Search results for: cyclic triaxial

Authors: S. A. Naeini, Z. Eftekhari

Abstract:

Liquefaction phenomenon in sand is nowadays a classical soil mechanics subject. Using a cyclic triaxial test apparatus, we use non-woven geotextile reinforcement to improve the liquefaction resistance of sand. The layer configurations used are zero, one, two and three horizontal reinforcing layers in a triaxial test sample. The influences of the number of geotextile layers, and cyclic stress ratio (CSR) were studied and described. The results illustrated that the geotextile inclusion increases liquefaction resistance.

Keywords: liquefaction resistance, geotextile, sand, cyclic triaxial test, cyclic stress ratio

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Authors: Arezoo Sadrinezhad, Kallol Sett, S. I. Hariharan

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In this paper, a probabilistic framework based on Fokker-Planck-Kolmogorov (FPK) approach has been applied to simulate triaxial cyclic constitutive behavior of uncertain soils. The framework builds upon previous work of the writers, and it has been extended for cyclic probabilistic simulation of triaxial undrained behavior of soils. von Mises elastic-perfectly plastic material model is considered. It is shown that by using probabilistic framework, some of the most important aspects of soil behavior under cyclic loading can be captured even with a simple elastic-perfectly plastic constitutive model.

Keywords: elasto-plasticity, uncertainty, soils, fokker-planck equation, fourier spectral method, finite difference method

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Authors: E. E. S. Uy, T. Noda, K. Nakai, J. R. Dungca

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Cyclic threshold shear strain is the cyclic shear strain amplitude that serves as the indicator of the development of pore water pressure. The parameter can be obtained by performing either cyclic triaxial test, shaking table test, cyclic simple shear or resonant column. In a cyclic triaxial test, other researchers install measuring devices in close proximity of the soil to measure the parameter. In this study, an attempt was made to estimate the cyclic threshold shear strain parameter using full-field measurement technique. The technique uses a camera to monitor and measure the movement of the soil. For this study, the technique was incorporated in a strain-controlled consolidated undrained cyclic triaxial test. Calibration of the camera was first performed to ensure that the camera can properly measure the deformation under cyclic loading. Its capacity to measure deformation was also investigated using a cylindrical rubber dummy. Two-dimensional image processing was implemented. Lucas and Kanade optical flow algorithm was applied to track the movement of the soil particles. Results from the full-field measurement technique were compared with the results from the linear variable displacement transducer. A range of values was determined from the estimation. This was due to the nonhomogeneous deformation of the soil observed during the cyclic loading. The minimum values were in the order of 10-2% in some areas of the specimen.

Keywords: cyclic loading, cyclic threshold shear strain, full-field measurement, optical flow

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Authors: Erica Elice Uy, Toshihiro Noda, Kentaro Nakai, Jonathan Dungca

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Deformation in a conventional cyclic triaxial test is normally measured by using point-wise measuring device. In this study, non-contact measurement technique was applied to be able to monitor and measure the occurrence of non-homogeneous behavior of the soil under cyclic loading. Non-contact measurement is executed through image processing. Two-dimensional measurements were performed using Lucas and Kanade optical flow algorithm and it was implemented Labview. In this technique, the non-homogeneous deformation was monitored using a mirrorless camera. A mirrorless camera was used because it is economical and it has the capacity to take pictures at a fast rate. The camera was first calibrated to remove the distortion brought about the lens and the testing environment as well. Calibration was divided into 2 phases. The first phase was the calibration of the camera parameters and distortion caused by the lens. The second phase was to for eliminating the distortion brought about the triaxial plexiglass. A correction factor was established from this phase. A series of consolidated undrained cyclic triaxial test was performed using a coarse soil. The results from the non-contact measurement technique were compared to the measured deformation from the linear variable displacement transducer. It was observed that deformation was higher at the area where failure occurs.

Keywords: cyclic loading, non-contact measurement, non-homogeneous, optical flow

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Authors: Seyed Abolhasan Naeini, Mohammad Mahdi Shojaedin

Abstract:

Oil leakage from the pipelines and the tanks carrying them, or during oil extraction, could lead to the changes in the characteristics and properties of the soil. In this paper, conducting a series of experimental cyclic triaxial tests, the effects of oil contamination on the liquefaction potential of sandy soils is investigated. The studied specimens are prepared by mixing the Firoozkuh sand with crude oil in 4, 8 and 12 percent by soil dry weight. The results show that the oil contamination up to 8% causes an increase in the soil liquefaction resistance and then with increase in the contamination, the liquefaction resistance decreases.

Keywords: cyclic triaxial test, liquefaction resistance, oil contamination, sandy soil

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Authors: R. Ziaie Moayed, M. Alibolandi

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Dynamic behavior of soil are evaluated relative to a number of factors including: strain level, density, number of cycles, material type, fine content, geosynthetic inclusion, saturation, and effective stress. This paper investigate the dynamic behavior of saturated reinforced sand under cyclic stress condition. The cyclic triaxial tests are conducted on remolded specimens under various CSR which reinforced by different arrangement of non-woven geotextile. Aforementioned tests simulate field reinforced saturated deposits during earthquake or other cyclic loadings. This analysis revealed that the geotextile arrangement played dominant role on dynamic soil behavior and as geotextile close to top of specimen, the liquefaction resistance increased.

Keywords: dynamic behavior, reinforced sand, triaxial test, non-woven geotextile

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Authors: Daniel Rosero, Johan S. Arana, Sebastian Arango, Alejandro Cruz, Isabel Gomez-Gutierrez, Peter Thomson

Abstract:

Santiago de Cali is located in the southwestern Colombia in a high seismic hazard zone. About 50% of the city is on the banks of the Cauca River, which is the second most important hydric affluent in the country and whose alluvial deposits contain potentially liquefiable sands. Among the methods used to study a site's liquefaction potential is the finite elements method which use constitutive models to simulate the soil response for different load types. Among the different constitutive models, the Modified UBCSand stands out to study the seismic behavior of sands, and especially the liquefaction phenomenon. In this paper, the dynamic behavior of a potentially liquefiable sand of Santiago de Cali is studied by cyclic triaxial and CPTu tests. Subsequently, the behavior of the sand is simulated using the Modified UBCSand constitutive model, whose parameters are calibrated using the results of cyclic triaxial and CPTu tests. The above with the aim of analyze the constitutive model applicability for studying the geotechnical problems associated to liquefaction in the city.

Keywords: constitutive model, cyclic triaxial test, dynamic behavior, liquefiable sand, modified ubcsand

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Authors: Natalie M. Wride, Xueyu Geng

Abstract:

Subgrade soils of railway infrastructure are subjected to a significant number of load applications over their design life. The use of slab track on existing and future proposed rail links requires a reduced maintenance and repair regime for the embankment subgrade, due to restricted access to the subgrade soils for remediation caused by cyclic deformation. It is, therefore, important to study the deformation behaviour of soft cohesive subsoils induced as a result of long term cyclic loading. In this study, a series of oedometer tests and cyclic triaxial tests (10,000 cycles) have been undertaken to investigate the undrained deformation behaviour of soft kaolin. X-ray Computer Tomography (CT) scanning of the samples has been performed to determine the change in porosity and soil structure density from the sample microstructure as a result of the laboratory testing regime undertaken. Combined with the examination of excess pore pressures and strains obtained from the cyclic triaxial tests, the results are compared with an existing analytical solution for long term settlement considering repeated low amplitude loading. Modifications to the analytical solution are presented based on the laboratory analysis that shows good agreement with further test data.

Keywords: creep, cyclic loading, deformation, long term settlement, train loading

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Authors: Sandeep Kumar, Mahesh Kumar Jat, Rajib Sarkar

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Soil reinforced with randomly distributed fibers is an attractive means to improve the performance of soil in a cost effective manner. Static and dynamic characterization of fiber reinforced soil have become important to evaluate adequate performance for all classes of geotechnical engineering problems. Present study investigates the behaviour of fiber reinforced cohesionless soil through numerical simulation of triaxial specimen. The numerical model has been validated with the existing literature of laboratory triaxial compression testing. A parametric study has been done to find out optimum fiber content for shear resistance. Cyclic triaxial testing has been simulated and the stress-strain response of fiber-reinforced sand has been examined considering different combination of fiber contents. Shear modulus values and damping values of fiber-reinforced sand are evaluated. It has been observed from results that for 1.0 percent fiber content shear modulus increased 2.28 times and damping ratio decreased 4.6 times. The influence of amplitude of cyclic strain, confining pressure and frequency of loading on the dynamic properties of fiber reinforced sand has been investigated and presented.

Keywords: damping, fiber reinforced soil, numerical modelling, shear modulus

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Authors: Priyanka Devi, Mohammad Muzzaffar Khan, G. Kalyan Kumar

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Liquefaction of saturated soils due to dynamic loading is an important and interesting area in the field of geotechnical earthquake engineering. When the soil liquefies, the structures built on it develops uneven settlements thereby producing cracks in the structure and weakening the foundation. The 1964 Alaskan Good Friday earthquake, the 1989 San Francisco earthquake and 2011 Tōhoku earthquake are some of the examples of liquefaction occurred due to an earthquake. To mitigate the effect of liquefaction, several methods such use of stone columns, increasing the vertical stress, compaction and removal of liquefiable soil are practiced. Grouting is one of those methods used to increase the strength of the foundation and develop resistance to liquefaction of soil without affecting the superstructure. In the present study, an attempt has been made to investigate the undrained cyclic behavior of locally available soil, stabilized by cement to mitigate the seismically induced soil liquefaction. The specimens of 75mm diameter and 150mm height were reconstituted in the laboratory using water sedimentation technique. A series of strain-controlled cyclic triaxial tests were performed on saturated soil samples followed by consolidation. The effects of amplitude, confining pressure and relative density on the dynamic behavior of sand was studied for soil samples with varying cement content. The results obtained from the present study on loose specimens and medium dense specimens indicate that (i) the higher the relative density, the more will be the liquefaction resistance, (ii) with increase of effective confining pressure, a decrease in developing of excess pore water pressure during cyclic loading was observed and (iii) sand specimens treated with cement showed reduced excess pore pressures and increased liquefaction resistance suggesting it as one of the mitigation methods.

Keywords: cyclic triaxial test, liquefaction, soil-cement stabilization, pore pressure ratio

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Authors: Z. Adnan, M. M. Habib

Abstract:

The laboratory tests for measuring the effects of small strain to the shear strength and maximum stiffness development of post-cyclic degradation of hemic peat are reviewed in this paper. A series of laboratory testing has been conducted to fulfil the objective of this research to study the post-cyclic behaviour of peat soil and focuses on the small strain characteristics. For this purpose, a number of strain-controlled static, cyclic and post-cyclic triaxial tests were carried out in undrained condition on hemic peat soil. The shear strength and maximum stiffness of hemic peat are evaluated immediately after post-cyclic monotonic testing. There are two soil samples taken from West Johor and East Malaysia peat soil. Based on these laboratories and field testing data, it was found that the shear strength and maximum stiffness of peat soil decreased in post-cyclic monotonic loading than its initial shear strength and stiffness. In particular, degradation in shear strength and stiffness is more sensitive for peat soil due to fragile and uniform fibre structures. Shear strength of peat soil, τ_max = 12.53 kPa (Beaufort peat, BFpt) and 36.61 kPa (Parit Nipah peat, PNpt) decreased than its initial 58.46 kPa and 91.67 kPa. The maximum stiffness, G_max = 0.23 and 0.25 decreased markedly with post-cyclic, G_max = 0.04 and 0.09. Simple correlations between the G_max and the τ_max effects due to small strain, ε = 0.1, the G_max values for post-cyclic are relatively low compared to its initial G_max. As a consequence, the reported values and patterns of both the West Johor and East Malaysia peat soil are generally the same.

Keywords: post-cyclic, strain, maximum stiffness, shear strength

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Authors: M. Kamal Elbokl

Abstract:

The beneficial effects of reinforcing the subgrade soil in pavement system with randomly distributed polypropylene fibers were investigated. For this issue, two types of soils and one type of fiber were selected. Proctor, CBR and unconfined compression tests were conducted on unreinforced samples as well as reinforced ones at different concentrations and aspect ratio of fibers. OMC, CBR and modulus of elasticity were investigated and thereby, the optimum value of aspect ratio and fiber content were determined. The static and repeated triaxial tests were also conducted to study the behaviour of fiber reinforced soils under both static and repeated loading. The results indicated that CBR values of reinforced sand and clay were 3.1 and 4.2 times of their unreinforced values respectively. The modulus of elasticity of fiber reinforced soils has increased by 100% for silty sandy soil and 60.20% for silty clay soil due to fiber reinforcement. The reinforced soils exhibited higher failure stresses in the static triaxial tests than the unreinforced ones due to the apparent bond developed between soil particle and the fiber. Fiber reinforcement of subgrade soils can play an important role in control the rut formation in the pavement system.

Keywords: polypropylene fibers, CBR, static triaxial, cyclic triaxial, resilient strain, permanent strain

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Authors: Poonam Yadav, Dong Bok Lee

Abstract:

Isothermal oxidation at 800°C for 50h and Cyclic oxidation at 600°C and 800°C for 40h of Pure Ti and Ti64 were performed in a muffle furnace. In Cyclic oxidation, massive scale spallation occurred, and the oxide scale cracks and peels off were observed at high temperature, it represents oxide scale that formed during cyclic oxidation was spalled out owing to stresses due to thermal shock generated during repetitive oxidation and subsequent cooling. The thickness of scale is larger in cyclic oxidation than the isothermal case. This is due to inward diffusion of oxygen through oxide scales and/or pores and cracks in cyclic oxidation.

Keywords: cyclic, diffusion, isothermal, cyclic

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Authors: M. Nghizaderokni, A. Janalizadechobbasty, M. Azizi, M. Naghizaderokni

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The liquefaction resistance of soils can be evaluated using laboratory tests such as cyclic simple shear, cyclic triaxial, cyclic tensional shear, and field methods such as Standard Penetration Test (SPT), Cone Penetration Test (CPT), and Shear Wave Velocity (Vs). This paper outlines a great correlation between shear wave velocity and standard penetration resistance of granular soils was obtained. Using Seeds standard penetration test (SPT) based soil liquefaction charts, new charts of soil liquefaction evaluation based on shear wave velocity data were developed for various magnitude earthquakes.

Keywords: soil, liquefaction, shear wave velocity, standard penetration resistance

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Authors: Jing Li, Xiuli Li

Abstract:

This paper studies a special class of linear codes, called skew cyclic codes, over the ring R= F_q+uF_q+…+u^k-1F_q, where q is a prime power. A Gray map ɸ from R to F_q and a Gray map ɸ' from Rⁿ to Fⁿ_q are defined, as well as an automorphism Θ over R. It is proved that the images of skew cyclic codes over R under map ɸ' and Θ are cyclic codes over F_q, and they still keep the dual relation.

Keywords: skew cyclic code, gray map, automorphism, cyclic code

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Authors: Eusebio Jr. Lina, Ederlina Nocon

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Cyclic codes are a fundamental subclass of linear codes that enjoy a very interesting algebraic structure. The class of skew cyclic codes (or θ-cyclic codes) is a generalization of the notion of cyclic codes. This a very large class of linear codes which can be used to systematically search for codes with good properties. A linear code with complementary dual (LCD code) is a linear code C satisfying C ∩ C^⊥ = {0}. This subclass of linear codes provides an optimum linear coding solution for a two-user binary adder channel and plays an important role in countermeasures to passive and active side-channel analyses on embedded cryptosystems. This paper aims to identify LCD codes from the class of skew cyclic codes. Let F_q be a finite field of order q, and θ be an automorphism of F_q. Some conditions for a skew cyclic code to be LCD were given. To this end, the properties of a noncommutative skew polynomial ring F_q[x, θ] of automorphism type were revisited, and the algebraic structure of skew cyclic code using its skew polynomial representation was examined. Using the result that skew cyclic codes are left ideals of the ring F_q[x, θ]/〈x^n-1〉, a characterization of a skew cyclic LCD code of length n was derived. A necessary condition for a skew cyclic code to be LCD was also given.

Keywords: LCD cyclic codes, skew cyclic LCD codes, skew cyclic complementary dual codes, theta-cyclic codes with complementary duals

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Authors: Monalisha Nayak, T. G. Sitharam

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Liquefaction is a major threat for sites consists of or on sandy soil. But this present study concentrates on the behavior of fine soil under cyclic loading. This paper presents the study of liquefaction susceptibility of marine silty clay to clayey silt for an offshore site near western Yemen. The submerged and loose sediment condition of marine soil of an offshore site can favour liquefaction during earthquakes. In this regard, the liquefaction susceptibility of the site was carried out based on both field test results and laboratory test results. From field test results of seismic cone penetration test (SCPT), liquefaction susceptibility was assessed considering normalized cone tip resistance, and normalized friction ratio and results give an idea regarding both cyclic mobility and flow liquefaction. Laboratory cyclic triaxial tests were also conducted on saturated undisturbed and remoulded sample to study the effect of cyclic loading on strength and strain characteristics. Liquefaction susceptibility of the marine soft soil was also carried out based on index properties like grain size distribution, natural moisture content and liquid limit of soil.

Keywords: index properties, liquefaction, marine soil, seismic cone penetration test (SCPT)

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Authors: Deepshikha Verma, V. N. Rajasekharan Pillai

Abstract:

The present study reports the synthesis of cyclic PNC-28 peptides with solid-phase peptide synthesis method. In the first step, we synthesize the linear PNC-28 Peptide and in the second step, we cyclize (N-to-C or head-to-tail cyclization) the linear PNC-28 peptide. The molecular formula of cyclic PNC-28 peptide is C64H88N12O16 and its m/z mass is ≈1233.64. Elemental analysis of cyclic PNC-28 is C, 59.99; H, 6.92; N, 13.12; O, 19.98. The characterization of LC-MS, CD, FT-IR, and 1HNMR has been done to confirm the successful synthesis and cyclization of linear PNC-28 peptides.

Keywords: CD, FTIR, 1HNMR, cyclic peptide

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Authors: Nadine Ali Hassan, Ngoc Son Nguyen, Didier Marot, Fateh Bendahmane

Abstract:

This paper aims at presenting a study of the effect of scalping methods on the mechanical properties of coarse soils by resorting to numerical simulations based on the discrete element method (DEM) and experimental triaxial tests. Two reconstitution methods are used, designated as scalping method and substitution method. Triaxial compression tests are first simulated on a granular materials with a grap graded particle size distribution by using the DEM. We study the effect of these reconstitution methods on the stress-strain behavior of coarse soils with different fine contents and with different ways to control the densities of the scalped and substituted materials. Experimental triaxial tests are performed on original mixtures of sands and gravels with different fine contents and on their corresponding scalped and substituted samples. Numerical results are qualitatively compared to experimental ones. Agreements and discrepancies between these results are also discussed.

Keywords: coarse soils, mechanical behavior, scalping, replacement, triaxial devices

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Authors: L. Pavithra, R. Sharmila, Shivani Sridhar

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Columns severe structural damage needs proportioning a significant portion of earthquake energy can be dissipated yielding in the beams. Presence of axial load along with cyclic loading has a significant influence on column. The objective of this paper is to present the analytical results of columns subjected to biaxial cyclic loading.

Keywords: RC column, Seismic behaviour, cyclic behaviour, biaxial testing, ductile behaviour

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Authors: Seyed Abolhasan Naeini, Hamidreza Rahmani

Abstract:

Laboratory consolidated undrained triaxial (CU) tests were carried out to study the strength behavior of silty soil reinforced with randomly plastic waste bottle chips. Specimens mixed with plastic waste chips in triaxial compression tests with 0.25, 0.50, 0.75, 1.0, and 1.25% by dry weight of soil and tree different length including 4, 8, and 12 mm. In all of the samples, the width and thickness of plastic chips were kept constant. According to the results, the amount and size of plastic waste bottle chips played an important role in the increasing of the strength parameters of reinforced silt compared to the pure soil. Because of good results, the suggested method of soil improvement can be used in many engineering problems such as increasing the bearing capacity and settlement reduction in foundations.

Keywords: reinforcement, silt, soil improvement, triaxial test, waste bottle chips

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Authors: Shaymaa Kennedy, Sam Clark, Paul Shaply

Abstract:

With the upcoming construction of high-speed rail HS2 in the UK, a number of issues surrounding the construction technology and track design need to be answered. In this paper performance of subsoil subjected to dynamic loads were studied. The material of study is Mudrock backfill, a weak prevalent rock which response under indicative loading of high-speed rail line is unknown. This paper aims to investigate the use of different track types and the influence they will have on the underlying soil, in order to evaluate the behaviour of it. Ballstless track is a well-established concept in Europe, and the investigation the benefit of the form of construction due to its known savings in maintenance costs. Physical test using a triaxial cyclic loading machine was conducted to assess the expected mechanical behaviour of mudrock under a range of dynamic loads which could be generated beneath different track constructions. Some further parameters are required to frame the problem including determining the stress change with depth and cyclic response are vital to determine the residual plastic strain which is a major concern. In addition, Stress level is discussed in this paper, which are applied to recreate conditions of soil in the laboratory. Results indicate that stress levels are highly influential on the performance of soil at shallower depth and become insignificant with increasing depth.

Keywords: stress level, dynamic load, residual plastic strain, high speed railway

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Authors: Najibullah Arsalan, Masaru Akaishi, Motohiro Sugiyama

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When constructing a structure on soft rock, adequate research and study are required concerning the shear behavior in the over-consolidation region because soft rock is considered to be in a heavily over-consolidated state. In many of the existing studies concerning the strength of soft rock, triaxial compression tests were conducted using isotropically consolidated samples. In this study, the strength of diatomaceous soft rock anisotropically consolidated under a designated consolidation pressure is examined in undrained triaxial compression tests, and studies are made of the peak and residual strengths of the sample in the over-consolidated state in the initial yield surface and the anisotropic yield surface.

Keywords: diatomaceouse mudstone, shear strength, yield surface, triaxial compression test

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Authors: Negadi Kheira, Arab Ahmed, Kamal Elbokl Mohamed, Setti Fatima

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In order to evaluate influences of roots on soil shear strength, monotonic drained and undrained triaxial laboratory tests were carried out on reconstituted specimens at various confining pressure (σc’=50, 100, 200, 300, 400 kPa) and a constant relative density (Dr = 50%). Reinforcement of soil by fibrous roots is crucial for preventing soil erosion and degradation. Therefore, we investigated soil reinforcement by roots of acacia planted in the area of Chlef where shallow landslides and slope instability are frequent. These roots were distributed in soil in two forms: vertically and horizontally. The monotonic test results showed that roots have more impacts on the soil shear strength than the friction angle, and the presence of roots in soil substantially increased the soil shear strength. Also, the results showed that the contribution of roots on the shear strength mobilized increases with increase in the confining pressure.

Keywords: soil, monotonic, triaxial test, root fiber, undrained

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Authors: T. Pathinathan, M. Peter

Abstract:

Fuzzy graphs incorporate concepts from graph theory with fuzzy principles. In this paper, we make a study on the properties of fuzzy graphs which are non-cyclic and are of two-dimensional in structure. In particular, this paper presents 2D structure or the structure of double layer for a non-cyclic fuzzy graph whose underlying crisp graph is non-cyclic. In any graph structure, introducing 2D structure may lead to an inherent cycle. We propose relevant conditions for 2D structured non-cyclic fuzzy graphs. These conditions are extended even to fuzzy graphs of the 3D structure. General theoretical properties that are studied for any fuzzy graph are verified to 2D structured or double layered fuzzy graphs. Concepts like Order, Degree, Strong and Size for a fuzzy graph are studied for 2D structured or double layered non-cyclic fuzzy graphs. Using different types of fuzzy graphs, the proposed concepts relating to 2D structured fuzzy graphs are verified.

Keywords: double layered fuzzy graph, double layered non–cyclic fuzzy graph, order, degree and size

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Authors: Ahmed Hosny Abdel-Rahman, Mohamed Abdel-Moneim

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Reinforced earth structures are generally subjected to cyclic loading generated from earthquakes. This paper presents a summary of the results and analyses of a testing program carried out in a large-scale multi-function geosynthetic testing apparatus that accommodates soil samples up to 1.0 m3. This apparatus performs different shear and pullout tests under both static and cyclic loading. The testing program was carried out to investigate the controlling factors affecting soil/geogrid interaction under cyclic loading. The extensibility of the geogrids, the applied normal stresses, the characteristics of the cyclic loading (frequency, and amplitude), and initial static load within the geogrid sheet were considered in the testing program. Based on the findings of the testing program, the effect of these parameters on the pullout resistance of geogrids, as well as the displacement mobility under cyclic loading were evaluated. Conclusions and recommendations for the design of reinforced earth walls under cyclic loading are presented.

Keywords: geogrid, soil, interface, cyclic loading, pullout, large scale testing

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Authors: Ying Yi Wu

Abstract:

The study of finite groups is a central topic in algebraic structures, and one of the most fundamental questions in this field is the classification of finite groups up to isomorphism. In this paper, we investigate the cyclic property of groups of prime order, which is a crucial result in the classification of finite abelian groups. We prove the following statement: If p is a prime, then every group G of order p is cyclic. Our proof utilizes the properties of group actions and the class equation, which provide a powerful tool for studying the structure of finite groups. In particular, we first show that any non-identity element of G generates a cyclic subgroup of G. Then, we establish the existence of an element of order p, which implies that G is generated by a single element. Finally, we demonstrate that any two generators of G are conjugate, which shows that G is a cyclic group. Our result has significant implications in the classification of finite groups, as it implies that any group of prime order is isomorphic to the cyclic group of the same order. Moreover, it provides a useful tool for understanding the structure of more complicated finite groups, as any finite abelian group can be decomposed into a direct product of cyclic groups. Our proof technique can also be extended to other areas of group theory, such as the classification of finite p-groups, where p is a prime. Therefore, our work has implications beyond the specific result we prove and can contribute to further research in algebraic structures.

Keywords: group theory, finite groups, cyclic groups, prime order, classification.

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Authors: Ma Yuan, Zhang Mengxi, Akbar Javadi, Chen Longqing

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The structure of sand-filled embankment with cover layer is treated with tipping clay modified with lime on the outside of the packing, and the geotextile is placed between the stuffing and the clay. The packing is usually river sand, and the improved clay protects the sand core against rainwater erosion. The sand-filled embankment with cover layer has practical problems such as high filling embankment, construction restriction, and steep slope. The reinforcement can be applied to the sand-filled embankment with cover layer to solve the complicated problems such as irregular settlement caused by poor stability of the embankment. At present, the research on the sand-filled embankment with cover layer mainly focuses on the sand properties, construction technology, and slope stability, and there are few studies in the experimental field, the deformation characteristics and stability of reinforced sand-filled embankment need further study. In addition, experimental research is relatively rare when the cyclic load is considered in tests. A subgrade structure of geogrid-reinforced sand-filled embankment with cover layer was proposed. The mechanical characteristics, the deformation properties, reinforced behavior and the ultimate bearing capacity of the embankment structure under cyclic loading were studied. For this structure, the geogrids in the sand and the tipping soil are through the geotextile which is arranged in sections continuously so that the geogrids can cross horizontally. Then, the Unsaturated/saturated Soil Triaxial Test System of Geotechnical Consulting and Testing Systems (GCTS), USA was modified to form the loading device of this test, and strain collector was used to measuring deformation and earth pressure of the embankment. A series of cyclic loading model tests were conducted on the geogrid-reinforced sand-filled embankment with a cover layer under a different number of reinforcement layers, the length of reinforcement and thickness of the cover layer. The settlement of the embankment, the normal cumulative deformation of the slope and the earth pressure were studied under different conditions. Besides cyclic loading model tests, model experiments of embankment subjected cyclic-static loading was carried out to analyze ultimate bearing capacity with different loading. The experiment results showed that the vertical cumulative settlement under long-term cyclic loading increases with the decrease of the number of reinforcement layers, length of the reinforcement arrangement and thickness of the tipping soil. Meanwhile, these three factors also have an influence on the decrease of the normal deformation of the embankment slope. The earth pressure around the loading point is significantly affected by putting geogrid in a model embankment. After cyclic loading, the decline of ultimate bearing capacity of the reinforced embankment can be effectively reduced, which is contrary to the unreinforced embankment.

Keywords: cyclic load; geogrid; reinforcement behavior; cumulative deformation; earth pressure

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Authors: Rabia Chaudhry, Andrew Dawson

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Identification of steady/critical state of coarse granular soil is challenging at conventional pressures. This study examines the drained and undrained triaxial tests for large strains on loose to dense, uniformly graded, Leighton Buzzard Fraction A sand. The triaxial tests are conducted under controlled test conditions. The comparison of soil behavior on shear strength characteristics at different effective stresses has been studied at the medium to large strains levels and the uniqueness of the critical state was discussed. The test results showed that there were two steady/critical state lines for drained and undrained conditions at confining pressures less than 1000 kPa. A critical state friction angle is not constant and the overall scatter in the steady/critical state line for the tested sand is ±0.01 in terms of void ratio at stress levels less than 1000 kPa.

Keywords: critical state, stress strain behavior, fabric/structure, triaxial tests

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Authors: Khyati Sharma, A. Satyanarayana Reddy

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The topic of how many subgroups exist within a certain finite group naturally arises in the study of finite groups. Over the years, different researchers have investigated this issue from a variety of angles. The significant contributions of the key mathematicians over the time have been summarized in this article. To this end, we classify finite groups into three categories viz. (a) Groups for which the number of subgroups is less than |G|, (b) equals to |G|, and finally, (c) greater than |G|. Because every element of a finite group generates a cyclic subgroup, counting cyclic subgroups is the most important task in this endeavor. A brief survey on the number of cyclic subgroups of finite groups is also conducted by us. Furthermore, we also covered certain arithmetic relations between the order of a finite group |G| and the number of its distinct cyclic subgroups |C(G)|. In order to provide pertinent context and possibly reveal new novel areas of potential research within the field of research on finite groups, we finally pose and solicit a few open questions.

Keywords: abstract algebra, cyclic subgroup, finite group, subgroup

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