Steady-state Line Research Articles

Predicting undrained static response of sand with non-plastic fines in terms of equivalent granular state parameter

The influence of non-plastic fines on undrained monotonic behaviour of sand was investigated over a wide range of fines content (FC = 0–40%), global void ratio and initial mean effective stress ($$ p_{0}^{\prime } $$ = 100 kPa to 500 kPa), by performing triaxial compression tests with isotropic and anisotropic consolidation. For the sand–silt mixtures, steady-state line in the e − log(p′) space was found to be dependent on fines content with the existence of a limiting fines content, which defines the transition from a “fines in sand” to a “sand in fines” soil fabric. It is demonstrated that by means of the concept of equivalent granular void ratio, e*, all steady-state/critical state data points can be well described by a unique relationship in the e* − log(p′) space called the equivalent steady-state line (EG-SSL), regardless of fines content. The equivalent granular state parameter (ψ*), defined in terms of e*, and the EG-SSL can be effectively adopted for predicting the undrained monotonic behaviour of sand–silt mixtures and the onset of static instability, irrespective of fines content and initial state of the sand–silt mixtures.

A Modified Bridge Switch-Type Flux-Coupling Nonsuperconducting Fault Current Limiter for Suppression of Fault Transients

This paper proposes a modified bridge switch-type flux-coupling nonsuperconducting fault current limiter (BSFC-NSFCL) for suppressing the fault current and voltage sag. A flux-coupling reactor and a bidirectional bridge switch are combined to perform the functions of steady-state line current sharing and fault current suppression. The modified BSFC-NSFCL mainly utilizes the magnetic flux cancellation effect to make the limiter behave as a short circuit on the circuit during normal operation. Hence, there is almost no impact on the power system when the limiter is used. When a fault event occurs, the bridge switch turns off immediately, and then, the magnetic flux cancellation effect disappears. Thus, the impedance of primary coil inserts into the circuit to restrict the fault current and voltage sag phenomena. Once the fault is removed, the bridge switch turns on again, and the BSFC-NSFCL recovers to the normal operation. The modified NSFCL is more cost-effective and easy to be implemented than the flux-coupling superconducting fault current limiter. Theoretical analysis for the BSFC-NSFCL has been fully developed and proven by MATLAB software. Finally, the analytical, simulated, and experimental results have been carried out to verify the feasibility and performance of the proposed BSFC-NSFCL.

Effect of the minimum void ratio on the vertical intercept of the steady state line of non-plastic soils

The steady state line (SSL) plays a key role in understanding and modelling the mechanical response of soils. Accordingly, understanding how the SSL correlates to soil index properties is of primary importance. A previous study reported that the vertical location of the SSL (Γ1) in void ratio (e) versus mean effective stress (ρ') space is correlated to the minimum void ratio (emin). However, the correlation only included soils with narrow particle size distributions (PSD) and low fines content (FC). In the current study, published data corresponding to 30 non-plastic soils were re-processed to further explore the applicability of the r1-emincorrelation. The results indicate that the r1-emincorrelation is linear (R2 = 0.85) and valid regardless of the coefficient of uniformity (Cu), FC, and particle shape. The r1-emindataset presented herein was also compared to a previously published dataset, and good agreement was observed. It is proposed that the r1-emjncorrelation can be very useful to understand how the Γ1 of different non-plastic soils compare to one another, and to minimise the extent of triaxial testing required when characterising a soil deposit from an SSL standpoint. Limitations of the r1-emin correlation are also discussed.

Coupling Strategies for Finite Element Modeling of Thermal Elastohydrodynamic Lubrication Problems

This paper investigates coupling strategies for finite element modeling (FEM) of thermal elastohydrodynamic lubrication (TEHL) problems. The TEHL problem involves a strong coupling between several physics: solid mechanics, fluid mechanics, and heat transfer. Customarily, this problem is split into two parts (elastohydrodynamic (EHD) and thermal) and the two problems are solved separately while an iterative procedure is established between their respective solutions. This weak coupling strategy involves a loss of information, as each problem is not made intimately aware of the evolution of the other problem's solution during the resolution procedure. This typically leads to slow convergence rates. The current work offers a full coupling strategy for the TEHL problem, i.e., both the EHD and thermal parts are solved simultaneously in a monolithic system. The system of equations is generated from a finite element discretization of the governing field variables: hydrodynamic pressure, solids elastic deformation, and temperature. The full coupling strategy prevents any loss of information during the resolution procedure leading to very fast convergence rates (solution is attained within a few iterations only). The performance of the full coupling strategy is compared to that of different weak coupling strategies. Out of simplicity, only steady-state line contacts are considered in this work. Nevertheless, the proposed methodology, results, and findings are of a general nature and may be extrapolated to circular or elliptical contacts under steady-state or transient conditions.

Deadbeat Weighted Average Current Control With Corrective Feed-Forward Compensation for Microgrid Converters With Nonstandard LCL Filter

Microgrid converters are required to have the capability of both grid-tied mode and islanding mode operation. For this dual-mode operation, large shunt capacitors are often used in the interfacing converter output LCL filter, as it can help to stabilize supply voltage and to reduce switching ripple pollutions to sensitive loads during autonomous islanding operation. At the same time, this modification causes a few challenges, including the low-frequency harmonic distortions, the steady-state tracking errors and the slow dynamic response, to the line current regulation during grid-tied operation. To overcome these drawbacks, a modified weighted average current controller is developed. First, to realize a fast line current response, a deadbeat control of weighted average current is developed based on a reduced-order virtual filter plant. Second, a grid voltage feed-forward term is added to the weighted average current reference to mitigate the steady-state line current tracking errors. Note that this compensation term is directly added to the current reference, thus, it is very well decoupled from the closed-loop current regulator. In addition, it can be seen that the low-order line current harmonics caused by grid voltage distortion is inherently compensated by this proposed corrective feed-forward control.

Undrained behaviour of granular material and the role of fabric in isotropic and K0 consolidations: DEM approach

The behaviour of granular material was investigated by simulating an undrained triaxial compression test for three-dimensional assembly of ellipsoid particles over a wide range of void ratio, e, and mean confining stress, p′. The assembly was either isotropically consolidated or K0 consolidated prior to undrained shearing up to 30% axial strain to reach steady-state conditions. A unique steady-state line was obtained, irrespective of the consolidation path. The micro-mechanical quantities, such as coordination number and von Mises fabric in terms of second invariant of deviatoric fabric, FvM, also reached steady-state values. The normalised anisotropic fabric variable, A, and the trace of the joint stress–fabric tensor, KF, evolved during undrained simulation and reached the steady-state value at the end of shearing. This forms a unique relationship in KF–p′–e space and the projection of this relationship in e–log(p′) space is the classical steady-state line. This underpins the concept of fabric evolution and steady-state fabric in anisotropic critical state theory. The relationships of state parameter, ψ, and stress ratio at instability, ηIS = (q/p′)IS, were dependent on consolidation path, and the difference was not related to coordination number, but to FvM. However, a new phenomenon was observed that stress ratio, η, at the end of K0 consolidation and ηIS may reach beyond the steady-state stress ratio, M. Experimental data are needed to verify this; until then such behaviour should be regarded as unproven.

Factors Affecting Steady State Locus in Triaxial Tests

Models based on critical state soil mechanics (“CSSM”) require careful calibration of laboratory parameters in order to ensure accurate prediction of the behavior of soil under in situ conditions. This paper presented research on the testing of two distinct materials, a silt and a silty sand. Several triaxial tests were conducted under drained and undrained conditions, with low to very high confining pressures. Distinct mechanical responses were observed: some samples liquefied, some softened, and others hardened when loaded under undrained conditions. The degree of saturation, the induced anisotropy and the induced stress-path were found to influence the state limits between these distinct behaviors. This affected the steady state line (“SSL”) position defined by specimens showing strain softening in the experiment. Furthermore, the “critical state line” was only achieved when the specimens experienced strain hardening despite the stress-path during shear and the initial state conditions. Therefore, as these factors can impact the steady state line (SSL) position, it is essential when assessing the geomechanical behavior of the soil that these factors are monitored and controlled under laboratory conditions according to the in situ state condition and stress-path during shear. In the future, constitutive models have therefore to be adapted in order to determine the influence of these conditioning factors in the ultimate CSSM reference lines positions.

Firoozkuh Sand: Introduction of a Benchmark for Geomechanical Studies

The large-strain undrained behavior of Firoozkuh No. 161 sand is studied. It is observed that type of sand behavior is significantly affected by relative density (i.e., void ratio), the initial value of mean principal effective stress, and the shear mode. For samples subjected to the mode of triaxial compression, a clear steady-state line in both the q-p and e-p planes was obtained. For extension tests, dilation was not terminated at the end of the tests. As a result, the steady-state line for the mode of triaxial extension is only estimated in the q-p plane. Using three independent state parameters implemented within a bounding surface plasticity platform, the mechanical behavior of the tests is simulated. A reasonable correspondence between the experimental data and all three approaches is observed.

Transmission expansion planning model considering conductor thermal dynamics and high temperature low sag conductors

The means for transporting more power through an existing transmission corridor have been given considerable attention in recent studies. Reconductoring a path with a conductor that has a higher thermal capacity, such as a high temperature low sag (HTLS) conductor, is one possible option with minimal structural modification and out-of-service time. Parallel line additions or HTLS parallel line additions are other options that can increase transfer capabilities and reduce operating costs. Thermal constraint relaxation is another option, which is an operational based method that allows the line flow to exceed the steady-state line rating for a certain penalty price. Since such operation may deteriorate the expected service time of the conductor, the penalty price should be determined properly. In this study, the above options are captured to create the proposed transmission expansion planning model. In addition, a conductor degradation model is introduced to capture the associated degradation costs due to operating conductors at elevated temperatures. Numerical simulations conducted on the IEEE-24 and IEEE-118 bus system indicate the effectiveness of the proposed approach to increase system capacity while preserving current right-of-ways (ROWs).

Undrained Behavior of Sand-Fines Mixtures and Their State Parameter

AbstractThe influence of fines on the undrained behavior of sand was investigated experimentally over a range of fines content and effective mean stress. The role of fines on compressibility and formation of meta-stable soil fabric was analyzed. For a fines content in the range of 5–30%, most of the specimens manifested reverse behavior opposed to the normal behavior of clean sand. The addition of fines led to shifting of both the isotropic consolidation line and the steady-state line, increased compressibility, and occurrence of reverse behavior. All these behavior attributes are linked when the test results are interpreted in the context of the critical-state soil mechanics framework. In particular, reverse behavior is associated with an isotropic consolidation line that locates above the steady-state line. Several quantitative measures for characterizing the undrained deviator stress-strain responses were proposed, and these measures manifested correlation with the state parameter at the start of undra...

Prediction of Undrained Monotonic and Cyclic Liquefaction Behavior of Sand with Fines Based on the Equivalent Granular State Parameter

AbstractThe undrained behavior of sand with fines under both monotonic and cyclic loading was investigated experimentally by triaxial testing. The testing program covers fines content ranging from 0 to 30%, and a wide range of initial void ratios and confining stresses. The spectrum of cyclic loading includes one- and two-way cyclic loading, and in the latter case, the cyclic loading may be symmetrical or nonsymmetrical. The influence of fines content can be captured by using the equivalent granular void ratio, e∗, in lieu of the void ratio, e. All steady-state data points can be described by a single relationship referred to as the equivalent granular steady-state line. This study proposes the concept of the equivalent granular state parameter, ψ∗, for capturing the combined effects of the stress state, density state, and fines content. The observed behavior can then be related to e∗ and/or ψ∗. Irrespective of fines contents, the behavior under monotonic loading can be classified into three types, and ψ∗...

Some comments on the flow velocity and thinning of Svenbreen, Dickson Land, Svalbard

In this study a differential GPS survey of flow velocity and surface elevation change of a small glacier Svenbreen, central Svalbard, is presented and discussed. The maximum measured velocity was 3.21 m a-1 at 463 m a.s.l., close the theoretical steady-state equilibrium line altitude. After decades of thinning known from earlier research, the glacier surface has been continuing to lower over the analysed time span 2010-2012 by 1.82 m a-1 at the front at 185 m a.s.l. and 0.08 m a-1 at 541 m a.s.l. Since the glacier dynamics is very low, the study concludes that negative mass balance is the main driver of negative geometry changes and that no new distinct landforms will be formed in the near-future in the glacier forefield.

Monotonic triaxial experiments to evaluate steady-state and liquefaction susceptibility of Babolsar sand

In this study, drained and undrained triaxial tests under isotropic and anisotropic consolidations were conducted on reconstituted samples of Babolsar sand, which underlies a densely populated, seismic region of the southern coast of the Caspian Sea, Mazandaran, Iran. It was demonstrated that the sand experienced all possible states of liquefiable soil: flow failure, limited flow, and dilation. The steady-state and flow liquefaction lines of this sand were presented and compared with previously tested sands. It is shown that the initial stress anisotropy can affect the potential of volume change and pore pressure generation. The steady-state line (SSL), however, remains identical for the isotropically and anisotropically consolidated specimens under drained and undrained conditions. The tests data were then analyzed in order to investigate the liquefaction susceptibility of this sand in terms of parameters such as the state parameter, relative state parameter index, and lateral earth pressure ratio at failure.

Two-dimensional Green's functions for fluid and thermoelastic two-phase plane

The two-dimensional Green's functions for a steady-state line heat source in the interior of fluid and thermoelastic two-phase plane are derived in this paper. By virtue of the compact two-dimensional general solutions which are expressed in harmonic functions, four newly introduced harmonic functions with undetermined constants are constructed. Then, all the thermoelastic components in the fluid and thermoelastic two-phase plane can be derived by substituting these harmonic functions into the corresponding general solutions. And the undetermined constants can be obtained by the corresponding conditions of compatibility, boundary and equilibrium. Numerical results are given graphically by contours.

Simplified probabilistic state concept characterization of sandy soils and application to liquefaction resistance assessment

Probabilistic relationships are developed for the simplified characterization of a sandy soil’s state within the state concept framework. The relationships require knowledge of conventional geotechnical characterization parameters (i.e., median particle diameter, fines content and particle shape) and in situ field data (i.e., SPT N1 values). The salient features of the proposed relationships are illustrated by comparing the reference and in situ states of Toyoura sand, obtained in laboratory tests, with those obtained from the simplified relationships. Sensitivity analyses are utilized to understand the uncertainties in the simplified relationships which have the most significant impact on common problems of flow liquefaction and cyclic mobility resistance of sandy soils. The presented results illustrate that uncertainty in the position of the steady-state line at zero confining stress is the most significant uncertainty in flow liquefaction assessment, followed by in situ void ratio, and slope of the steady-state line. Analyses using the simplified state concept relationships within an elastic-plastic constitutive model illustrate that the in situ relative density is the key uncertainty in cyclic liquefaction resistance. Finally, it is shown that the uncertainty in cyclic liquefaction resistance due to uncertainty in situ void ratio is largely consistent with that obtained from empirical predictions of cyclic liquefaction resistance.

Power-based control of an electric oil pump for an automatic-transmission-based hybrid electric vehicle

A power-based control algorithm for an electric oil pump for a six-speed automatic-transmission-based hybrid electric vehicle was proposed. The new technology estimates the viscosity factor without having to measure the temperature of the automatic transmission fluid and controls the electric oil pump based on the required power. The viscosity factor was determined on a three-dimensional (3D) map by measuring the steady-state line pressure and the power and speed of the electric oil pump. Using the viscosity factor, the electric oil pump was controlled to supply the target line pressure according to the command power that was determined from the 3D viscosity factor–line pressure–power map. To save energy, multi-stage control was suggested which was based on low power, high power and medium power, according to the driving conditions of the vehicle. The test results showed that the proposed control method based on the electric oil pump power properly followed the target line pressure regardless of the change in the temperature of the automatic transmission fluid. In addition, when the line pressure changed owing to the additional flow rate consumption, e.g. during engine clutch engagement, the power-based control method easily followed the line pressure using only the target power, without needing to set the driving speed of the electric oil pump for each temperature. It was also found that control based on the electric oil pump power could save the driving power of the electric oil pump, unlike the situation with speed-based control, considering the product deviations.

Comprehensive Line Selection Method Based on the Relative Intensity of Transient Signal

When single-phase to ground fault happens in non-effectively earthed systems, in order to select the fault line more accurately, this paper puts forward the concept that relative intensity of the transient signal (Q). And based on this, a new method processing nonlinear and the non-stationary single named Hilbert-Huang transform (HHT) was combined with the steady-state zero sequence current method, named a new line selection method which synthesized the transient and steady state quantity. The method makes full use of transient and steady-state line information, to make up for the shortage of the previous method which using single criterion to detect fault line. At last, it was showed that this method is not affected by the fault initial phase Angle and grounding resistance by MATLAB, and also its accuracy and feasibility have been verified.

Ultrahigh-resolution spectroscopy with atomic or molecular dark resonances: Exact steady-state line shapes and asymptotic profiles in the adiabatic pulsed regime

Exact and asymptotic line shape expressions are derived from the semiclassical density matrix representation describing a set of closed three-level $\ensuremath{\Lambda}$ atomic or molecular states including decoherences, relaxation rates, and light shifts. An accurate analysis of the exact steady-state dark-resonance profile describing the Autler-Townes doublet, the electromagnetically induced transparency or coherent population trapping resonance, and the Fano-Feshbach line shape leads to the linewidth expression of the two-photon Raman transition and frequency shifts associated to the clock transition. From an adiabatic analysis of the dynamical optical Bloch equations in the weak field limit, a pumping time required to efficiently trap a large number of atoms into a coherent superposition of long-lived states is established. For a highly asymmetrical configuration with different decay channels, a strong two-photon resonance based on a lower states population inversion is established when the driving continuous-wave laser fields are greatly unbalanced. When time separated resonant two-photon pulses are applied in the adiabatic pulsed regime for atomic or molecular clock engineering, where the first pulse is long enough to reach a coherent steady-state preparation and the second pulse is very short to avoid repumping into a new dark state, dark-resonance fringes mixing continuous-wave line shape properties and coherent Ramsey oscillations are created. Those fringes allow interrogation schemes bypassing the power broadening effect. Frequency shifts affecting the central clock fringe computed from asymptotic profiles and related to the Raman decoherence process exhibit nonlinear shapes with the three-level observable used for quantum measurement. We point out that different observables experience different shifts on the lower-state clock transition.

Equivalent granular state parameter and undrained behaviour of sand–fines mixtures

State parameter defined using void ratio, e, and the steady-state line has been shown to be effective in predicting the undrained behaviour of sand. However, steady-state line for sand with fines is dependent on fines content. To overcome this problem, the concept of equivalent granular void ratio, e*, has been well investigated. However, the conversion from e to e* has been essentially a back-analysis process. A methodology for converting e to e* without the need of a back-analysis process was first presented. The concept of equivalent granular state parameter, ψ*, defined in terms of e*, and equivalent granular steady-state line was then developed. An extensive experimental study was conducted to investigate whether ψ* can capture the effects of fines content, and thus can be used to correlate undrained behaviour of sand–fines mixtures without the need of separately considering the effects of fines content. This study suggested that the effective stress path and deviatoric stress–strain responses in undrained shearing can be correlated with the ψ* value at the start of undrained shearing irrespective of fines content.

A probabilistic finite element analysis of embankment stability under transient seepage conditions

Flood protection structures lend themselves to probabilistic design given the large uncertain variables. Taking into account the historical discharge statistics of rivers, the annual probability of failure by slope instability of an embankment along the river Elbe in Eastern Germany is determined using a finite element analysis. The effect of transient seepage within the embankment and its effect on embankment stability are considered. Whereas a steady-state seepage line is most critical for the embankment stability, a transient seepage calculation including the rise and drop of the river water level reveals stability reserves. It has been demonstrated that the First-Order Reliability Method with Adaptive Response Surface is an efficient calculation technique for coupling numerical simulations to a reliability analysis.