• Title/Summary/Keyword: Elastic Shear Modulus

Search Result 298, Processing Time 0.022 seconds

Directional Variation of Apparent Elastic Constants and Associated Constraints on Elastic Constants in Transversely Isotropic Rocks (횡등방성 암석에서 겉보기 탄성정수의 방향성 변화와 탄성정수 제약조건)

  • Youn-Kyou Lee
    • Tunnel and Underground Space
    • /
    • v.33 no.3
    • /
    • pp.150-168
    • /
    • 2023
  • The anisotropic behavior of rocks is primarily attributed to the directional arrangement of rock-forming minerals and the distribution characteristics of microcracks. Notably, sedimentary and metamorphic rocks often exhibit distinct transverse isotropy in terms of their strength and deformation characteristics. Consequently, it is crucial to gain accurate insights into the deformation and failure characteristics of transversely isotropic rocks during rock mechanics design processes. The deformation of such rocks is described by five independent elastic constants, which are determined through laboratory testing. In this study, the characteristics of the directional variation of apparent elastic constants in transversely isotropic rocks were investigated using experimental data reported in the literature. To achieve this, the constitutive equation proposed by Mehrabadi & Cowin was introduced to calculate the apparent elastic constants more efficiently and systematically in a rotated Cartesian coordinate system. Four transversely isotropic rock types from the literature were selected, and the influence of changes in the orientation of the weak plane on the variations of the apparent elastic modulus, apparent shear modulus, and apparent Poisson's ratio was analyzed. Based on the investigation, a new constraint on the elastic constants has been proposed. If the proposed constraint is satisfied, the directional variation of the apparent elastic constants in transversely isotropic rocks aligns with intuitive predictions of their tendencies.

Measuring elastic modulus of bacterial biofilms in a liquid phase using atomic force microscopy

  • Kim, Yong-Min;Kwon, Tae-Hyuk;Kim, Seungchul
    • Geomechanics and Engineering
    • /
    • v.12 no.5
    • /
    • pp.863-870
    • /
    • 2017
  • With the increasing interest in using bacterial biofilms in geo-engineering practices, such as soil improvement, sealing leakage in earth structures, and hydraulic barrier installation, understanding of the contribution of bacterial biofilm formation to mechanical and hydraulic behavior of soils is important. While mechanical properties of soft gel-like biofilms need to be identified for appropriate modeling and prediction of behaviors of biofilm-associated soils, elastic properties of biofilms remain poorly understood. Therefore, this study investigated the microscale Young's modulus of biofilms produced by Shewanella oneidensis MR-1 in a liquid phase. The indentation test was performed on a biofilm sample using the atomic force microscopy (AFM) with a spherical indentor, and the force-indentation responses were obtained during approach and retraction traces. Young's modulus of biofilms was estimated to be ~33-38 kPa from these force-indentation curves and Hertzian contact theory. It appears that the AFM indentation result captures the microscale local characteristics of biofilms and its stiffness is relatively large compared to the other methods, including rheometer and hydrodynamic shear tests, which reflect the average macro-scale behaviors. While modeling of mechanical behaviors of biofilm-associated soils requires the properties of each component, the obtained results provide information on the mechanical properties of biofilms that can be considered as cementing, gluing, or filling materials in soils.

Experimental and numerical investigation of uplift behavior of umbrella-shaped ground anchor

  • Zhu, Hong-Hu;Mei, Guo-Xiong;Xu, Min;Liu, Yi;Yin, Jian-Hua
    • Geomechanics and Engineering
    • /
    • v.7 no.2
    • /
    • pp.165-181
    • /
    • 2014
  • In the past decade, different types of underreamed ground anchors have been developed for substructures requiring uplift resistance. This article introduces a new type of umbrella-shaped anchor. The uplift behavior of this ground anchor in clay is studied through a series of laboratory and field uplift tests. The test results show that the umbrella-shaped anchor has higher uplift capacity than conventional anchors. The failure mode of the umbrella-shaped anchor in a large embedment depth can be characterized by an arc failure surface and the dimension of the plastic zone depends on the anchor diameter. The anchor diameter and embedment depth have significant influence on the uplift behavior. A finite element model is established to simulate the pullout of the ground anchor. A parametric study using this model is conducted to study the effects of the elastic modulus, cohesion, and friction angle of soils on the load-displacement relationship of the ground anchor. It is found that the larger the elastic modulus and the shear strength parameters, the higher the uplift capacity of the ground anchor. It is suggested that in engineering design, the soil with stiffer modulus and higher shear strength should be selected as the bearing stratum of this type of anchor.

Free vibration analysis of FG plates resting on the elastic foundation and based on the neutral surface concept using higher order shear deformation theory

  • Benferhat, Rabia;Daouadji, Tahar Hassaine;Mansour, Mohamed Said;Hadji, Lazreg
    • Earthquakes and Structures
    • /
    • v.10 no.5
    • /
    • pp.1033-1048
    • /
    • 2016
  • An analytical solution based on the neutral surface concept is developed to study the free vibration behavior of simply supported functionally graded plate reposed on the elastic foundation by taking into account the effect of transverse shear deformations. No transversal shear correction factors are needed because a correct representation of the transversal shearing strain obtained by using a new refined shear deformation theory. The foundation is described by the Winkler-Pasternak model. The Young's modulus of the plate is assumed to vary continuously through the thickness according to a power law formulation, and the Poisson ratio is held constant. The equation of motion for FG rectangular plates resting on elastic foundation is obtained through Hamilton's principle. Numerical examples are provided to show the effect of foundation stiffness parameters presented for thick to thin plates and for various values of the gradient index, aspect and side to thickness ratio. It was found that the proposed theory predicts the fundamental frequencies very well with the ones available in literature.

Probabilistic Behavior of Laminated Composite Plates with Random Material Properties (재료 물성치의 불확실성에 의한 복합적층판 변위의 확률적 거동)

  • Noh, Hyuk-Chun
    • Proceedings of the Computational Structural Engineering Institute Conference
    • /
    • 2008.04a
    • /
    • pp.27-32
    • /
    • 2008
  • The laminated composite materials have been applied to various mechanical structures due to their high performance to weight ratios. In this study, we suggest a stochastic finite element scheme for the probabilistic analysis of the composite laminated plates. The composite materials consist of two different materials which constitute the matrix and fiber. The material properties in the major and minor directions are determined depending on the volume fraction of these two materials. In this study, the elastic modulus and shear modulus are considered as random and the effect of these random properties on the behavior of the composite plate is investigated. We adopt the weighted integral scheme in the formulation, which has been recognized as the most accurate method in the statistical methodologies. For verification of the proposed scheme, Monte Carlo analysis is also performed for the comparison with the proposed scheme.

  • PDF

Rheology of flocculated kaolinite dispersions

  • McFarlane A.J.;Addai-Mensah J.;Bremmell K.
    • Korea-Australia Rheology Journal
    • /
    • v.17 no.4
    • /
    • pp.181-190
    • /
    • 2005
  • Rheological characterisation of flocculated kaolinite pulps has been undertaken to elucidate particle interactions underpinning the dewatering behaviour induced by flocculation with polyethylene oxide (PEO), anionic polyacrylamide (PAM A) and their blends. Shear yield stress $(\tau_y)$ analysis indicated that polymer mediated particle interactions were markedly amplified upon shear of PEG based pulps. In contrast, PAM A based pulps showed a significant decrease in yield values upon shear. Steady stress measurements analysed using a modified Ellis model indicated subtle differences between the respective linear viscoelastic plateaus of the pulps. Furthermore, modified shear thinning behaviour was evident in PEG based pulps. Estimation of elastic and viscous moduli (G', G') was made using dynamic stress analysis for comparison with values determined from vane measurements. Despite a noticeable difference in the magnitude of G' between the two methods, similar trends indicating sheared PEG-based pulps to be more elastic than PAM based pulps, were observed. Floc microstructural observations obtained in support of rheological properties indicate that PEG flocculant induces significantly more compact particle aggregation within the clay pulps under shear consistent with the yield stress data, in contrast to PAM A, or indeed unsheared PEG based pulps. Consequentially, sheared PEG based pulps show significantly improved dewatering behaviour. The implications of the results, potential benefits and drawbacks of flocculation with PEG and PAM A are discussed with respect to improvements in current dewatering processes used in the minerals industry.

Void Ratio Evaluation of Unsaturated Soils by Compressional and Shear Waves (압축파와 전단파를 이용한 불포화토의 간극비 산정)

  • Byun, Yong-Hoon;Cho, Se-Hyun;Yoon, Hyung-Koo;Choo, Yun-Wook;Kim, Dong-Su;Lee, Jong-Sub
    • Journal of the Korean Geotechnical Society
    • /
    • v.28 no.12
    • /
    • pp.41-51
    • /
    • 2012
  • Soils are commonly unsaturated in the near surface. The stiffness of soils is affected by the amount of air and water. The objective of this study is to evaluate the porosity of the unsaturated soils by using the elastic waves including compressional and shear waves. The elastic waves are measured at different degrees of saturation by controlling the matric suction. Thus, the unsaturated soils are characterized at different levels of the matric suction. Shear and compressional waves are measured by using the bender elements and the piezo disk elements, respectively. Both transducers are installed on the walls of the rectangular cell. The unsaturated soils are prepared by using uniform size sands and silts. Test results show that both compressional and shear wave velocities change according to the matric suction. The elastic modulus, the shear modulus, and the Poisson's ratio are estimated based on the measured elastic wave velocities. In addition, the void ratio of the unsaturated soils estimated using elastic wave velocities matches well with the volume based void ratio. This study demonstrates that the elastic waves can be effectively used for the characterization of unsaturated soils.

Deformational Characteristics of Cohesive Soils Using Resonant Column / Torsional Shear Testing Equipment (공진주/비틂 전단(RC/TS)시험기를 이용한 점성토의 변형특성)

  • 김동수
    • Geotechnical Engineering
    • /
    • v.11 no.1
    • /
    • pp.113-126
    • /
    • 1995
  • Both resonant column (RC) and torsional shear(TS) tests were performed at small to intermediate strain levels to investigate deformational characteristics of cohesive soils. The effects of variables such as strain amplitude, loading frequency, and number of loading cycles were studied. Plasticity index was found to be an important variables in evaluating these effects. Soils tested include undisturbed silts and clays and compacted subgrade soils. At small strains below the elastic threshold, shear modulus is independent of number of loading cycles and strain amplitude. Small strain material damping exists wi th ranges be tween 1.1% and 1.7% for 75 tests. The elastic threshold strain increases as confining pressure and plasticity index increases. Above the cyclic threshold strain, the modulus of cohesive soil decreases with increasing number of cycles while damping ratio is almost independent of number of load cycles. Moduli and damping ratios of cohesive soils obtanined by RC test are higher than those from 75 test because of the frequency effect. Shear modulus of cohesive soil increases linearly as a function of the logarithm of loading frequency.

  • PDF

Viscoelastic behavior on composite beam using nonlinear creep model

  • Jung, Sung-Yeop;Kim, Nam-Il;Shin, Dong Ku
    • Steel and Composite Structures
    • /
    • v.7 no.5
    • /
    • pp.355-376
    • /
    • 2007
  • The purpose of this study is to predict and investigate the time-dependent creep behavior of composite materials. For this, firstly the evaluation method for the modulus of elasticity of whole fiber and matrix is presented from the limited information on fiber volume fraction using the singular value decomposition method. Then, the effects of fiber volume fraction on modulus of elasticity of GFRP are verified. Also, as a creep model, the nonlinear curve fitting method based on the Marquardt algorithm is proposed. Using the existing Findley's power creep model and the proposed creep model, the effect of fiber volume fraction on the nonlinear creep behavior of composite materials is verified. Then, for the time-dependent analysis of a composite material subjected to uniaxial tension and simple shear loadings, a user-provided subroutine UMAT is developed to run within ABAQUS. Finally, the creep behavior of center loaded beam structure is investigated using the Hermitian beam elements with shear deformation effect and with time-dependent elastic and shear moduli.

Estimation of Elastic Modulus of Jointed Rock Mass under Tunnel Excavation Loading (터널 굴착하중 조건에서의 절리암반의 탄성계수 예측)

  • Son, Moorak;Lee, Won-Ki;Hwang, Young-Cheol
    • Journal of the Korean Geotechnical Society
    • /
    • v.30 no.7
    • /
    • pp.17-26
    • /
    • 2014
  • Tunneling-induced displacement in a jointed rock mass is an important factor to control tunnel stability and to secure a demanded space and construction quality. The magnitude of the inducible displacements is significantly affected by an elastic modulus and therefore, in a rock mass where a joint controls tunnel behavior, it is very important to estimate an elastic modulus of jointed rock mass reliably. Elastic modulus of jointed rock mass is affected by many factors such as rock type, joint condition, and loading condition. Nevertheless, most existing studies were focused on rough empirical relationships based on compressive loading conditions, which are different from tunnel excavation loading conditions, without a systematic approach of rock, joint, and loading conditions together. Therefore, this study considered rock and joint conditions systematically to estimate an elastic modulus of jointed rock mass under tunnel excavation loading. The controlled factors considered in this study are rock types and joint conditions (joint shear strength, joint inclination angle, number of joint sets, and joint spacing). Numerical parametric studies have been carried out with a consideration of different rock and joint conditions; the results have been compared with existing empirical relationships; and charts of elastic modulus change of different rock and joint conditions have been provided. The results are expected to have a great practical use for estimating the convergence induced by tunnel excavation in jointed rockmass.