate orientation has been considered either horizontal or parallel to the slope, with the pullout force applied perpendicular to the plate. It has been found that the pullout capacity for horizontal anchors, even on slopes, remains the same as that on horizontal ground surface as long as the average embedment ratio is kept constant. Whereas for anchors which are aligned parallel to the slope the collapse load decreases continuously with the increase in the inclination of slope. © 1997 John Wiley & Sons, Ltd.

Upper bound solution for pullout capacity of anchors on sandy slopes

The ultimate bearing capacity of a new strip footing placed on a cohesionless soil medium, in the presence of an existing strip footing, the load on which is assumed to be known, has been determined. Both the footings are assumed to be perfectly rigid and rough. The analysis is carried out by using an upper bound finite element limit analysis. For different clear spacing (S) between the footings, the values of the efficiency factor (ξγ) were determined; where ξγ is defined as the ratio of the failure load for an interfering new footing of a given width (B) to that for a single isolated footing having the same width. For ϕ   30°, on the other hand if the applied load on the existing footing is approximately greater than half the failure load for a single isolated footing having the same width, the peak magnitude of ξγ was found to occur at around S/B ≈ 0.1 rather than at S/B = 0. The increase in ξγ becomes further significant with an increase in the magnitude of the load on the existing footing.

Ultimate Bearing Capacity of a Footing Considering the Interference of an Existing Footing on Sand

The effect of the spring mounting cushion inserted in between a machine base and its concrete footing has been examined experimentally by conducting a number of block vibrations tests. The machine was subjected to steady state vertical harmonic loading. Experiments were performed with two different stiffness values of the spring mounting cushion. The employment of the spring mounting cushion, with the stiffness much smaller than that of soil strata, offers a drastic reduction in the resonant displacement amplitudes of the footing. It also results in a significant decrease in the resonant frequency of the foundation. The resonant displacement amplitudes of both the footing and the machine were found to become lower with the smaller stiffness value of the springs. The resonant frequency for the machine base, in all the experiments, was found to be invariably the same as that of the footing.

Dynamic Response of Footing and Machine with Spring Mounting Base

A series of resonant column tests have been performed in the torsional mode of vibration to assess the effect of saturation, starting from the near dry state to the fully saturated state, on the damping ratio of sands corresponding to the threshold strain level. Tests were carried out on three different gradations of sand for various combinations of relative density and effective confining pressure. For fine sands, a certain optimum degree of saturation exists at which the damping ratio minimizes; it is known that a decrease in Sr from a fully saturated state leads to a continuous increase in the matric suction. With an increase in the relative density, the optimum degree of saturation for fine sand increases marginally from 1.38 to 1.49%, but does not show any dependency on the effective confining pressure. In contrast, the minimum values of the damping ratio for medium and coarse sands are found to always correspond to the near dry state. The damping ratio decreases continuously with increases i...

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Damping of Sands for Varying Saturation

A number of resonant column tests were conducted in torsion on aluminium cylindrical bars. By changing the length to diameter ratio of these specimens, the resonant frequency was varied between 52 and 332 Hz. The values of the shear wave velocity (VS) and damping ratio (D) determined from these tests were found to remain acceptable up to a resonant frequency of about 175 Hz. Thereafter, with an increase in the torsional stiffness of the specimen, there was a significant decrease in VS of up to 32.2%, corresponding to a resonant frequency of 332 Hz, and a considerable increase in the damping was noticed. An apparent increase in the mass polar moment of inertia of the driving mechanism was also observed at a greater resonant frequency. The study reveals that, even for a stiff specimen, it is possible using the resonant column tests to accurately determine the dynamic properties of the specimen, provided that the length to diameter ratio of the specimen is increased so that the resonant frequency remains smaller than 175 Hz.

Jyant Kumar

Papers

Upper bound solution for pullout capacity of anchors on sandy slopes

Ultimate Bearing Capacity of a Footing Considering the Interference of an Existing Footing on Sand

Dynamic Response of Footing and Machine with Spring Mounting Base

Damping of Sands for Varying Saturation

Effect of sample torsional stiffness on resonant column test results