Steady-state Line Research Articles

Equivalent state parameter dependency on gradation properties of medium sand-fines mixtures

Multiple studies confirm that determining the liquefaction resistance of sand-silt mixtures is more intricate compared to pure sand. Furthermore, it has been observed that the global void ratio fails to accurately predict the behavior of silty sand soils due to the fines particles, which can occupy voids between sand grains without significantly contributing to resisting external forces. To address this, a new parameter called equivalent void ratio (e*) has been proposed to better forecast the response of medium sand-fines mixtures. To investigate this further, a series of compression triaxial tests were conducted on mixtures comprising medium sand with low plastic fines. These mixtures were prepared in the laboratory with an initial relative density and subjected to varying confining pressures. The test results were utilized to assess the undrained shear strength of medium sand-silt mixtures based on the equivalent void ratio (e*) and to establish the equivalent granular steady-state line, which serves as a reference for calculating the equivalent state parameter (ψ*). Analysis of the obtained data suggests a correlation between the equivalent void ratio (e*) and the equivalent state parameter (ψ*) with the grading characteristics (such as D10, D50, Cu, D10R, D50R, and CUR) of the medium silty sand.

Vibration and force properties of an actuator formed from a piezoelectric stack within a frame structure

This paper examines the vibration and force properties of an actuator formed from a piezoelectric stack within a frame structure. Such configuration avoids the use of the traditional “earth-connected” support and allows the convenient attachment of the actuator to structures, such as power transformer tanks. The steady-state sensitivity of the actuator is analyzed, which comprised a linear frequency response function of the actuator system and a steady-state line frequency spectra of the transducer force at the frequency of the input voltage and its odd harmonics. The sensitivity is first analyzed by examining the forces transmitted to a rigid base structure through the stack and two legs of the frame when the actuator is excited by a single-frequency voltage input. The magnitude of the steady-state sensitivity at the frequency of the input voltage is approximately 15 dB higher than that at the other frequencies. The force transmitted through the piezoelectric stack is approximately twice as large as that through the two frame legs and with opposite phase. Next, the properties of transmitted forces when the rigid base structure is replaced by a beam and a plate of infinite size are also investigated. The interaction between the actuator and the elastic base structure has little effect on the magnitudes of the transmitted forces except at the resonace frequency of the actuator structure. However, the induced structural response is greatly affected and should be considered when describing the excitation capacity of the actuator. This capacity could be illustrated by the power flow between the actuator and the base structure and by the spatial distribution of the structural vibration induced by the actuator.

Applicability of shear wave velocity to evaluate state of granular materials with fines

Evaluation of state of cohesionless soils is a key issue in majority of geotechnical projects, especially when the major concern is liquefaction phenomenon. Standard approaches based on static or dynamic penetration tests are of limited or no use in granular materials containing considerable amount of fines. Therefore, there is a need to look for alternative approaches to identify state of materials containing certain amount of fines. One of a conceivable approaches rests on shear wave velocity (Vs) measurement. It results from the fact that Vs reflects state of stress and void ratio as well. A little is known to what extent shear wave velocity might reflect state of soil, especially, when it contains certain amount of fines. The paper concerns possibility of evaluation of state of cohesionless soils containing fines on the basis of shear wave velocity. The approach is based on hybrid approach i.e. laboratory and field measurement of shear waves velocity which enables projection of correlation between void ratio and normalized shear wave velocity measured in the laboratory for a given soil on a field profile. Thus, the determined void ratio profile is used to determine undrained shear strength on the basis of steady state line determined in the laboratory for the same soil batch. This procedure was carried out for twokinds of soil containing 10 and 36% of fines, which represent a sand-like material and transition zone behavior. Comments concerning applicability of this approach are given in the conclusion.

The dynamics of unsteady frictional slip pulses

Self-healing slip pulses are major spatiotemporal failure modes of frictional systems, featuring a characteristic size [Formula: see text] and a propagation velocity [Formula: see text] ([Formula: see text] is time). Here, we develop a theory of slip pulses in realistic rate- and state-dependent frictional systems. We show that slip pulses are intrinsically unsteady objects-in agreement with previous findings-yet their dynamical evolution is closely related to their unstable steady-state counterparts. In particular, we show that each point along the time-independent [Formula: see text] line, obtained from a family of steady-state pulse solutions parameterized by the driving shear stress [Formula: see text], is unstable. Nevertheless, and remarkably, the [Formula: see text] line is a dynamic attractor such that the unsteady dynamics of slip pulses (when they exist)-whether growing ([Formula: see text]) or decaying ([Formula: see text])-reside on the steady-state line. The unsteady dynamics along the line are controlled by a single slow unstable mode. The slow dynamics of growing pulses, manifested by [Formula: see text], explain the existence of sustained pulses, i.e., pulses that propagate many times their characteristic size without appreciably changing their properties. Our theoretical picture of unsteady frictional slip pulses is quantitatively supported by large-scale, dynamic boundary-integral method simulations.

Unprecedented liquefaction flow of gentle slopes containing non-plastic fines

In two recent earthquakes in Hokkaido, Japan, liquefied sand unusually flowed underground in very gentle man-made fill slopes, creating large ground surface depressions. In both cases, a significant amount of non-plastic fines was present in the loose fine sands. When tested in undrained triaxial tests, these sands were found far more contractive and easier to flow than the sand of the same density without fines. This strongly suggested that the high fines content was the major cause of the strange flow failures because it made the sand flowable on the contractive side of the steady-state line. Another series of cyclic torsional simple shear tests on contractive sands with fines under initial shear stress indicated that the flow failure can initiate even in a gentle slope. This is when the effective stress path comes across a straight yield line drawn from the origin on the τ − σc′ diagram uniquely defined irrespective of stress paths. A scenario to replicate the unusual flow failures was developed based on the field study and test results.

Initiation and mobility of recurring loess flowslides on the Heifangtai irrigated terrace in China: Insights from hydrogeological conditions and liquefaction criteria

Heifangtai terrace is famous in China for its irrigation-induced loess landslides. The frequently recurring loess flowslides initiated along the platform margin of the irrigated Heifangtai terrace have caused 42 fatalities and significant economic losses due to their long-runout and high-speed mobility. Yet it is still unclear if the recurring loess flowslides almost always initiate in the same places, and their initiated conditions and subsequent mobility behaviors have not been fully evaluated. To better understand such under-researched questions, we selected three typically recurring loess flowslides on the Heifangtai irrigated area. We performed multiple geophysical surveys using electrical resistivity tomography (ERT) and multichannel analysis of surface waves (MASW). We tested water content, density, and strength of loess using in-situ profile sampling. In addition, we examined the steady-state shear behaviors of saturated loess utilizing a ring shear apparatus under undrained conditions. The geophysical signatures and in-situ loess property profiles showed that hydrogeological conditions are crucial to initiating the recurring loess flowslides. The results also demonstrated that the shear liquefaction behavior of saturated loess controls the mobility after the failure of the loess flowslides. Liquefaction potential was assessed based on a chart showing the liquidity and plasticity index, pore pressure ratio, and steady-state line, which were developed as new criteria of liquefaction susceptibility assessment. The novel criteria essentially contain general information about fine-grained soil's nature, state, and behavior. These findings provide a better understanding of the dynamic mechanisms of the loess flowslides and their implications for landslide hazard mitigation.

Instability of Compacted Residual Soil

Static liquefaction of loose sands has been observed to initiate at stress ratios far less than the steady-state stress ratio. Different collapse surface concepts largely based on undrained triaxial test results have been proposed in the literature to explain the above instability phenomenon of loose sands. Studies of the instability behavior of fill material derived from residual soils remain limited. The present study investigated the instability behavior of a compacted residual soil using the conventional undrained triaxial tests and specially equipped constant shear triaxial tests. The test results were characterized in the p’: q: v space using the current state parameter with respect to the steady-state line for the residual soil. A modified collapse surface that has gradients varying with p’ and v was proposed for the loose residual soil to represent the instability states of undrained loading. Under constant shear stress conditions, the soil can mobilize stress ratios higher than those defined by the modified collapse surface. An instability surface was therefore presented for the instability states reached in static loading. Further, an alternative method of deducing the instability surface from the undrained stress paths was introduced.

The Effect of Fine Content on Undrained Shear Strength Behavior and Steady State Line of Silty Sands

İnce dene içeren kum zeminlerin drenajsız kayma dayanımı davranışı konsolidasyon sonrası başlangıç koşulları yanısıra, ince dane içeriği, boşluk oranı değişimi ve ortalama efektif gerilme düzeyinden etkilenmektedir. Dolayısı ile ince dane içeren zeminlerin davranışlarının değerlendirilmesi için temiz kuma göre daha fazla parametre ele alınmalıdır. Kritik durum zemin mekaniği (CSSM), tüm bu parametreleri göz önünde bulundurarak bu zemin türlerinin davranışını anlamak için uygun bir çerçevedir. Bu çaşışmada %10, %20; %30, %40 ve %50 ince dane içeren kum-silt karışımı örnekleri üzerinde 50 kPa, 100 kPa ve 200 kPa efektif konsolidasiyon basınçları altına bir dizi statik üç eksenli basınç deneyleri gerçekleştirilmiştir. Deneysel sonuçlar, örneklerin drenajsız kayma dayanımı davranışlanının ve durağan durum çizgisinin (SSL) ince dane içeriğinden önemli ölçüde etkilendiğini göstermektedir. Belirli bir eşik ince dane içeriğine kadar durağan duzum çizgisi (SSL) konumunun temiz kum konumundan aşağıya doğru hareket ettiği ve bu değerin ötesinde, ince içeriğin artmasıyla yukarı doğru hareket ettiği görülmüştür. Bu da ince dane içeriğinin değişimi ile birlikte örneklerin kayma dayanımı davranışının ve sıkışma eğiliminin değiştiğini göstermektedir. Bununla birlikte durağan durum parametre (Mss) ve durağan durumundaki mobilize sürtünme açısı (φss) değerlerinin de ince dane içeriğinden etkilendiği görülmüştür.

Analysis on the behavior of line differential protective relaying with solar PV penetration

Power System Protection is very important in electrical power system as it minimizes power supply interruption to customers, and also prevents damages to electrical equipment. Lately, renewable energy (RE) penetration in power system helps to support and fulfil the increasing demand of electricity to customers. However, the contribution of power from RE such as solar photovoltaic (PV) will increase the fault level and lead to reverse power flow; thus, it will affect power system protection reliability. This paper focuses on evaluating the reliability of differential protection relay during steady state, internal and external faults conditions when the power system is without and with solar PV penetration. Steady state and three-phase symmetrical line fault will be simulated in IEEE 39 bus test system using Power System Simulation for Engineering (PSS<sup>®</sup>E) software.

Influence of non-plastic fine on static iquefaction and undrained monotonic behavior of sandy gravel

Many geological hazards such as landslide, liquefaction, slope failure and rockfall occur in mixed gravelly alluvium or colluvium deposits, highlighting the importance of studying gravel–sand–silt mixtures. Although many natural strata are built using these mixtures, they are not entirely understood. A fundamental experimental study was designed to explore the influence of non-plastic fine content on the undrained behavior of gravel-sand-silt mixtures as common geomaterials in nature. Undrained monotonic triaxial tests were carried out. Three types of sandy gravels with different sand-to-gravel ratios were selected as base gravels. The impacts of the non-plastic fine content on the stress–strain behavior, static liquefaction potential, steady sate line, residual strength and critical state friction angle were studied. The laboratory results show that both sand-to-gravel ratio and non-plastic fine content have significant impacts on the undrained response of gravelly mixtures. It was observed that mixtures with zero non-plastic fines content exhibit the non-flow liquefaction behavior. However, adding silt content up to 45% shows the limited liquefaction or flow behavior, depending on the base gravelly soils and fine content percentage. A threshold for non-plastic fine content was found to be 35%–45%. Below this threshold, the steady state line shifts downward as silt content increases, and then shifts upward with further increase in the silt contents. The identical trend was also noted for residual strength and critical state friction angle. For silt contents below the threshold, the equivalent intergranular void ratio concept (modified with a new logical assumption) was used to analyze the behavior of gravelly mixtures. The results clearly indicate that the accurate value of equivalent intergranular void ratio can fully explain the behavior of sandy gravel-fine mixtures, similar to sand-fine mixtures. From a microstructure perspective, both sand and silt content act as fine-grains in gravelly mixtures and should be considered when studying the mechanical properties of theses mixtures.

Post-erosion mechanical response of internally unstable soil of varying size and flow regime

One of the leading causes of dam failure is internal erosion. The impact of erosion of non-plastic fine particles, known as suffusion, on the soil structure and strength has been studied experimentally. However, influences including sample size have not been thoroughly investigated. Internally unstable gap-graded cohesionless soil samples with various sizes were investigated using an erosion-triaxial apparatus. Samples were subjected to downward inflows of different seepage velocities. The results indicated that the potential for clogging increased with an increase in specimen length, leading to less fine particle erosion. Internal erosion changed the mechanical soil behaviour even after the loss of fines equal to 5% of the overall sample volume. Eroded specimens with similar intergranular void ratios showed similar undrained post-erosion behaviour. However, the magnitude of the post-erosion initial undrained peak shear strength is a function of coarse particle interlocking, residual fine content, and equivalent intergranular contact index. It was also found that the steady state line remained unchanged after erosion of fine particles and the mobilized friction angle at the steady state line is independent of the residual fine content.

A thermal EHL investigation for size effect of finite line contact on bush-pin hinge pairs in industrial chains

PurposeThis paper aims to study the influence of the dimension change of bush-pin on the pressure, oil film thickness, temperature rise and traction coefficient in contact zone by using a thermal elastohydrodynamic lubrication (EHL) model for finite line contact. Concretely, the effects of the equivalent curvature radius of the bush and the pin, and the length of the bush are investigated.Design/methodology/approachIn this paper, the contact between the bush and pin is simplified as finite line contact. The lubrication state is studied by numerical simulation using steady-state line contact thermal EHL. A constitutive equation Ree–Eyring fluid is used in the calculations.FindingsIt is found that by selecting an optimal equivalent radius of curvature and prolonging the bush length can improve the lubrication state effectively.Originality/valueUnder specific working conditions, there exists an optimal equivalent radius to maximize the minimum oil film thickness in the contact zone. The increase of generatrix length will weaken the stress concentration effect in the rounded corner area at both ends of the bush, which can improve the wear resistance of chain.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-10-2019-0448.

Calculation and analysis of the steady-state line ampacity weather sensitivity coefficients

The continuous increase in electrical power demand entails the need for larger ratings of overhead lines. For spatial, economic and ecological reasons, contemporary solutions are focused on incrementing the ratings of existing lines. One of these solutions is the real-time determination of line ampacity according to the measured or predicted weather and/or line parameters. The paper is focused on a novel calculation procedure and analysis of the steady-state line ampacity (SSLA) weather sensitivity coefficients (WSCs). The calculation of WSCs is based on the sensitivity analysis of the methodology for the SSLA given in Cigre N° 601 Technical Brochure. On the one hand these WSCs allow a fast estimate of the potential in the introduction of real-time ampacity calculation concept. On the other hand they give a good basis on the requirements for the measurement equipment installed in contemporary dynamical line rating systems (DLRSs). The interrelations between the WSCs and the SSLA are investigated using correlation and regression analysis. Finally, according to the typical design parameters of overhead lines the WSCs and their interrelations with the SSLA are calculated and analysed for typical aluminium steel-reinforced conductors (ACSRs) present in the Croatian transmission system.

Earthquake-induced flow liquefaction in fines-containing sands under initial shear stress by lab tests and its implication in case histories

Volume change of sands in shearing is either contractive or dilative depending on relative positions to SSL (Steady State Line) on the void ratio versus effective stress state diagram. This strongly affects how sands tend to liquefy during earthquakes and behave thereafter under initial shear stresses loaded by sloping ground or nearby structures. Torsional simple shear undrained cyclic loading test results are addressed here to categorize liquefaction behavior of sand specimens with various relative densities and fines contents Fc so that the specimens are positioned on both sides of SSL under the effect of different initial shear stress. A flow-type failure on the contractive side of SSL is particularly focused, and how to evaluate its potential in terms of Fc under initial shear stress is discussed. Lastly, unprecedented liquefaction-induced flow failures recently occurred in very gentle slopes are addressed to discuss their basic mechanism and possible scenario in view of the findings in the laboratory tests.

Liquefaction susceptibility of non-plastic silty sands using hypoplastic model simulations

ABSTRACT A detailed numerical analysis was performed on sands and non-plastic silty sands to examine the soil behaviour under triaxial loading conditions. An advanced hypoplastic soil element model has been used for the numerical simulations. The model parameters are constant for the given soil material and are determined easily by using mathematical formulations after conducting the basic experiments in the laboratory. The numerical model is validated with experimental data of triaxial tests before performing the numerical investigations. It is aimed to study the liquefaction resistance of sand and silty sands based on the critical state line (CSL), steady state line (SSL) and stress ratio at 20% failure strain under static loading. Results indicate that as the fines content increases, the CSL or SSL shifts to downwards, i.e., dilation decreases within the given range of pressures which indicate that the liquefaction susceptibility of sand increases with the addition of the fines content.

Liquefaction of a coal ash investigated by monotonic and cyclic triaxial tests

The critical state soil mechanics (CSSM) has been, recently, introduced as the major analytical framework for synthesising liquefaction behaviours of granular soils. However, liquefaction studies on coal ash have not been synthesised within the CSSM framework. Therefore, a series of monotonic and cyclic triaxial tests covering a range of initial states and testing conditions were conducted to evaluate static and cyclic liquefaction behaviours of coal ash. From the monotonic test results, a unique steady state line (SSL) was established for coal ash. Cyclic test results showed that cyclic liquefaction can be categorised into three distinct forms: cyclic instability, cyclic mobility and hybrid behaviour. Test results suggest that the occurrence of cyclic instability is related to static instability. Furthermore, the forms, if cyclic liquefaction occurred, were governed by the location of the initial state relative to the SSL.

Size effect on thermal elastohydrodynamic lubrication of industrial chain bush-pin hinge pair

PurposeThe purpose of this paper is to use elastohydrodynamic lubrication (EHL) theory to study the variation of the equivalent curvature radius “R” on the change of oil film thickness, pressure, temperature rise and friction coefficient in the contact zone between bush-pin in industrial chain drive.Design/methodology/approachIn this paper, the contact between bush and pin is simplified as infinitely long line contact. The lubrication state is studied by numerical simulation using steady-state line contact thermal EHL. The two constitutive equations, namely, Newton fluid and Ree–Eyring fluid are used in the calculations.FindingsIt is found that with the increase of equivalent curvature radius, the thickness of oil film decreases and the temperature rise increases. Under the same condition, the friction coefficient of Newton fluid is higher than that of Ree–Eyring fluid. When the load increases, the oil film thickness decreases, the temperature rise increases and the friction coefficient decreases; and the film thickness increases with the increase of the entraining speed under the condition “R < 1,000 mm”.Research limitations/implicationsThe infinite line contact assumption is only an approximation. For example, the distances between the two inner plates are 5.72 mm, by considering the two parts assembled into the inner plates, the total length of the bush is less than 6 mm. The diameter of the pin and the bore diameter of the bush are 3.28 and 3.33 mm. However, the infinite line contact is also helpful in understanding the general variation of oil film characteristics and provides a reference for the future study of finite line contact of chain problems.Originality/valueThe change of the equivalent radius R on the variation of the oil film in the contact of the bush and the pin in industrial chain drive was investigated. The size effect influences the lubrication characteristic greatly in the bush-pin pair.

Limit void ratios and steady-state line of non-plastic soils

The significant amount of laboratory testing required to determine the steady-state line (SSL) of soils has led to an interest in understanding how the SSL correlates with simpler soil index properties. Correlations proposed so far for non-plastic soils are only applicable to sands with fines content (FC) up to about 35%, but many geotechnical applications involve higher FC values. This work explores FC-independent correlations between the SSL and the limit void ratios by adopting the familiar straight line idealisation of the SSL projection on e–log(p′) space. Two parameters, Γn and λ, are used to represent the vertical location and the slope of the SSL, respectively. Using a database of 149 non-plastic soils, it is shown that there is a functional correlation between Γn and the minimum void ratio (emin) that is independent of particle size distribution, including FC, and particle angularity. A weak λ–emin correlation is also observed which can provide some guidance with respect to compressibility. Although the accuracy of the correlations is insufficient to make reliable quantitative SSL estimations, they are useful in guiding the selection process of samples whose SSLs have to be formally determined in order to characterise the SSL variability of non-plastic soil deposits.

Discussion: Limit void ratios and steady-state line of non-plastic soils

Discussion: Limit void ratios and steady-state line of non-plastic soils

Liquefaction Susceptibility of Silty Sands Based On Steady State Line Concept

Liquefaction Susceptibility of Silty Sands Based On Steady State Line Concept