Liquefaction Mechanism Research Articles

The study on loess liquefaction in China: a systematic review

Sandy soil liquefaction is common phenomena in engineering construction. However, in fact, saturated or nearly saturated loess liquefaction is also common phenomenon in loess area. In recent decades, large earthquakes around the world are frequent, loess is widely distributed worldwide, and loess liquefaction is one of the hot issues in loess dynamics. China has the most typical loess landform in the world, and Chinese scholars have done in-depth research on loess liquefaction. In this paper, the phenomena, mechanism, influencing factors, microscopic characteristics, evaluation methods and prevention methods of loess liquefaction in China are reviewed systematically. At the same time, improvement of loess saturation technology and new theory of loess liquefaction proposed by Chinese scholars are also analyzed. The results indicated that damages of foundations, landslides and collapses are the main phenomena of disasters caused by loess liquefaction; shear capacity of soil particles due to friction is close to zero during loess liquefaction; the main influencing factors of loess liquefaction are effective confining pressure, load frequency, cyclic stress ratio, saturation, over consolidation ratio; most of soluble salts have been dissolved, which is one of the main causes of loess liquefaction, and structure of loess particles has also been destroyed; evaluation methods of loess liquefaction mainly include the standard method and the Seed–Idriss simplified discriminant method; pore water pressure and strain conform to “A type curve” in loess liquefaction; pile foundation reinforcement, dynamic consolidation, chemical treatment are the main prevention methods of loess liquefaction.

Experimental Study on the Liquefaction Mechanism of Iron Ore Fines Cargoes

The liquefaction of Iron Ore Fines (IOF) during maritime transportation has got more attention in recent years. To study its liquefaction mechanism, the undrained monotonic loading tests on saturated IOF were conducted by using compression tri-axial apparatus. The static liquefaction behaviors of IOF under different densities and confining pressures were investigated. And different phenomenon has been observed on the IOF specimen. For the loose IOF specimen, slight dilate was observed and the phase transformation occurs in its stress-path curve under a high confining pressure. There is no phase transition in the intermediate density IOF sample, which shows more complex behavior. For the dense IOF specimen, a contractive behavior appears firstly then a long dilate starts. In view of these abnormal behaviors, the flow pattern failure mechanism of IOF is discussed, which provides a basis for the safe transportation of this kind of goods.

Liquefaction case studies of gravelly soils during the 2008 Wenchuan earthquake

The 2008 Wenchuan earthquake caused widespread liquefaction of gravelly soils (i.e., gravelly sands and sandy gravels), which phenomena show many differences compared to those of typical sands. To study the liquefaction mechanism and triggering evaluation of gravelly soils during this event, comprehensive case studies with measurement of shear wave velocity on both liquefied and non-liquefied sites were carried out according to a suite of recommended procedures for site investigation, field testing and data processing. Three typical cases were provided to illustrate the distinct characteristics of ground motion, liquefaction manifestation, soil profiles and field testing, and explore the possible mechanisms of liquefaction. Eighty-one well identified case histories were obtained, which feature the updated estimation of ground motion parameters from the USGS ShakeMap and the probabilistic treatment of the datasets. The preliminary analyses on liquefaction triggering boundary curves, shear wave velocities of these case histories and the applicability of the Ishihara criterion (1985) indicate that the gravel content plays a key role in the liquefaction mechanism and the consequences of gravelly soil deposits, and the liquefaction evaluation of gravelly sands and sandy gravels should be treated separately.

Mechanism of semen liquefaction and its potential for a novel non-hormonal contraception†.

Semen liquefaction is a proteolytic process where a gel-like ejaculated semen becomes watery due to the enzymatic activity of prostate-derived serine proteases in the female reproductive tract. The liquefaction process is crucial for the sperm to gain their motility and successful transport to the fertilization site in Fallopian tubes (or oviducts in animals). Hyperviscous semen or failure in liquefaction is one of the causes of male infertility. Therefore, the biochemical inhibition of serine proteases in the female reproductive tract after ejaculation is a prime target for novel contraceptive development. Herein, we will discuss protein components in the ejaculates responsible for semen liquefaction and any developments of contraceptive methods in the past that involve the liquefaction process.

Histotripsy Liquefaction of Large Hematoma for Intracerebral Hemorrhage Using Millisecond-Length Ultrasound Pulse Groups Combined With Fundamental and Second Harmonic Superposition: A Preliminary Study

Intracerebral hemorrhage is a life-threatening acute cerebrovascular disease characterized by a 30-d mortality rate of 40% and substantial disability for those who survive. The objective of this study is to investigate the feasibility of histotripsy-mediated efficient and fine liquefaction of large-volume hematoma by utilizing a protocol of millisecond-length ultrasound pulse groups combined with fundamental and second harmonic superposition. Experiments were initially performed in an in vitro hematoma phantom, using a two-element confocal-annular array. Results showed that a single ellipsoid shape, histotripsy lesion with major dimensions of 10.8 ± 1.2 mm axially and 4.8 ± 0.2 mm laterally was successfully generated. Controllability of the lesion shape and size could be realized by modulating treatment parameters in single-spot experiments. Large-volume hematomas were efficiently and finely liquefied through multisonications via a treatment strategy under the relatively optimized treatment parameters. Liquefied contents were evacuated and analyzed using a particle sizing system. The size of the lysates for the most part ranged from 4–8 μm, with more than 99% of them being smaller than 10 μm. Experiments were then conducted in an optically transparent tissue phantom to explore the liquefaction mechanisms. The phantom was composed of polyacrylamide hydrogel, embedded with bovine serum albumin (BSA), and a thin phantom layer consisted of red blood cells in the BSA polyacrylamide gel was inlayed in the BSA gel phantom. The related mechanisms, such as the frequent boiling that occurred at multiple positions and the enhanced cavitation, revealed the quick development of the lesion in the phantom and the efficient liquefaction of the clot. These results indicated that the proposed histotripsy approach is feasible for the efficient, precise and fine liquefaction of large-volume hematoma and may be developed as a useful tool for intracerebral hemorrhage treatment.

Siltli Kumlarda Gerilme Kontrollü ve Deformasyon Kontrollü Sıvılaşma Testlerinin Karşılaştırılması

The liquefaction behavior of silty sands with different grain diameters and fine grain content during the earthquake is not the same and understanding the liquefaction mechanism of such soils continues to be one of the important subjects of geotechnical earthquake engineering. For this purpose, deformation controlled and stress-controlled tests were performed on silty-sand samples prepared by mixing 5% and 30% silt to 20/30 and 30/50 sands of two different grades using cyclic simple shear tester. The results showed that there was no significant difference between the results of deformation controlled and stress-controlled tests. However, with the increase of silt content, the resistance to liquefaction of silty-sand samples of both 20/30 sand and 30/50 sand decreased. In addition, the resistance to liquefaction of all samples increased with increasing relative density.

Experimental Study on Mechanism of Wave-Induced Liquefaction of Sand-Clay Seabed

In this study, a series of laboratory experiments for the response of wave induced clay-sand seabed were carried out to clarify the mechanism of liquefaction of clayey seabed. The experiments were conducted in an 80 m long wave flume. In the tests, the sand-clay beds were mixed with various clay contents (CC) from 0.5% to 15% and were tested for given wave conditions. The pore water pressure and the water elevation were measured in each test. Soil properties tests and scanning electron microscope (SEM) experiments on different seabed samples were carried out to further explore the mechanism of liquefaction. The experimental results indicated that the amplitude and accumulation of the excess pore water pressure (EPP) varied with different CC in the sand-clay bed. With the introduction of CC, micro-structure and properties (such as permeability and compressibility) of bed soils changed. Sand-clay bed presented more susceptibility to liquefy compared with pure sand bed. CC promoted seabed liquefaction, even if the added amount was very small (CC is 0.5%), however when CC exceeded a certain value (10% in this study), the mixed bed will not be liquefied. This phenomenon can be well explained by the micro-structure of sand-clay bed. CC within a sandy seabed, does not only affect the permeability, but also change the compressibility of seabed soils. For example, the microfabric of seabed vulnerable to liquefaction is loose. Clay aggregations generally gathered at the sand particle contact points. This microfabric is easily compressed under wave loads and allowed pore water to flow, resulting in the accumulation of pore water pressure. On the other hand, the microfabric of seabed that was resistant to liquefaction appeared to be more compact. Due to clay-filled gaps between the sand particles, the pore water is more difficult to flow when seabed was compressed. Furthermore, the tendency of seabed liquefaction is closely related to CC.

A novel experimental system for studying the sand liquefaction characteristics from macroscopic and microscopic points of view

A novel experimental system for studying the macro- and micro-liquefaction behaviors of sand deposits was designed, developed, and applied in this paper. The developed system mainly consists of a shaking table sub-system, a visualized model container, and a fast-shutter-speed micro-image acquisition sub-system. Liquefaction tests on saturated Fujian sand deposit with less permeable Zhuhai clay overburden were conducted to check the performances of the system and study the micro-liquefaction behaviors. Throughout the total liquefaction process, the excess pore water pressures and micro-liquefaction images were recorded and analyzed. It was shown that satisfactory performances can be provided by the developed experimental system. The results showed that the obtained micro-fabrics of sand particles (i.e., the orientations of the contact normal and the long axis of sand particles, the average contact number, and apparent void ratio) agree well with the macro behaviors (i.e., the excess pore water pressure) throughout the total process of liquefaction. Void redistribution during liquefaction was observed beneath the overburden. The developed novel experimental system helps to illuminate the mechanisms of sand liquefaction from the micro-perspective.

Catalytic alcohothermal liquefaction of wet microalgae with supercritical methanol

Microalgae are promising feedstock for the production of biofuel due to their high productivity and low interference with food production for their cultivation and usage. Owing to their aquatic production environment, however, energy-intensive dewatering and drying processes may be required before their conversion to biofuel. In order to avoid these processes, their liquefaction through hydrothermal means has attracted attention, with extensive research works. The present research proposes and examines alcohothermal liquefaction of wet microalgae, in an attempt to modify and improve microalgae liquefaction characteristics. Thus supercritical methanol was employed as a reaction media for liquefaction of wet Chlorella vulgaris, and the effects of water presence as well as the effects of heterogeneous oxide catalysts were examined. This methanothermal liquefaction gave high bio-oil yield of 54.5 C% (feed microalgae basis) compared to 30.5 C% by hydrothermal for non-catalytic reaction at 385 °C. With Zr(WO4)2 catalyst methanothermal bio-oil yield increased further to 65.6 C%. The presence of water in the methanol medium somewhat decreased the bio-oil yield, while some of the catalysts mitigated the decrease: at 50 wt% water content in methanol, MnO2, ZnO2 and ZrO2 gave bio-oil yield of 55.5 C%, 59.5 C% and 57.6 C%, respectively. Possible mechanism of catalytic methanothermal liquefaction of wet microalgae is discussed.

Study on liquefaction mechanism of saturated sand considering stress redistribution

Most of the saturated soil in actual condition is anisotropically consolidated, and can liquefy during minor earthquake. Based on the analysis of stress state in actual soil, the present paper considers that the stress redistributed during loading process, which result in the liquefaction. However, in present conventional element tests, the liquefaction in anisotropically consolidated saturated sands (ACS) cannot be induced under dynamic cyclic loading without stress reversal. It contributes to the uncertainty about the liquefaction resistance of soil and the development model of excess pore water pressure (PWP). A brief theoretical interpretation within the theory of limit state of soils is given to explain why the liquefaction in ACS could not be induced using the conventional element test under dynamic cyclic load with low or moderate amplitude, and the validity of the theoretical analysis is verified by experiments. The stress redistribution is realized by confining the lateral deformation based on the conventional test, and the liquefaction in ACS under minor cyclic load is realized. Furthermore, a new concept called “continued liquefaction” is proposed. Apart from “transient liquefaction”, the PWP, the total confining pressure and the total vertical stress are always at the same level, and the mean effective stress of sands is always zero in the “continued liquefaction” stage. Finally, a suggestion that the development model of PWP should be established on the basis of the ratio of the PWP to the initial vertical stress is recommended.

Understanding the liquefaction mechanism of Beypazarı lignite in tetralin with ultraviolet irradiation using discrete time models

This study has proposed four different liquefaction models consisting of both reversible and irreversible reaction steps with three lumped parameters, asphaltenes, preasphaltenes, and oils, for the liquefaction of Turkish lignite (Beypazarı-Çayırhan). The coal had been liquefied in tetralin using a solvent/coal ratio of 5/1 at four different ultraviolet irradiation light sources of 90, 120, 150, and 180 W. The validity of the proposed models is specified by first order linear discrete-time models with the experimental data. Furthermore, the reaction rates of the proposed liquefaction models are determined using a Matlab program with the use of Kalman filter. The validation of proposed models for the liquefaction of Beypazarı lignite is defined using the sum of the squared differences of the models and experimental data. The results demonstrate that models which consist of reversible steps provide a better fit with experimental data compared to models consisting of irreversible steps. While the liquefaction step from reactive coal to oils demonstrates a maximum reaction rate constant of 2*10−2 h−1, the other steps from reactive coal to either preasphaltenes or asphaltenes show lower reaction rate constants, about 1*10−2 h−1. In addition to the fact that the formation of preasphaltenes and asphaltenes from reactive coal takes place slowly, a major proportion of the oils are formed directly from reactive coal.

Agricultural and Forest Residues towards Renewable Chemicals and Materials Using Microwave Liquefaction

Microwave-assisted liquefaction is regarded as a promising thermochemical approach to produce renewable and sustainable chemicals and materials from lignocellulosic biomass. Agricultural and forest residues as sources of lignocellulosic biomass have great potential in this regard. With process optimizations, several biomass types have been subjected to liquefaction in different solvents with various catalysts. The products from recent microwave liquefaction with and without further fractionation have been thoroughly analyzed and used for the synthesis of biomaterials. Renewable chemicals, polyurethane foams with partial use of renewable raw materials, and phenolic resins have been the main products from microwave-liquefied products. Further research on microwave liquefaction mechanisms and scalable production should be enhanced to fully evaluate the economic and environmental benefits. This work presents an overview on achievements using liquefaction in combination with microwave energy to convert lignocellulosic biomass into value-added products and chemicals.

Enhanced landslide mobility by basal liquefaction: The 2014 State Route 530 (Oso), Washington, landslide

AbstractLandslide mobility can vastly amplify the consequences of slope failure. As a compelling example, the 22 March 2014 landslide near Oso, Washington (USA), was particularly devastating, traveling across a 1-km+-wide river valley, killing 43 people, destroying dozens of homes, and temporarily closing a well-traveled highway. To resolve causes for the landslide’s behavior and mobility, we conducted detailed postevent field investigations and material testing. Geologic and structure mapping revealed a progression of geomorphological structures ranging from debris-flow lobes at the distal end through hummock fields, laterally continuous landslide blocks, back-rotated blocks, and finally colluvial slides and falls at the landslide headscarp. Primary structures, as well as stratigraphic and vegetation patterns, in the landslide deposit indicated rapid extensional motion of the approximately 9 × 106 m3 source volume in a closely timed sequence of events. We identified hundreds of transient sand boils in the landslide runout zone, representing evidence of widespread elevated pore-water pressures with consequent shear-strength reduction at the base of the slide. During the event, underlying wet alluvium liquefied and allowed quasi-intact slide hummocks to extend and translate long distances across the flat valley. Most of the slide material itself did not liquefy. Using geotechnical testing and numerical modeling, we examined rapid undrained loading, shear and collapse of loose saturated alluvium, and strong ground shaking as potential liquefaction mechanisms. Our analyses show that some layers in the alluvium can liquefy when sheared, as could occur with rapid undrained loading. Simultaneous ground shaking could have contributed to pore-pressure generation as well. Two key elements, a large and rapid failure overriding wet liquefiable sediments, enabled the landslide’s high mobility. Basal liquefaction may enhance mobility of other landslides in similar settings.

On the prediction of liquefaction resistance of unsaturated sands

The increasing interest in the undrained cyclic behaviour of unsaturated soils is justified by the evidence of the beneficial effect of desaturation on liquefaction resistance and is thus strictly connected with the need to put forth sound tools to be used in the design of Induced Partial Saturation (IPS) interventions. IPS is still far from being a routine technology because of the lack of such design tools, as well as of simple technologies to obtain and preserve it on site. This paper offers a contribution to the first issue, based on the energetic interpretation of laboratory results that highlights the role of the volumetric and deviatoric components of the specific energy spent during undrained cycling on the liquefaction mechanism. Independent experimental results taken from the literature are successfully simulated using this interpretation. Then, stemming from the theoretical and experimental considerations reported in the first part of the paper, two possible approaches to calculate the desired degree of saturation of a loose sand (design goal for IPS) are introduced and discussed.

Investigation on solvolysis liquefaction mechanism of Chlorella pyrenoidosa in ethanol–water solvent based on major model compounds: Protein and starch

This work explored the liquefaction mechanism of Chlorella pyrenoidosa in ethanol−water solvent. Model compounds (soya protein and corn starch) were liquefied in water, ethanol and ethanol−water solvents to investigate the synergistic effect between ethanol and water on the biocrude oil yield. To reveal the cross-interaction between protein and starch, the effect of different mixed ratios on biocrude oil yield was studied. The protein/carbohydrate ratio of feedstock was adjusted by mixing starch with microalgae to reveal the effect of Maillard reaction on the yield and quality of biocrude oil. The results showed that ethanol–water solvent contributed better to the decomposition of protein and starch compared with pure water and ethanol. The ratios of protein/starch at 2/1 and microalgae/starch at 100/14 achieved the highest biocrude oil yield and energy recovery. Based on chemical compositions of biocrude oil and light oil, a possible reaction pathway of solvolysis liquefaction of microalgae in ethanol–water solvent was proposed.

Ultrasonic tracking of a sinking ball in a vibrated dense granular suspension

Observing and understanding the motion of an intruder through opaque dense suspensions such as quicksand remains a practical and conceptual challenge. Here we use an ultrasonic probe to monitor the sinking dynamics of a steel ball in a dense glass bead packing (3D) saturated by water. We show that the frictional model developed for dry granular media can be used to describe the ball motion induced by horizontal vibration. From this rheology, we infer the static friction coefficient and effective viscosity that decrease when increasing the vibration intensity. Our main finding is that the vibration-induced reduction of the yield stress and increase of the sinking depth are presumably due to micro-slips induced at the grain contacts but without visible plastic deformation due to macroscopic rearrangements, in contrast to dry granular packings. To explain these results, we propose a mechanism of acoustic lubrication that reduces the inter-particle friction and leads to a decrease of the yield stress. This scenario is different from the mechanism of liquefaction usually invoked in loosely packed quicksands where the vibration-induced compaction increases the pore pressure and decreases the confining pressure on the solid skeleton, thus reducing the granular resistance to external load.

Process optimization of biomass liquefaction in isopropanol/water with Raney nickel and sodium hydroxide as combined catalysts

Liquefaction co-catalyzed by Raney nickel and NaOH in isopropanol (2-PrOH)/H2O is an efficient method for transforming lignocellulosic biomass into bio-oil. The present study investigated the effect of reaction temperature, residence time, and dosage of the catalysts on the yield and composition of bio-oil. To understand the liquefaction mechanism, the transformation of lignin and cellulose at the same conditions was investigated as well. The results indicated that 240 °C was the optimum temperature in terms of bio-oil yield. It was also found that residence time had a great effect on not only the bio-oil yield but also the composition and higher heating value (HHV) of the bio-oil. Increasing the dosage of the catalysts also improved the yield and HHV of bio-oil. Most phenols in bio-oil were originated from lignin, while most ketones and hydrocarbons were produced by cellulose.

Understanding the mechanism of cornstalk liquefaction in water/ethanol mixtures through Py-GC/MS analysis of the solid residues

Few investigations have been made to apply thermal analysis methods on solid residue analysis to understand biomass liquefaction mechanistic information. To investigate the mechanism of cornstalk liquefaction in water/ethanol mixtures, the solid residues remaining after the liquefaction process were characterized by thermogravimetric analysis (TGA) and analytical pyrolysis (Py-GC/MS). Pyrolysis temperature and liquefaction temperature have synergetic effects on the distributions and yields of various chemical groups during the pyrolysis process. The thermal stabilities of the solid residues remaining after the cornstalk liquefaction process increased with the increase of liquefaction temperature. Compared with raw cornstalk pyrolysis, the proportions of total phenol compounds from solid residue pyrolysis at 400 °C, 500 °C and 600 °C were reduced. The volatilized compounds identified by Py-GC/MS analysis of solid residues and cornstalks displayed significant variability in the peak area and composition distribution. These changes reflect different mechanistic information during the biomass liquefaction process. These results indicate that analytical pyrolysis of the solid residues remaining after biomass liquefaction in water/ethanol mixtures could provide new information about the mechanism of the liquefaction process.

Energy-based evaluation of liquefaction potential of uniform sands

Since behaviors of loose, dense, silty sands vary under seismic loading, understanding the liquefaction mechanism of sandy soils continues to be an important challenges of geotechnical earthquake engineering. In this study, 36 deformation controlled cyclic simple shear tests were performed and the liquefaction potential of the sands was investigated using three different relative densities (40, 55, 70%), four different effective stresses (25, 50, 100, 150 kPa) and three different shear strain amplitudes (2, 3.5, 5%) by using energy based approach. Experiments revealed the relationship between per unit volume dissipated energy with effective stress, relative density and shear strain. The dissipate energy per unit volume was much less affected by shear strain than effective stress and relative density. In other words, the dissipated energy is strongly dependent on relative density and effective stress. These results show that the dissipated energy per unit volume is very useful and may contain the non-uniform loading conditions of the earthquake spectrum. When multiple regression analysis is performed on experiment results, a relationship is proposed that gives liquefaction energy of sandy soils depending on relative density and effective stress parameters.

Cyclic Behaviors of Saturated Sand-Gravel Mixtures under Undrained Cyclic Triaxial Loading

ABSTRACT A few well-documented liquefaction case studies of gravelly soils during major earthquakes have increased concerns regarding the liquefaction susceptibility of gravelly sand soils. Understanding the failure mechanism of sand-gravel mixtures under undrained cyclic loading is important for better assessing their liquefaction susceptibility. The liquefaction mechanism and susceptibility of isotropically and anisotropically consolidated sand-gravel mixtures are investigated under undrained cyclic loading in a solid cylinder apparatus; and, the influences of the varying material properties, compactness states, and particle gradations are systematically studied. The authors introduce an index of the average flow coefficient (k a) that describes the fluidity of saturated sand-gravel mixtures, and then propose the elaboration of a new liquefaction mechanism of saturated sand-gravel mixtures. The specimens would experience cyclic liquefaction when the excess pore pressure ratio reaches 100% under undrained isotropic consolidation, whereas the cyclic mobility would be induced when the cumulative axial strain reaches 5% under undrained anisotropic consolidation. Particles with both sizes smaller than 0.25 mm and mass contents less than 30% in sand-gravel mixtures primarily play a role of the fillers of intergranular voids (fines in coarse). The skeleton void ratio (e sgk) is a unique physical state index to characterize the liquefaction susceptibility of saturated sand-gravel mixtures with the filler content less than 30%. The negative correlation between the cyclic resistance ratio (CRR) and e sgk can be expressed as the power function. Abbreviations: A cl: Closed-loop area of each loading cycle in Fig. 5; ACU: Anisotropically consolidated undrained; CRR: Cyclic resistance ratio; CRR 15: CRR in 15 cycle; CRR 25: CRR in 25 cycle; CSR: Cyclic stress ratio, Applied cyclic stress ratio in CTX test in the form of Equation (7); CTX: test Cyclic triaxial test; C u, C c: Coeffıcients of uniformity and curvature for the particle-size distribution curve; D, d: Size of coarse and small spherical particles in an idealized binary packing model; D 50: Median diameter of host coarse soils in binary mixtures; d 50: Median diameter; median diameter of host fine soils in binary mixtures; DA: Double-amplitude; D r: Relative density; initial relative density; D r0: Post-consolidation relative density; e: Global void ratio; initial void ratio; e 0: Post-consolidation void ratio; e min, e max: Minimum and maximum void ratios; e sgk: Skeleton void ratio; FC: Fines content for particles with the sizes less than 0.075 mm; FC th: Fines content threshold value; f f: Filler content by weight for particles with sizes less than 0.25 mm in the coarse-dominated grain contact sand-gravel mixtures; G c: Gravel content; G s: Specific gravityHCA Hollow cylinder apparatus; ICU: Isotropically consolidated undrained; k a: Index of the average flow coefficient; K c: Consolidation stress ratio, defined as the ratio of to m, n Fitting coefficients in Equations 11–13; N l: Number of cycles required to cause an r u = 100% for ICU CTX test or ε p = 5% for ACU CTX test; q: Deviatoric stress; q cyc: Peak cyclic deviatoric stress; q s: Initial static deviatoric stress; R: Roundness proposed by Power (1953); R d: Particle size disparity ratio in binary packing model; r u: Excess pore pressure ratio, defined as the ratio of Δ u to; Δu: Excess pore pressure change induced by the action of cyclic shear stressSA Single-amplitude; α d: Cyclic shear stress ratio of any plane in the specimen; β: Inclination angle to the horizontal axis in Mohr’s stress circle serve; : Shear strain rate; ,: Maximum and minimum shear strain rate of each loading cycle in Fig. 5; ε: Axial strain; ε p: Accumulated permanent axial strain; η: Apparent viscosity in fluid mechanics; ρ d: Dry densities; ,: Initial effective vertical and lateral consolidation stress; σ d: Applied sinusoidal cyclic axial stress amplitude; : Initial effective normal stress of any plane in the specimen; τ: Shear stress; τs : Initial shear stress of any plane in the specimen; τ d: Cyclic shear stress amplitudes of any cyclic shear effect plane; τ max, τ min: Maximum and minimum shear stress of each loading cycle in Fig. 5