The log delta log t method for the determination of the coefficient of consolidation

The behaviour of saturated soils undergoing consolidation is very complex, It may not follow Terzaghi's theory over the entire consolidation process, Different soils may behave in such a way as to fit into Terzaghi's theory over some specific stages of the consolidation process (percentage of consolidation), This may be one of the reasons for the difficulties faced by the existing curve-fitting procedures in obtaining the coefficient of consolidation, c(v). It has been shown that the slope of the initial linear portion of the theoretical log U-log T curve is constant over a wider range of degree of consolidation, U, when compared with the other methods in use, This initial well-defined straight line in the log U-log T plot intersects the U = 100% line at T = pi/4, which corresponds to U = 88.3%, The proposed log delta-log t method is based on this observation, which gives the value of c(v) through simple graphical construction, In the proposed method, which is more versatile, identification of the characteristic straight lines is very clear; the intersection of these lines is more precise and the method does not depend upon the initial compression for the determination of c(v).

Hidden order in serrated flow of metallic glasses

We report results of statistical and dynamic analysis of the serrated stress-time curves obtained from compressive constant strain-rate tests on two metallic glass samples with different ductility levels in an effort to extract hidden information in the seemingly irregular serrations. Two distinct types of dynamics are detected in these two alloy samples. The stress-strain curve corresponding to the less ductile Zr65Cu15Ni10Al10 alloy is shown to exhibit a finite correlation dimension and a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. In contrast, for the more ductile Cu47.5Zr47.5Al5 alloy, the distributions of stress drop magnitudes and their time durations obey a power-law scaling reminiscent of a self-organized critical state. The exponents also satisfy the scaling relation compatible with self-organized criticality. Possible physical mechanisms contributing to the two distinct dynamic regimes are discussed by drawing on the analogy with the serrated yielding of crystalline samples. The analysis, together with some physical reasoning, suggests that plasticity in the less ductile sample can be attributed to stick-slip of a single shear band, while that of the more ductile sample could be attributed to the simultaneous nucleation of a large number of shear bands and their mutual interactions. (C) 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Secondary compression factor

When the variation of secondary compression, with log(10) t is non-linear, the quantification of secondary settlement through the coefficient of secondary compression, C-alpha epsilon, becomes difficult which frequently leads to an underestimate of the settlement, Log(10) delta - log(10) t representation of such true-compression data has the distinct advantage of exhibiting linear secondary compression behaviour over an appreciably larger time span. The slope of the secondary compression portion of the log(10) e - log(10) t curve expressed as Delta(log e)/(log t) and called the 'secondary compression factor', m, proves to be a better alternative to C-alpha epsilon and the prediction of secondary settlement is improved.

Minimal set of generators for the derivation module of certain monomial curves

Let K be a field of characteristic zero and let m(0),..., m(e-1) be a sequence of positive integers. Let C be an algebroid monomial curve in the affine e-space A(K)(e) defined parametrically by X-0 = T-m0,..., Xe-1 = Tme-1 and let A be the coordinate ring of C. In this paper, we assume that some e - 1 terms of m(0),..., m(e-1) form an arithmetic sequence and construct a minimal set of generators for the derivation module Der(K)(A) of A and write an explicit formula for mu (Der(K)(A)).

Rapid method of consolidation testing

The determination of consolidation characteristics forms an important aspect in the design of foundations and other earth-retaining structures. The conventional consolidation test as originally proposed by Teaaghi takes considerable time (more than 15 days in highly compressible soils with low coefficient of consolidation) and effort. Any effort to reduce the duration of testing will be desirable from several considerations. In this paper, an attempt has been made to propose a rapid method of consolidation testing. In the proposed method, the next load increment is applied as soon as the necessary time required to identify the percent consolidation is reached and to evaluate the coefficient of consolidation by one of the popular curve-fitting procedures. The rectangular hyperbola method has been used to identify the percent consolidation reached after any load increment, and to determine the coefficient of consolidation, before making the next load increment. The time required to complete the test using the rapid consolidation method could be as low as 4-5 h compared with 1 or 2 weeks in the case of the conventional consolidation test.

Sensing of delaminations in composite laminates using embedded magnetostrictive particle layers

This is an exploratory study to illustrate the feasibility of detecting delamination type of damage in polymeric laminates with one layer of magnetostrictive particles. One such beam encircled with excitation and sensing coils is used for this study. The change in stress gradient of the magnetostrictive layer in the vicinity of delamination shows up as a change in induced voltage in the sensing coil, and therefore provides a means to sense the presence of delamination. Recognizing the constitutive behavior of the Terfenol-D material is highly nonlinear, analytical expressions for the constitutive relations are developed by using curve fitting techniques to the experimental data. Analytical expressions that relate the applied excitation field with the stress and magnetic flux densities induced in the magnetostrictive layer are developed. Numerical methods are used to find the relative change in the induced voltage in the sensing coil due to the presence of delamination. A typical example of unidirectional laminate, with embedded delaminations, is used for the simulation purposes. This exploratory study illustrates that the open-circuit voltage induced in the sensing coil changes significantly (as large of 68 millivolts) with the occurrence of delamination. This feature can be exploited for device off-line inspection techniques and/or linking monitoring procedures for practical applications.

Solutions of cubic equations in quadratic fields

Let K be any quadratic field with O-K its ring of integers. We study the solutions of cubic equations, which represent elliptic curves defined over Q, in quadratic fields and prove some interesting results regarding the solutions by using elementary tools. As an application we consider the Diophantine equation r + s + t = rst = 1 in O-K. This Diophantine equation gives an elliptic curve defined over Q with finite Mordell-Weil group. Using our study of the solutions of cubic equations in quadratic fields we present a simple proof of the fact that except for the ring of integers of Q(i) and Q(root 2), this Diophantine equation is not solvable in the ring of integers of any other quadratic fields, which is already proved in [4].

Stability and mobility of sand-bed channels affected by seepage

Seepage effects on the stability, mobility, and incipient motion of sand-bed particles are experimentally investigated. Seepage through a sand bed in a downward direction (suction) reduces the stability of particles, and it can even initiate their movement. The bed erosion is increased with the increased rates of suction. Whereas the seepage in an upward direction (injection) increases the stability of bed particles, it does not aid initiating their movement. The rate of bed erosion is reduced or even stopped by the increased infection rates. Hydrodynamic conditions leading to the so-called "pseudoincipient motion'' with suction (for the initiation of particles movement that are otherwise at rest under no-seepage conditions), and with injection (for only arresting the particles movement that are otherwise moving initially) are evaluated. The conventional Shields curve cannot be used to predict such pseudoincipient motion conditions with seepage. The concepts thus developed are useful for a better understanding of the sediment transport mechanics and in the design of stable alluvial channels affected by seepage.

Tensile flow behaviour of 2.25Cr-1Mo ferritic steel base metal and simulated heat affected zone structures of 2.25Cr-1Mo weld joint

Tensile tests in the temperature range 298 to 873 K have been performed on 2.25Cr-1Mo base metal and simulated heat affected zone (HAZ) structures of its weld joint, namely coarse grain bainite, fine grain bainite and intercritical structure. Tensile flow behaviour of all the microstructural conditions could be adequately described by the Hollomon equation (sigma = K-1 epsilon(n1)) at higher (> 623 K) temperatures. Deviation from the Hollomon equation was observed at low strains and lower (< 623 K) temperatures. The Ludwigson modification of Hollomon's equation, sigma = K-1 epsilon(n1) + exp (K-2 + n(2) epsilon), was found to describe the flow curve. In general, the flow parameters n(1), K-1, n(2) and K-2 were found to decrease with increase in temperature except in the intermediate temperature range (423 to 623 K). Peaks/plateaus were observed in their variation with temperature in the intermediate temperature range coinciding with the occurrence of serrated flow in the load-elongation curve. The n(1) Value increased and the K-1 value decreased with the type of microstructure in the order: coarse grain bainite, fine grain bainite, base metal and intercritical structure. The variation of nl with microstructure has been rationalized on the basis of mean free path (MFP) of dislocations which is directly related to the inter-particle spacing. Larger MFP of dislocations lead to higher strain hardening exponents n(1).

Converging swirling liquid jets from pressure swirl atomizers: Effect of inner air pressure

Converging swirling liquid jets from pressure swirl atomizers injected into atmospheric air are studied experimentally using still and cine photographic techniques in the context of liquid-liquid coaxial swirl atomizers used in liquid rocket engines. The jet exhibits several interesting flow features in contrast to the nonswirling liquid jets (annular liquid jets) studied in the literature. The swirl motion creates multiple converging sections in the jet, which gradually collapse one after the other due to the liquid sheet breakup with increasing Weber number (We). This is clearly related to the air inside the converging jet which exhibits a peculiar variation of the pressure difference across the liquid sheet, DeltaP, with We. The variation shows a decreasing trend of DeltaP with We in an overall sense, but exhibits local maxima and minima at specific flow conditions. The number of maxima or minima observed in the curve depends on the number of converging sections seen in the jet at the lowest We. An interesting feature of this variation is that it delineates the regions of prominent jet flow features like the oscillating jet region, nonoscillating jet region, number of converging sections, and so on. Numerical predictions of the jet characteristics are obtained by modifying an existing nonswirling liquid jet model by including the swirling motion. The comparison between the experimental and numerical measurements shows that the pressure difference across the liquid sheet is important for the jet behavior and cannot be neglected in any theoretical analysis. (C) 2002 American Institute of Physics.

Fracture energy and softening behavior of high-strength concrete

An experimental investigation on the fracture properties of high-strength concrete (HSC) is reported. Three-point bend beam specimens of size 100 x 100 x 500 mm were used as per RILEM-FMC 50 recommendations. The influence of maximum size of coarse aggregate on fracture energy, fracture toughness, and characteristic length of concrete has been studied. The compressive strength of concrete ranged between 40 and 75 MPa. Relatively brittle fracture behavior was observed with the increase in compressive strength. The load-CMOD relationship is linear in the ascending portion and gradually drops off after the peak value in the descending portion. The length of the tail end portion of the softening curve increases as the size of coarse aggregate increases. The fracture energy increases as the maximum size of coarse aggregate and compressive strength of concrete increase. The characteristic length of concrete increases with the maximum size of coarse aggregate and decreases as the compressive strength increases, (C) 2002 Elsevier Science Ltd. All rights reserved.

Investigation of reversible and irreversible polarizations in thin films of SrBi2(Ta-0.5,Nb-0.5)(2)O-9

The reversible and irreversible components of the total polarization in a thin film of SrBi2(Ta-0.5,Nb-0.5)(2)O-9 were calculated. The C-V loop was integrated to obtain the reversible part of the total polarization. The reversible polarization was only 20% of the total polarization and showed almost no hysteresis. However, the dielectric constant due to the total polarization was almost the same as that for the reversible polarization in the saturation region of the large signal P-E hysteresis loop. The reversible part was subtracted from the total polarization to calculate the irreversible counterpart of it. The irreversible polarization showed a near-square shaped hysteresis loop, while the reversible polarization was obeying the Rayleigh law. The small signal hysteresis was simulated from the parameters obtained from the Rayleigh-curve fit with the experimental curve and then it was compared with the result obtained from direct measurement with small amplitude. (C) 2002 Elsevier Science B.V. All rights reserved.

Nonlinear Finite-Element Modeling of Batter Piles under Lateral Load

In this paper, a finite-element model is developed in which the nonlinear soil behavior is represented by a hyperbolic relation for static load condition and modified hyperbolic relation, which includes both degradation and gap for a cyclic load condition. Although batter piles are subjected to lateral load, the soil resistance is also governed by axial load, which is incorporated by considering the P-Δ moment and geometric stiffness matrix. By adopting the developed numerical model, static and cyclic load analyses are performed adopting an incremental-iterative procedure where the pile is idealized as beam elements and the soil as elastoplastic spring elements. The proposed numerical model is validated with published laboratory and field pile test results under both static and cyclic load conditions. This paper highlights the importance of the degradation factor and its influence on the soil resistance-displacement (p-y) curve, number of cycles of loading, and cyclic load response.

Studies on compressive failure features in syntactic foam material

Syntactic foam made by mechanical mixing of glass hollow spheres in epoxy resin matrix is characterized for compressive properties in the present study. Volume fraction of hollow spheres in the syntactic foam under investigation is kept at 67.8%. Effect of specimen aspect ratio on failure behavior and stress-strain curve of the material is highlighted. Considerable differences are noted in the macroscopic fracture features of the specimen and the stress-strain curve with the variation in specimen aspect ratio, although compressive yield strength values were within a narrow range. Post compression test scanning electron microscopic observations coupled with the macroscopic observations taken during the test helped in explaining the deviation in specimen behavior and in gathering support for the proposed arguments.

Water content - void ratio swell-shrink paths of compacted expansive soils

This paper addresses the behaviour of compacted expansive soils under swell-shrink cycles. Laboratory cyclic swell-shrink tests were conducted on compacted specimens of two expansive soils at surcharge pressures of 6.25, 50.00, and 100.00 kPa. The void ratio and water content of the specimens at several intermediate stages during swelling until the end of swelling and during shrinkage until the end of shrinkage were determined to trace the water content versus void ratio paths with an increasing number of swell-shrink cycles. The test results showed that the swell-shrink path was reversible once the soil reached an equilibrium stage where the vertical deformations during swelling and shrinkage were the same. This usually occurred after about four swell-shrink cycles. The swelling and shrinkage path of each specimen subjected to full swelling - full shrinkage cycles showed an S-shaped curve (two curvilinear portions and a linear portion). However, the swelling and shrinkage path occurred as a part of the S-shaped curve, when the specimen was subjected to full swelling - partial shrinkage cycles. More than 80% of the total volumetric change and more than 50% of the total vertical deformation occurred in the central linear portion of the S-shaped curve. The volumetric change was essentially parallel to the saturation line within a degree of saturation range of 50-80% for the equilibrium cycle. The primary value of the swell-shrink path is to provide information regarding the void ratio change that would occur for a given change in water content for any possible swell-shrink pattern. It is suggested that these swell-shrink paths can be established with a limited number of tests in the laboratory.