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.

Numerical Analysis on Magnetic-induced Shear Modulus of Magnetorheological Elastomers Based on Multi-chain Model

Based on the magnetic interaction energy, using derivative of the magnetic energy density, a model is proposed to compute the magnetic-induced shear modulus of magnetorheological elastomers. Taking into account the influences of particles in the same chain and the particles in all adjacent chains, the traditional magnetic dipole model of the magnetorheological elastomers is modified. The influence of the ratio of the distance etween adjacent chains to the distance between adjacent particles in a chain on the magnetic induced shear odulus is quantitatively studied. When the ratio is large, the multi-chain model is compatible with the single chain model, but when the ratio is small, the difference of the two models is significant and can not be neglected. Making certain the size of the columns and the distance between adjacent columns, after constructing the computational model of BCT structures, the mechanical property of the magnetorheological elastomers composed of columnar structures is analyzed. Results show that, conventional point dipole model has overrated the magnetic-induced shear modulus of the magnetorheological elastomers. From the point of increasing the magnetic-induced shear modulus, when the particle volume fraction is small, the chain-like structure exhibits better result than the columnar structure, but when the particle volume fraction is large,the columnar structure will be better.

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.

Shear modulus and damping ratio of sand-granulated rubber mixtures

Recycled waste tires when mixed with soil can play an important role as lightweight materials in retaining walls and embankments, machine foundations and railroad track beds in seismic zones. Having high damping characteristic, rubbers can be used as either soil alternative or mixed with soil to reduce vibration when seismic loads are of great concern. Therefore, the objective of this work was to evaluate the dynamic properties of such mixtures prior to practical applications. To this reason, torsional resonant column and dynamic triaxial experiments were carried out and the effect of the important parameters like rubber content and ratio of mean grain size of rubber solids versus soil solids(D50,r/D50,s) on dynamic response of mixtures in a range of low to high shearing strain amplitude from about 4×10-4% to 2.7% were investigated. Considering engineering applications, specimens were prepared almost at the maximum dry density and optimum moisture content to model a mixture layer above the ground water table and in low precipitation region. The results show that tire inclusion significantly reduces the shear modulus and increases the damping ratio of the mixtures. Also decrease in D50,r/D50,s causes the mixture to exhibit more rubber-like behavior. Finally, normalized shear modulus versus shearing strain amplitude curve was proposed for engineering practice.

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.

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.

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.

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.

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.

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.

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.

Photoacoustic elastography based on laser-excited shear wave

Elastography can be used as a diagnostic method for quantitative characterization of tissue hardness information and thus,differential changes in pathophysiological states of tissues.In this study,we propose a new method for shear wave elastography(SWE)based on laser-excited shear wave,called photoacoustic shear wave elastography(PASWE),which combines photoacoustic(PA)technology with ultrafast ultrasound imaging.By using a focused laser to excite shear waves and ultrafast ultrasonic imaging for detection,high-frequency excitation of shear waves and noncontact elastic imaging can be realized.The laser can stimulate the tissue with the light absorption characteristic to produce the thermal expansion,thus producing the shear wave.The frequency of shear wave induced by laser is higher and the frequency band is wider.By tracking the propagation of shear wave,Young’s modulus of tissue is reconstructed in the whole shear wave propagation region to further evaluate the elastic information of tissue.The feasibility of the method is verified by experiments.Compared with the experimental results of supersonic shear imaging(SSI),it is proved that the method can be used for quantitative elastic imaging of the phantoms.In addition,compared with the SSI method,this method can realize the noncontact excitation of the shear wave,and the frequency of the shear wave excited by the laser is higher than that of the acoustic radiation force(ARF),so the spatial resolution is higher.Compared to the traditional PA elastic imaging method,this method can obtain a larger imaging depth under the premise of ensuring the imaging resolution,and it has potential application value in the clinical diagnosis of diseases requiring noncontact quantitative elasticity.

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.

Application of real-time shear wave elastography to Achilles tendon hardness evaluation in older adults

BACKGROUND Real-time shear wave elastography(SWE)is a non-invasive imaging technique used to measure tissue stiffness by generating and tracking shear waves in real time.This advanced ultrasound-based method provides quantitative information regarding tissue elasticity,offering valuable insights into the mechanical properties of biological tissues.However,the application of real-time SWE in the musculoskeletal system and sports medicine has not been extensively studied.AIM To explore the practical value of real-time SWE for assessing Achilles tendon hardness in older adults.METHODS A total of 60 participants were enrolled in the present study,and differences in the elastic moduli of the bilateral Achilles tendons were compared among the following categories:(1)Age:55-60,60-65,and 65-70-years-old;(2)Sex:Male and female;(3)Laterality:Left and right sides;(4)Tendon state:Relaxed and tense state;and(5)Tendon segment:Proximal,middle,and distal.RESULTS There were no significant differences in the elastic moduli of the bilateral Achilles tendons when comparing by age or sex(P>0.05).There were,however,significant differences when comparing by tendon side,state,or segment(P<0.05).CONCLUSION Real-time SWE plays a significant role compared to other examination methods in the evaluation of Achilles tendon hardness in older adults.

Method to analyze wrinkled membranes with zero shear modulus and equivalent stiffness

To solve the problems of divergence,low accuracy and project application of membrane wrinkling analysis,an analysis method of zero shear modulus and equivalent stiffness was proposed.This method is an improvement to the previous method (Method I) of local coordinate transposition and stiffness equivalence.The new method is derived and the feasibility is theoretically proved.A small-scale membrane structure is analyzed by the two methods,and the results show that the computational efficiency of the new method (Method II) is approximately 23 times that of Method I.When Method II is applied to a large-scale membrane stadium structure,it is found that this new method can quickly make the second principal stress of one way wrinkled elements zero,and make the two principal stresses of two-way wrinkled elements zero as well.It could attain the correct load responses right after the appearance of wrinkled elements,which indicates that Method II can be applied to wrinkling analysis of large-scale membrane structures.

Experimental study of seismic cyclic loading effects on small strain shear modulus of saturated sands

The seismic loading on saturated soil deposits induces a decrease in effective stress and a rearrangement of the soil-particle structure, which may both lead to a degradation in undrained stiffness and strength of soils. Only the effective stress influence on small strain shear modulus Gmax is considered in seismic response analysis nowadays, and the cyclic shearing induced fabric changes of the soil-particle structure are neglected. In this paper, undrained cyclic triaxial tests were conducted on saturated sands with the shear wave velocity measured by bender element, to study the influences of seismic loading on Gmax. And Gmax of samples without cyclic loading effects was also investigated for comparison. The test results indicated that Gmax under cyclic loading effects is lower than that without such effects at the same effective stress, and also well correlated with the effective stress variation. Hence it is necessary to reinvestigate the determination of Gmax in seismic response analysis carefully to predict the ground responses during earthquake more reasonably.

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.