A novel relationship between elastic modulus and void ratio associated with principal stress for coral calcareous sand

Elastic moduli,e.g.shear modulus G and bulk modulus K,are important parameters of geotechnical materials,which are not only the indices for the evaluation of the deformation ability of soils but also the important basic parameters for the development of the constitutive models of geotechnical materials.In this study,a series of triaxial loading-unloading-reloading shear tests and isotropic loading-unloadingreloading tests are conducted to study several typical mechanical properties of coral calcareous sand(CCS),and the void ratio evolution during loading,unloading and reloading.The test results show that the stress-strain curves during multiple unloading processes are almost parallel,and their slopes are much greater than the deformation modulus at the initial stage of loading.The relationship between the confining pressure and the volumetric strain can be defined approximately by a hyperbolic equation under the condition of monotonic loading of confining pressure.Under the condition of confining pressure unloading,the evolution of void ratio is linear in the e-lnp0 plane,and these lines are a series of almost parallel lines if there are multiple processes of unloading.Based on the experimental results,it is found that the modified Hardin formulae for the elastic modulus estimation have a significant deviation from the tested values for CCS.Based on the experimental results,it is proposed that the elastic modulus of soils should be determined by the intersection line of two spatial surfaces in the G/K-e-p’/pa space(pa:atmosphere pressure).“Ye formulation”is further proposed for the estimation of the elastic modulus of CCS.This new estimation formulation for soil elastic modulus would provide a new method to accurately describe the mechanical behavior of granular soils.

Soil disturbance evaluation of soft clay based on stress-normalized smallstrain stiffness

Soil disturbance includes the change of stress state and the damage of soil structure.The field testing indices reflect the combined effect of both changes and it is difficult to identify the soil structure disturbance directly from these indices.In the present study,the small-strain shear modulus is used to characterize soil structure disturbance by normalizing the effective stress and void ratio based on Hardin equation.The procedure for evaluating soil sampling disturbance in the field and the further disturbance during the subsequent consolidation process in laboratory test is proposed,and then validated by a case study of soft clay ground.Downhole seismic testing in the field,portable piezoelectric bender elements for the drilled sample and bender elements in triaxial apparatus for the consolidated sample were used to monitor the shear wave velocity of the soil from intact to disturbed and even remolded states.It is found that soil sampling disturbance degree by conventional thin-wall sampler is about 30%according to the proposed procedure,which is slightly higher than that from the modified volume compression method proposed by Hong and Onitsuka(1998).And the additional soil disturbance induced by consolidation in laboratory could reach about 50%when the consolidation pressure is far beyond the structural yield stress,and it follows the plastic volumetric strain quite well.

Dynamic shear modulus of undisturbed soil under different consolidation ratios and its effects on surface ground motion

The dynamic shear modulus for three types of undisturbed soil under different consolidation ratios is presented by using the resonant column test method. Its effects on surface ground motion is illustrated by calculation. The test results indicate that the power function is a suitable form for describing the relationship between the ratio of the maximum dynamic shear modulus due to anisotropic and isotropic consolidations and the increment of the consolidation ratio. When compared to sand, the increment of the maximum dynamic shear modulus for undisturbed soil due to anisotropic consolidation is much larger. Using a one-dimensional equivalent linearization method, the earthquake influence factor and the characteristic period of the surface acceleration are calculated for two soil layers subjected to several typical earthquake waves. The calculated results show that the difference in nonlinear properties due to different consolidation ratios is generally not very notable, but the degree of its influence on the surface acceleration spectrum is remarkable for the occurrence of strong earthquakes. When compared to isotropic consolidation, the consideration of actual anisotropic consolidation causes the characteristic period to decrease and the earthquake influence factor to increase.

Dynamic shear modulus and damping ratio characteristics of undisturbed marine soils in the Bohai Sea,China

This paper presents results from a series of stress-controlled undrained cyclic triaxial tests on the undisturbed marine silty clay,silt,and fine sand soils obtained from the Bohai Sea,China.Emphasis is placed on the major factors for predominating the dynamic shear modulus(G)and damping ratio(λ)in the shear strain amplitude(γ_(a))from 10^(-5) to 10^(-2),involving depth,sedimentary facies types,and water content of marine soils.The empirical equations of the small-strain shear modulus(G_(max))and damping ratio(λ_(min))using a single-variable of depth H are established for the three marine soils.A remarkable finding is that the curves of shear modulus reduction(G/G_(max))and the damping ratio(λ)with increasing γ_(a) of the three marine soils can be simply determined through a set of explicit expressions with the two variables of depth H and water content W.This finding is validated by independent experimental data from the literature.At the similar depths,the G value of the marine soils of terrestrial facies is the largest,followed b_(y) the neritic facies,and the G value of the marine soils of abyssal facies is the smallest.The sedimentary facies types of the marine soils have slight effect on theλvalue.Another significant finding is that the shear modulus reduction curves plotted against the γ_(a) of the three marine soils at the similar depths are significantly below those of the corresponding terrigenous soils,while the damping curves plotted against γ_(a) are just the opposite.The results presented in this paper serve as a worthful reference for the evaluation of seabed seismic site effects in the Bohai Sea due to lack of experimental data.

Probabilistic characterization of cyclic shear modulus reduction for normally to moderately over-consolidated clays

Evaluation of the cyclic shear modulus of soils is a crucial but challenging task for many geotechnical earthquake engineering and soil dynamic issues. Improper determination of this property unnecessarily drives up design and maintenance costs or even leads to the construction of unsafe structures. Due to the complexities involved in the direct measurement, empirical curves for estimating the cyclic shear modulus have been commonly adopted in practice for simplicity and economical considerations. However, a systematic and robust approach for formulating a reliable model and empirical curve for cyclic shear modulus prediction for clayey soils is still lacking. In this study, the Bayesian model class selection approach is utilized to identify the most significant soil parameters affecting the normalized cyclic shear modulus and a reliable predictive model for normally to moderately over-consolidated clays is proposed. Results show that the predictability and reliability of the proposed model out performs the well-known empirical models. Finally, a new design chart is established for practical usage.

Shear modulus of shock-compressed LY12 aluminium up to melting point

Asymmetric plate impact experiments are conducted on LY12 aluminium alloy in a pressure range of 85-131 GPa. The longitudinal sound speeds axe obtained from the time-resolved particle speed profiles of the specimen measured with Velocity Interferometer System for Any Reflector （VISAR） technique, and they are shown to be good agreement with our previously reported data of this alloy in a pressure range of 20-70 GPa, and also with those of 2024 aluminium reported by McQueen. Using all of the longitudinal speeds and the corresponding bulk speeds calculated from the Gruneisen equation of state （EOS）, shear moduli of LY12 aluminium alloy are obtained. A comparison of the shear moduli in the solid phase region with those estimated from the Steinberg model demonstrate that the latter are systematically lower than the measurements. By re-analysing the pressure effect on the shear modulus, a modified equation is proposed, in which the pressure term of P/η^1/3 in the Steinberg model is replaced by a linear term. Good agreement between experiments and the modified equation is obtained, which implies that the shear modulus of LY12 aluminium varies linearly both with pressure and with temperature throughout the whole solid phase region. On the other hand, shear modulus of aluminium in a solid-liquid mixed phrase region decreases gradually and smoothly, a feature that is very different from the drastic dropping at the melting point under static conditions.

Analytical Solution for Wave-Induced Response of Seabed with Variable Shear Modulus

A plane strain analysis based on the generalized Biot＇s equation is utilized to investigate the wave-induced response of a poro-elastic seabed with variable shear modulus. By employing integral transform and Frobenins methods, the transient and steady solutions for the wave-inducod pore water pressure, effective stresses and displacements are analytically derived in detail. Verification is available through the reduction to the simple case of homogeneous seabed. The numerical results indicate that the inclusion of variable shear modulus significantly affects the wave-induced seabed response.

Effects of fabric anisotropy on elastic shear modulus of granular soils

The fabric anisotropy of a granular soil deposit can strongly infl uence its engineering properties and behavior. This paper presents the results of a novel experimental study designed to examine the effects of fabric anisotropy on smallstrain stiffness and its evolution with loading on the elastic shear modulus of granular materials under a K0 condition. Two primary categories of fabric anisotropy, i.e., deposition-induced and particle shape-induced, are investigated. Toyoura sand deposits with relative densities of 40% and 80% were prepared using deposition angles oriented at 0o and 90o. Piezoelectric transducers were used to obtain the elastic shear modulus in the vertical and horizontal directions(Gvh and Ghh). The measurements indicate distinct differences in the values of G with respect to the different deposition angles. Particle shapeinduced fabric anisotropy was examined using four selected sands. It was concluded that sphericity is a controlling factor dominating the small-strain stiffness of granular materials. The degree of fabric anisotropy proves to be a good indicatorin the characterization of stress-induced fabric evolution during loading and unloading stress cycles. The experimental data were used to calibrate an existing micromechanical model, which was able to represent the behavior of the granular material and the degree of fabric anisotropy reasonably well.

Thermal effects and evolution of the defect concentration based on shear modulus relaxation data in a Zr-based metallic glass

A relationship between thermal effects and relaxation of the high-frequency shear modulus upon heat treatment of bulk Zr48(Cu5/6Ag1/6)44Al8 metallic glass is found.This relationship is attributed to the relaxation of a interstitial-type defect system frozen-in from the melt upon glass production.Calorimetric data show that thermal effects occurring on heating include heat release below the glass transition temperature,heat absorption above it and heat release caused by crystallization.The equation derived within the Interstitialcy theory can be used to calculate the shear modulus relaxation using the calorimetric data.The obtained results are used to trace the defect concentration as functions of temperature and thermal prehistory.

A Modified approach for calculating dynamic shear modulus of stiff specimens by resonant column tests

An error analysis of the dynamic shear modulus of stiff specimens from tests performed by a new resonant column device developed by the Institute of Engineering Mechanics, China was conducted. A modified approach for calculating the dynamic shear modulus of the stiff specimens is presented. The error formula of the tests was deduced and parameters that impact the accuracy of the test were identified. Using six steel specimens with known standard stiffness as a base, a revised dynamic shear modulus calculation for stiff specimens was formulated by comparing three of the models. The maximum error between the test results and the calculated results shown by curves from both the free-vibration and the resonant-vibration tests is less than 6%. The free-vibration and resonant-vibration tests for three types of stiff samples with a known modulus indicate that the maximum deviation between the actual and the tested value using the modified approach were less than 10%. As a result, the modified approach presented here is shown to be reliable and the new device can be used for testing dynamic shear modulus of any stiff materials at low shear strain levels

High-pressure Raman study of osmium and rhenium up to 200 GPa and pressure dependent elastic shear modulus C_(44)

High-pressure Raman scattering from hexagonal close-packed(HCP) metals Os and Re have been extended up to 200 GPa, and the pressure-dependent shear modulus C_(44)has been deduced from the Raman-active mode E_(28), which is generated from the adjacent vibration of atoms in hexagonal planes, providing the valuable information about the elastic properties for HCP metals under high pressure. Combined with the available data of HCP metals from previous works,a further study indicates that the C_(44)/C_(44)ratio would be close to a constant value, 0.01, with increasing atomic number of metals. The results obtained from high-pressure Raman scattering will allow us to probe the elastic anisotropy of the HCP metals at very high pressure.

Effect of consolidation ratios on maximum dynamic shear modulus of sands

The dynamic shear modulus (DSM) is the most basic soil parameter in earthquake or other dynamic loading conditions and can be obtained through testing in the field or in the laboratory. The effect of consolidation ratios on the maximum DSM for two types of sand is investigated by using resonant column tests. And, an increment formula to obtain the maximum DSM for cases of consolidation ratio κc>1 is presented. The results indicate that the maximum DSM rises rapidly when κc is near 1 and then slows down, which means that the power function of the consolidation ratio increment κc-1 can be used to describe the variation of the maximum DSM due to κc>1. The results also indicate that the increase in the maximum DSM due to κc>1 is significantly larger than that predicted by Hardin and Black's formula.

EFFECTS OF TEMPERING TEMPERATURE AND TIME ON SHEAR MODULUS OF Fe-Mn BASED ALLOYS

Effects of the tempering temperature and time on the shear modulus of Fe-Mn based alloys have been studied.The results show that(ΔG/G)-Tcurves of tempered alloys containing Cr and Ti have two extreme values—maximum and minimum,and that the curves of tem- pered alloys containing Cr,Ni,W and C only have a maximum value.This is the reason that Ni,W and C decrease the transformation point T_N of the antiferromagnetism.The ΔG_λ ef- feet increases gradually with the rise of tempering temperature or with the increase of tem- pering time.

Prediction of a superhard material of ReN_4 with a high shear modulus

Using first-principles calculations, this paper systematically investigates the structural, elastic, and electronic properties of ReN4. The calculated positive eigenvalues of the elastic constant matrix show that the orthorhombic Pbca structure of ReN4 is elastically stable. The calculated band structure indicates that ReN4 is metallic. Compared with the synthesized superhard material WB4, it finds that ReN4 exhibits larger bulk and shear moduli as well as a smaller Poisson＇s ratio. In addition, the elastic constant c44 of ReN4 is larger than all the known 5d transition metal nitrides and borides. This combination of properties makes it an ideal candidate for a superhard material.

A Novel Linear Relationship for Calculating Dynamic Shear Modulus of Geomaterials

The dynamic shear modulus G of soil was determined using a dynamic triaxial test system（DTTS） together with a fitting method.First,a novel linear relationship between G and damping ratio λ was proposed,which was used to select the appropriate G.Then,a hyperbolic model was constructed using the optimized parameters a and b representing the intercept and slope,respectively,from the linear regression of 1/G and dynamic shear strain γd.Finally,the differences between the tested and predicted results for G were analyzed for different soil types.The experimental results show that this linear relationship can overcome the shortcomings of the nonlinear relationship found in the large deformation stage and can predict λ in the hysteresis loop that is not closed case.In addition to Baoji loess,G was slightly larger（10%） than the experimental curve in the elasto-plastic stage;however,the experimental results show that the attenuation curve of G for Baoji loess is greater than the calculated value in the elasto-plastic stage.The test and analysis results will improve the knowledge of the dynamic properties of soils and also provide reliable values of G for further evaluation of seismic safety at engineering sites.

Size dependency and potential field influence on deriving mechanical properties of carbon nanotubes using molecular dynamics

A thorough understanding on the mechanical properties of carbon nanotube （CNT） is essential in extending the advanced applications of CNT based systems. However, conducting experiments to estimate mechanical properties at this scale is extremely challenging. Therefore, development of mechanistic models to estimate the mechanical properties of CNTs along with the integration of existing continuum mechanics concepts is critically important. This paper presents a comprehensive molecular dynamics simulation study on the size dependency and potential function influence of mechanical properties of CNT. Commonly used reactive bond order （REBO） and adaptive intermolecular reactive bond order （A1REBO） potential functions were considered in this regard. Young＇s modulus and shear modulus of CNTs are derived by integrating classical continuum mechanics concepts with molecular dynamics simulations. The results indicate that the potential function has a significant influence on the estimated mechanical properties of CNTs, and the influence of potential field is much higher when studying the torsional behaviour of CNTs than the tensile behaviour.

Skeletal muscle stiffness as measured by magnetic resonance elastography after chronic spinal cord injury:a cross-sectional pilot study

Skeletal muscle stiffness is altered after spinal cord injury(SCI).Assessing muscle stiffness is essential for rehabilitation and pharmaceutical interventions design after SCI.The study used magnetic resonance elastography to assess the changes in stiffness after chronic SCI compared to matched able-bodied controls and determine its association with muscle size,spasticity,and peak torque in persons with SCI.Previous studies examined the association between muscle stiffness and spasticity,however,we are unaware of other studies that examined the effects of muscle composition on stiffness after SCI.Ten participants(one female)with chronic SCI and eight(one female)matched able-bodied controls participated in this cross-sectional study.Magnetic resonance elastography was utilized to monitor stiffness derived from shear waves propagation.Modified Ashworth scale was used to evaluate spasticity scores in a blinded fashion.Peak isometric and isokinetic torques were measured using a biodex dynamometer.Stiffness values were non-significantly lower(12.5%;P=0.3)in the SCI group compared to able-bodied controls.Moreover,stiffness was positively related to vastus lateralis whole muscle cross-sectional area(CSA)(r2=0.64,P<0.005)and vastus lateralis absolute muscle CSA after accounting for intramuscular fat(r2=0.78,P<0.0007).Stiffness was also positively correlated to both isometric(r2=0.55-0.57,P<0.05)and isokinetic peak(r2=0.46-0.48,P<0.05)torques.Our results suggest that larger clinical trial is warranted to confirm the preliminary findings that muscle stiffness is altered after SCI compared to healthy controls.Stiffness appeared to be influenced by infiltration of intramuscular fat and modestly by the spasticity of the paralyzed muscles.The preliminary data indicated that the relationship between muscle stiffness and peak torque is not altered with changing the frequency of pulses or angular velocities.All study procedures were approved by the Institutional Review Board at the Hunter Holmes McGuire VA Medical Center,USA(IRB#:02314)on May 3,2017.

Interstitialcy theory of condensed matter states and its application to non-crystalline metallic materials

A comprehensive review of a novel promising framework for the understanding of non-crystalline metallic materials, i.e., interstitialcy theory of condensed matter states（ITCM）, is presented. The background of the ITCM and its basic results for equilibrium/supercooled liquids and glasses are given. It is emphasized that the ITCM provides a new consistent, clear, and testable approach, which uncovers the generic relationship between the properties of the maternal crystal,equilibrium/supercooled liquid and glass obtained by melt quenching.

Test on dynamic characteristics of subgrade of heavy-haul railway in cold regions

Dynamic characteristics of heavy-haul railway subgrade under vibratory loading in cold regions are investigated via low-temperature dynamie triaxial tests with multi-stage eyelic loading process. The relationship between dynamic shear stress and dynamic shear strain of frozen soil of subgrade under train loading and the influence of freezing temperatures on dynamic constitutive relation, dynamic shear modulus and damping ratio are observed in this study. Test results show that the dynamic constitutive relations of the frozen soils with different freezing temperatures comply with the hyperbolic model, in which model parameters a and b decrease with increasing freezing temperature. The dynamic shear modulus of the frozen soils decreases with increasing dynamic shear strains initially, followed by a relatively smooth attenuation tendency, whereas increases with decreasing freezing temperatures. The damping ratios decrease with decreasing freezing temperatures. Two linear functions are defined to express the linear relationships between dynamic shear modulus （damping ratio） and freezing temperature, respectively, in which corresponding linear coefficients are obtained through multiple regression analysis of test data.

Cyclic behavior of reinforced sand under principal stress rotation

Although the cyclic rotation of the principal stress direction is important,its effect on the deformation behavior and dynamic properties of the reinforced soil has not been reported to date.Tests carried out on large-scale hollow cylinder samples reveal that the cyclic rotation of the principal stress direction results in significant variations of strain components(ε,ε,εand γ) with periodic characteristics despite the deviatoric stress being constant during tests.This oscillation can be related to the corresponding variations in the stress components and the anisotropic fabric that rotate continuously along the principal stress direction.Sand under rotation appears to develop a plastic strain.Similar trends are observed for reinforced sand,but the shear interaction,the interlocking between particles and reinforcement layer,and the confinement result in significant reductions in the induced strains and associated irrecoverable plastic strains.Most of the strains occur in the first cycle,and as the number of cycles increases,the presence of strains becomes very small,which is almost insignificant.This indicates that the soil has reached anisotropic critical state(ACS),where a stable structure is formed after continuous orientation,realignment and rearrangement of the particles accompanied with increasing cyclic rotation.Rotation in the range of 60°-135° produces more induced strains even in the presence of the reinforcement,when compared with other ranges.This relates to the extension mode of the test in this range in which σ>σand to the relative approach between the mobilized plane and the weakest horizontal plane.Reinforcement results in an increase in shear modulus while it appears to have no effect on the damping ratio.Continuous cycles of rotation result in an increase in shear modulus and lower damping ratio due to the densification that causes a decrease in shear strain and less dissipation of energy.