Shear Modulus Reduction Research Articles

Nonlinear Characteristics of Floating Piles Under Rotating Machine Induced Vertical Vibration

This study presents a finite element based approach to evaluate the linear and nonlinear frequency–amplitude response of floating piles subject to rotating machine induced vertical vibrations. A Matlab program is developed to compute the response of a single pile with floating tip condition for a linear and two nonlinear soil models. The variation of complex soil stiffness parameters with frequency has also been presented using different boundary zone parameters (shear modulus reduction ratio, thickness ratio and damping ratio). A detailed investigation of soil–pile system stiffness and damping parameters has been done considering different values of soil–pile separation lengths and boundary zone parameters. To verify the effectiveness of this proposed approach vertical vibration tests were conducted in the field on a single pile of diameter 0.114 m and length of 2.85 m by constructing floating tip condition. The frequency–amplitude response obtained from field vibration test has been compared with the theoretical results for all the soil models. From the comparison results it is observed that the proposed theory can predict the nonlinear response of floating piles very efficiently with proper inclusion of boundary zone parameters and soil–pile separation lengths.

The near-field method for dynamic analysis of structures on soft soils including inelastic soil–structure interaction

The problem of soil–structure interaction analysis with the direct method is studied. The direct method consists of explicitly modeling the surrounding soil to bedrock and the structure resting on the soil. For the soil medium, usually the traditional equivalent linear method with a reduced shear modulus and an increased damping ratio for the soil is used. However, this method does not work in the vicinity of foundation where the soil behavior is highly nonlinear because of presence of large strains. This research proposes a modified equivalent linear method with a further reduction of the soil shear modulus in the near-field of foundation that results in validity of using the equivalent linear method throughout. For regular short, intermediate and tall structures resting on such soft soils, a series of dynamic time-history analysis is implemented using earthquake records scaled to a sample design spectrum and the nonlinear structural responses are compared for different assumptions of soil behavior including the elasto-plastic Mohr–Coulomb, the traditional equivalent linear, and the proposed modified equivalent linear method. This analysis validates the proposed method.

Effects of elevated temperature on the shear response of PET and PUR foams used in composite sandwich panels

Composite sandwich panels comprising fibre reinforced polymer (FRP) skins and lightweight material cores are being increasingly used in civil engineering. In several applications, such as façades, roof structures and bridge decks, these panels may experience a wide range of in-service temperatures. This paper presents experimental and analytical investigations about the effects of elevated temperature on the shear response of polyethylene terephthalate (PET) and polyurethane (PUR) foams used in composite sandwich panels. The experimental programme included (i) DMA and DSC/TGA tests, aimed at assessing the glass transition and decomposition processes underwent by those foams; and (ii) Iosipescu tests for temperatures ranging from −20°C to 120°C, in order to characterise their shear response. The analytical study comprised the assessment of the accuracy of different empirical (relaxation) models in describing the shear modulus reduction with temperature of those polymeric foams. Results obtained show that with increasing temperature, the shear responses of PET and PUR foams become more markedly non-linear. In addition, the shear moduli of these foams suffer considerable reductions, particularly for the PET foam; although at ambient temperature (∼20°C) the PET foam is 3 times stiffer than the PUR foam, at 80°C their shear moduli become similar, being respectively 24% and 66% of those at ambient temperature. All relaxation models assessed in this study were able to simulate with good accuracy the variation of the shear modulus of both foams with temperature.

Threshold Shear Strain for Dynamic Ramberg-Osgood Model in Soils Based on Thermomechanics

The threshold shear strain is a fundamental property of the soil behavior subjected to cyclic loading. Starting from the unloading and reloading hysteretic curves of dynamic Ramberg-Osgood model, construct small-strain dynamic dissipation function and explain small-strain dynamic characteristics by use of the skeleton curve back stress assumption. The plotting results of yield curves in true stress space indicate that there exist two threshold shear strains which are defined as the first threshold shear strain and the second threshold shear strain respectively which represent boundaries between fundamentally different dynamic characteristics of cyclic soil behavior. The yields of soil are controlled by the constant friction coefficient, the variable friction coefficient and dilatancy-related microstructural changes respectively. Both the first threshold shear strain and the second threshold shear strain do depend significantly on the maximum dynamic shear modulus coefficient and exponent. Comparison between the two threshold shear strain values and shear modulus reduction curves obtained on exactly the same soils confirms that the soil behavior is considerably at nonlinear at , the secant shear modulus, Gs, of the four soils studied is between 0.6 and 0.8 of its maximum value.

Electron tomography provides a direct link between the Payne effect and the inter-particle spacing of rubber composites.

Rubber-filler composites are a key component in the manufacture of tyres. The filler provides mechanical reinforcement and additional wear resistance to the rubber, but it in turn introduces non-linear mechanical behaviour to the material which most likely arises from interactions between the filler particles, mediated by the rubber matrix. While various studies have been made on the bulk mechanical properties and of the filler network structure (both imaging and by simulations), there presently does not exist any work directly linking filler particle spacing and mechanical properties. Here we show that using STEM tomography, aided by a machine learning image analysis procedure, to measure silica particle spacings provides a direct link between the inter-particle spacing and the reduction in shear modulus as a function of strain (the Payne effect), measured using dynamic mechanical analysis. Simulations of filler network formation using attractive, repulsive and non-interacting potentials were processed using the same method and compared with the experimental data, with the net result being that an attractive inter-particle potential is the most accurate way of modelling styrene-butadiene rubber-silica composite formation.

An experimental study of solid matrix weakening in water‐saturated Savonnières limestone

ABSTRACTPetrophysical properties of carbonate reservoirs are less predictable than that of siliciclastic reservoirs. One of the main reasons for this is the physical and chemical interactions of carbonate rocks with pore fluids. Such interactions can significantly change the elastic properties of the rock matrix and grains, making the applicability of Gassmann's fluid substitution procedure debatable. This study is an attempt to understand the mechanisms of fluid‐rock interactions and the influence of these interactions on elastic parameters of carbonates. We performed precise indentation tests on Savonnières limestone at a microscale level under dry, distilled water, and n‐Decane saturated conditions. Our experiments display softening of the rock matrix after water saturation. We have found that mainly the ooid cortices, peloid nuclei and prismatic intergranular cement are affected by water flooding. We also observed a shear modulus reduction in Savonnières limestone in an experiment performed at ultrasonic frequencies. One of the most important results obtained in our experimental study is that the Gassmann fluid substitution theory might not always be applicable to predict the elastic moduli of fluid‐saturated limestones.

First-principles study of spin transition and seismic properties of ferric iron-bearing post-perovskite with oxygen vacancy

The spin states, elastic properties and seismic velocities of ferric iron-bearing post-perovskite MgSiO3 (pPv) with single oxygen vacancy [Mg8(Si6,Fe2)O23 and Mg16(Si14,Fe2)O47] were calculated by first principles based on density functional theory. The effects of ferric iron and oxygen vacancy on seismic waves were studied for the host pPv subjected to a hydrostatic pressure. Calculations revealed a new spin transition from intermediate-spin to low-spin states with increasing pressure. As a result, the volume was reduced and the elastic constants were modified, producing a clear decrease in the seismic velocities of both compressive wave and shear wave due to the reduction of bulk modulus and shear modulus. The ferric iron and oxygen vacancy also had a minor effect on wave anisotropy.

Estimation of the Linear Spring Constant for a Laterally Loaded Monopile Embedded in Nonlinear Soil

In the case of large-diameter monopiles, pile deflection against lateral loads must be predicted accurately to determine the direct influence on the superstructure. One-dimensional (1D) linear models of the pile-soil system, which are simple to analyze, are more commonly used in practice than the sophisticated three-dimensional (3D) simulations. This study proposes an equivalent lateral strain concept to incorporate soil nonlinearity into an equivalent linear analysis of the pile-soil system. The spring constant is obtained by iterating over soil stiffness at different strain levels and finding equivalent lateral strain from updated pile deflection at each iteration. It requires the maximum shear modulus and modulus reduction curve for different layers of the soil profile. Correlation between the equivalent lateral strain and pile deflection has been developed by comparing results from 1D and 3D simulations of long piles. The existing correlations between the lateral spring constant and Young’s modulus of soil are too approximate to help in quantifying nonlinearity of soil accurately in this comparative study. Therefore, a more accurate relationship between spring constant and Young’s modulus of soil for long piles has been proposed by incorporating relative stiffness of soil and pile.

Magnetization measurements reveal the local shear stiffness of hydrogels probed by ferromagnetic nanorods

The local mechanical coupling of ferromagnetic nanorods in hydrogels was characterized by magnetization measurements. Nickel nanorods were synthesized by the AAO-template method and embedded in gelatine hydrogels with mechanically soft or hard matrix properties determined by the gelatine weight fraction. By applying a homogeneous magnetic field during gelation the nanorods were aligned along the field resulting in uniaxially textured ferrogels. The magnetization curves of the soft ferrogel exhibited not only important similarities but also characteristic differences as compared to the hard ferrogel. The hystereses measured in a field parallel to the texture axis were almost identical for both samples indicating effective coupling of the nanorods with the polymer network. By contrast, measurements in a magnetic field perpendicular to the texture axis revealed a much higher initial susceptibility of the soft as compared to the hard ferrogel. This difference was attributed to the additional rotation of the nanorods allowed by the reduced shear modulus in the soft ferrogel matrix. Two methods for data analysis were presented which enabled us to determine the shear modulus of the gelatine matrix which was interpreted as a local rather than macroscopic quantity in consideration of the nanoscale of the probe particles.

In-situ assessment of the dynamic properties of municipal solid waste at a landfill in texas

An understanding of dynamic properties of Municipal Solid Waste (MSW) is essential for seismic response analysis of MSW landfills in areas of moderate to high seismicity. A field testing program aimed at characterizing the dynamic properties of MSW was executed at two locations in a Subtitle D landfill in Austin, Texas. Shear and primary wave velocities were measured using small-scale crosshole and downhole seismic tests. The combination of these seismic methods allowed an assessment of the effect of waste composition on dynamic properties, anisotropy, and Poisson׳s ratio of the MSW. In addition, steady-state dynamic testing was performed using two mobile vibroseis shakers to evaluate in-situ the nonlinear relationship between shear modulus and shearing strain. Horizontal steady-state shaking at increasing stress level generated shearing strains from 0.001% to 0.2% allowing evaluation of shear modulus reduction curves over a wide shearing strain range. The effect of confining stress on the dynamic properties of the MSW was also evaluated using the substantial weight of the vibroseis as reaction to apply surcharge vertical loads at the surface of the MSW.

Dynamic shear modulus reduction and damping under high confining pressures for gravels

To provide a more reliable material property description for seismic analyses of high rockfill dams, this study investigates the dynamic properties of gravels under high confining pressures. The dynamic shear moduli G and damping ratios D of 12 gravels derived from cyclic triaxial tests are measured for confining pressures of 227–4000 kPa. As the confining pressure increases, the shear modulus reduction curve moves upwards slightly, while the damping variation curve moves downwards. However, the tested data of both the shear moduli and the damping ratios fall within the ranges recommended by previous studies, which are derived from data tested under lower confining pressures, because the influence of the confining pressure is countered by the impact of different loading frequencies during testing. Previously proposed empirical equations were found to fit the shear modulus reduction curves well for the test gravels, but could not precisely describe the variation of damping with strain. Furthermore, one important parameter in the damping equation is difficult to determine in practice for gravels with high confining pressures. A modified equation of damping is thus proposed in which all parameters are easy to obtain from test data.

Effect of vacancies and interstitials in the dumbbell configuration on the shear modulus and vibrational density of states of copper

It has been shown by the molecular dynamics method that the introduction of interstitials in the dumbbell configuration into the copper crystal leads to a significantly stronger shear modulus reduction than the vacancy introduction. Specific low-frequency modes appear in the spectrum of vibrational states of “defect” atoms. The vacancy formation enthalpy weakly depends on their concentration, and the interstitial dumbbell formation enthalpy at high concentrations can decrease by a factor of 8. In this case, the radial distribution function takes the form characteristic of noncrystalline materials. The results obtained confirm the interstitial theory of the condensed state.

Cartilage Nominal Strain Correlates With Shear Modulus and Glycosaminoglycans Content in Meniscectomized Joints

Postmeniscectomy osteoarthritis (OA) is hypothesized to be the consequence of abnormal mechanical conditions, but the relationship between postsurgical alterations in articular cartilage strain and in vivo biomechanical/biochemical changes in articular cartilage is unclear. We hypothesized that spatial variations in cartilage nominal strain (percentile thickness change) would correlate with previously reported in vivo articular cartilage property changes following meniscectomy. Cadevaric sheep knees were loaded in cyclic compression which was previously developed to mimic normal sheep gait, while a 4.7 T magnetic resonance imaging (MRI) imaged the whole joint. 3D cartilage strain maps were compared with in vivo sheep studies that described postmeniscectomy changes in shear modulus, phase lag, proteoglycan content and collagen organization/content in the articular cartilage. The area of articular cartilage experiencing high (overloaded) and low (underloaded) strain was significantly increased in the meniscectomized tibial compartment by 10% and 25%, respectively, while no significant changes were found in the nonmeniscectomized compartment. The overloaded and underloaded regions of articular cartilage in our in vitro specimens correlated with regions of in vivo shear modulus reduction. Glycosaminoglycans (GAG) content only increased at the underloaded articular cartilage but decreased at the overloaded articular cartilage. No significant correlation was found in phase lag and collagen organization/content changes with the strain variation. Comparisons between postsurgical nominal strain and in vivo cartilage property changes suggest that both overloading and underloading after meniscectomy may directly damage the cartilage matrix stiffness (shear modulus). Disruption of superficial cartilage by overloading might be responsible for the proteoglycan (GAG) loss in the early stage of postmeniscectomy OA.

A practical method for utilization of commercial cyclic testing apparatuses for computation of site response in central Adapazari

We suggest a practical method for estimating strain–modulus–damping relationships for utilization in equivalent-linear site response analyses, so that the necessity for more sophisticated sampling and testing procedures can be justified. The method employs the commercial cyclic testing apparatuses, which have limitations in low-strain ranges, and the in-situ seismic tests. The shear modulus at about 1% cyclic shear strain amplitude and the shear-wave velocity measured in-situ is used for building a hyperbolic relationship between shear stress and shear strain. An extension of Masing׳s rule and the constraint on hysteretic damping at 1% cyclic shear strain amplitude leads to a strain–damping relationship. By putting a particular emphasis on the soils of Adapazarı, a city famous for the concentrated damage on alluvium basin during the 1999 Kocaeli (Mw7.4) earthquake, we demonstrated the usefulness of the method, and concluded that the shear-modulus reduction and damping characteristics of Adapazarı soils can yield to site amplification factors greater than those predicted by strain–modulus–damping relationships presented in literature, and can more efficiently explain the concentration of damage on the alluvium basin. Through the comparisons of spectral amplification factors computed by equivalent-linear site response analyses, we justified the necessity to run a more sophisticated testing program on determination of cyclic stress–strain behavior of Adapazarı soils, and consequently to consider transient nonlinear site-response analyses in order to reduce the possible bias in calculation of spectral amplification factors.

Modulus and damping from shaking table tests of reinforced soil walls

The paper presents rational procedures to estimate normalised shear modulus and damping ratio from measured responses of reinforced soil model walls tested in a 1-g shaking table. Displacement measured at the top of the model walls and input base acceleration time histories are used to produce equivalent hysteretic responses of the model walls. Equivalent hysteretic loops at different strain amplitudes are developed and used to calculate normalised modulus degradation curves and damping ratio for the tested model walls. Model wall responses are also analysed using the single degree of freedom (SDOF) model to determine damping ratio and phase difference, and to verify the validity of SDOF model for application with reinforced soil walls.Results indicate that the normalised shear modulus significantly decreased at the early stage of the base shaking (i.e. γs < 0.03%). For example, about 68% and 80% reductions in shear modulus occurred at γs = 0.005% and 0.01% respectively. In addition, a 90% reduction in the normalised shear modulus realised at relatively strong input base acceleration (i.e. for γs > 0.03%). Minimum damping ratio of 5% to 10% for both model walls was obtained, increased to 15% to 20% at strain amplitude γs = 0.3%, and reached higher values thereafter. Finally, dynamic properties determined from the proposed method are compared with experimental and empirical relationships proposed in literature as well as resonant column test results.

The effect of transverse damage on the shear response of fiber reinforced laminates

Abstract Matrix damage, in the form of cracks parallel to the fiber due both to in-plane tensile loading perpendicular to the fibers and to in-plane shear loading, is a common failure mode for composite structures, yet little is known concerning their interaction. Past work has focused on experimental and analytical studies of axial and transverse stiffness reduction due to matrix cracks. By comparison, there is relatively little experimental work addressing shear modulus degradation from matrix damage. In this paper, a modified Isoipescu coupon is proposed to study the shear modulus degradation due to loading perpendicular to the fibers direction. The layup and coupon geometry were selected in a way that controls the severity of the damage and allows the measurement of shear and transverse stiffness degradation in the same coupon. The proposed method showed good agreement with results from tubular specimens and has advantages of simplified specimen fabrication using standard test fixtures. The results provided the first experimental comparison of shear modulus reduction, from transverse damage, to the predictive models. The results were compared with existing analytical and numerical models which over predicted the observed shear modulus reduction.

Particle impact velocities in a vibrationally fluidized granular flow: Measurements and discrete element predictions

Both the local impact and bulk flow velocities within a tub vibratory finisher were predicted using discrete element modeling (DEM) and compared to the measured values for spherical steel media. The sensitivities of the predicted impact velocities to uncertainties in the contact coefficients (friction, restitution and rolling friction) were studied, beginning with an analytical model of two-body collision. The sensitivity analysis was then extended to a simplified DE model of the flow within the vibratory finisher consisting of a single-layer of particles moving between parallel sheets of glass. It was observed that the impact and bulk flow velocities were relatively insensitive to uncertainties in the coefficients of friction and restitution. These coefficients were measured for the particle–particle and the particle–wall interactions for the steel media and tub wall using a linear tribometer and a laser displacement sensor. Several DE models with different numbers of particle layers between the glass partitions were compared, and it was concluded that the predicted impact and bulk flow velocities were dependent on the number of layers in the model. Consequently, the final DE model mimicked the key aspects of the experimental setup, including the submerged laser displacement sensor used to make the measurements of bulk flow and impact velocity. Another investigation showed that a reduced shear modulus could be used in the model to decrease run times without significantly affecting either the bulk flow or impact velocities. The DE method predictions of both impact velocity and bulk flow velocity were in reasonable agreement with the experimental measurements at points within the vibrationally-fluidized bed, with maximum differences of 20% and 30%, respectively.

Interseismic Strain Localization in the San Jacinto Fault Zone

We investigate interseismic deformation across the San Jacinto fault at Anza, California where previous geodetic observations have indicated an anomalously high shear strain rate. We present an updated set of secular velocities from GPS and InSAR observations that reveal a 2–3 km wide shear zone deforming at a rate that exceeds the background strain rate by more than a factor of two. GPS occupations of an alignment array installed in 1990 across the fault trace at Anza allow us to rule out shallow creep as a possible contributor to the observed strain rate. Using a dislocation model in a heterogeneous elastic half space, we show that a reduction in shear modulus within the fault zone by a factor of 1.2–1.6 as imaged tomographically by Allam and Ben-Zion (Geophys J Int 190:1181–1196, 2012) can explain about 50 % of the observed anomalous strain rate. However, the best-fitting locking depth in this case (10.4 ± 1.3 km) is significantly less than the local depth extent of seismicity (14–18 km). We show that a deep fault zone with a shear modulus reduction of at least a factor of 2.4 would be required to explain fully the geodetic strain rate, assuming the locking depth is 15 km. Two alternative possibilities include fault creep at a substantial fraction of the long-term slip rate within the region of deep microseismicity, or a reduced yield strength within the upper fault zone leading to distributed plastic failure during the interseismic period.

Elevating the fracture toughness of Cu49Hf42Al9 bulk metallic glass: Effects of cooling rate and frozen-in excess volume

A major challenge for the structural applications of bulk metallic glasses (BMGs) is to improve their fracture toughness. Here we demonstrate that by increasing the cooling rate during the casting of liquid Cu49Hf42Al9 into BMG, using a mixed argon and helium atmosphere, the notch toughness of the resultant BMG can be tripled relative to that obtained at slower cooling rates. The much elevated toughness is attributed to a ten-fold increase in the size of the plastic zone at crack tip, due to the proliferation of shear banding facilitated by enhanced propensity for shear transformations. The latter propensity is explained by the reduced shear modulus and microhardness, as well as increased enthalpy recovery, all of which are rooted in structural disorder as reflected by the lowered density and increased frozen-in excess volume. Such a structure-property correlation is systematically demonstrated by monitoring all these properties over a range of diameters of the as-cast BMG rods that correspond to cooling rate levels from 40 K/s to 103 K/s.

Normalized shear modulus reduction and damping ratio curves of quartz sand and rhyolitic crushed rock

This paper presents a laboratory investigation of the strain-dependent dynamic properties of volcanic granular soils composed of a rhyolitic crushed rock along with additional experiments on quartz sand through a high-amplitude resonant column testing program. The sands were tested in a dry state in torsional mode of vibration and thus the degradation of the normalized shear modulus and the increase of damping ratio in shear as a function of the shear strain amplitude (γ) were examined. It was revealed that, for a given mean effective confining pressure (σm') and coefficient of uniformity (Cu), the volcanic sands showed higher linearity in comparison to the quartz sands and that this trend became more pronounced with decreasing σm' and increasing Cu. In contrast to the general trend observed in the quartz soils, the confining pressure and the grain-size characteristics hardly affected the rate of normalized modulus degradation and damping increase in the volcanic sands. These differences are possibly related to the micro-mechanisms that dominate at particle contacts in the range of small to medium shear strain amplitudes. For example, the possible more pronounced crushing of the asperities during the elevation of the confining pressure and during the dynamic loading along with the lower inter-particle friction angle and stiffness of the volcanic sands of crushable particles in comparison to the quartz sands of stronger particles might play an important role in the energy dissipation during the dynamic excitation and thus on the rate of damping increase or modulus degradation.