Shear Modulus Reduction Research Articles

Ab initio study of the modification of elastic properties of α-iron by hydrostatic strain and by hydrogen interstitials

The effect of hydrostatic strain and of interstitial hydrogen on the elastic properties of α-iron is investigated using ab initio density-functional theory calculations. We find that the cubic elastic constants and the polycrystalline elastic moduli to a good approximation decrease linearly with increasing hydrogen concentration. This net strength reduction can be partitioned into a strengthening electronic effect which is overcome by a softening volumetric effect. The calculated hydrogen-dependent elastic constants are used to determine the polycrystalline elastic moduli and anisotropic shear moduli. For the key slip planes in α-iron, [ 1 1 ¯ 0 ] and [ 1 1 2 ¯ ] , we find a shear modulus reduction of approximately 1.6% per at.% H.

Mg based bulk metallic glasses: Glass transition temperature and elastic properties versus toughness

In this work, optimal compositions for bulk metallic glasses (BMGs) formation in the ternary Mg–Cu–Nd and Mg–Ni–Nd systems are located at the Mg57Cu34Nd9 and Mg64Ni21Nd15, respectively, with the critical diameter of 4mm for the rods fabricated by copper mold casting. As indicated by notch toughness testing, Mg64Ni21Nd15 BMG (KQ=5.1MPa√m) manifests higher toughness with respect to the Mg57Cu34Nd9 (KQ=3.6MPa√m), even though both BMGs have similar compressive fracture strength of 870–880MPa. Such an improvement in toughness for Mg BMGs correlates with the reduction of shear modulus and the enhancement of thermal stability to resist to the structural relaxation at room temperature, which is indicated by the elevated glass transition temperature Tg. Under the Mode I loading condition, morphology in fracture surface of the Mg64Ni21Nd15 BMG varies along the crack propagation path. Fractographic evolution of the fracture surface follows the Taylor's meniscus instability criterion. For the Mg-based BMGs, shear modulus scales with the glass transition temperature, and can be expressed as μ=4.7+625Tg/Vm[1–4/9(T/Tg)2/3]. Meanwhile, correlation between the calorimetric Tg and elastic properties at Tg can be rationalized with Egami's model.

Seismic lateral movement prediction for gravity retaining walls on granular soils

At present, methods based on allowable displacements are frequently used in the seismic design of earth retaining structures. However, these procedures ignore both the foundation soil deformability and the seismic amplification of the soil placed behind the retaining wall. Thus, they are not able to predict neither a rotational failure mechanism nor seismic induced lateral displacements with an acceptable degree of accuracy for the most general case. In this paper, a series of 2D finite-element analyses were carried out to study the seismic behavior of gravity retaining walls on normally consolidated granular soils. Chilean strong-motion records were applied at the bedrock level. An advanced non-linear constitutive model was used to represent both the backfill and foundation soil behavior. This elastoplastic model takes into account both the stress dependency of soil stiffness and coupling between shear and volumetric strains. In unloading–reloading cycles, the non-linear shear-modulus reduction with shear strain amplitude is considered. Interface elements were used to model soil–structure interaction. Routine-design charts were derived from the numerical analyses to predict the lateral movements at the base and top of gravity retaining walls located at sites with similar seismic characteristics to the Chilean subduction zone. Thus, wall seismic rotation can also be obtained. The developed charts consider wall dimensions, granular soil properties, bedrock depth, and seismic input motion characteristics. As shown, the proposed charts match well with available experimental data.

Precise determination of post-stishovite phase transition boundary and implications for seismic heterogeneities in the mid-lower mantle

The phase transition boundary between stishovite and CaCl2-type structure in pure SiO2 was investigated at 45–75GPa and 300–2490K based on the in situ X-ray diffraction measurements in a laser-heated diamond-anvil cell (LHDAC). Results show that the boundary has a positive dP/dT slope of 11.1MPa/K and the transition occurs about 70GPa at 2200K along the typical mantle geotherm. This corresponds to a depth of 1700km, somewhat shallower than the previous estimate. Seismic heterogeneities have been found in a wide depth range from 800 to 1850km in the upper to middle layers of the lower mantle. The post-stishovite phase transition is known to be ferroelastic-type, which causes a considerable reduction in shear modulus, leading to a large slow shear velocity anomaly. The almost pure SiO2 phase included in subducted crustal materials may be therefore responsible for the relatively deep mid-lower mantle seismic heterogeneities. The shallow lower mantle anomalies are possibly caused by the similar phase transition in SiO2 phase containing Al2O3 and H2O or by the phase transition in Al-bearing CaSiO3 perovskite from cubic to tetragonal structure.

Residual Stiffness of Cracked Cross-Ply Composite Laminates Under Multi-Axial In-plane Loading

In this paper, the Equivalent Constraint Model (ECM) together with a 2-D shear lag stress analysis approach is applied to predict residual stiffness properties of polymer and ceramic matrix [0/90n/0] cross-ply laminates subjected to in-plane biaxial loading and damaged by transverse and longitudinal matrix cracks. It is found that the longitudinal Young’s modulus, shear modulus and major Poisson’s ratio undergo large degradation as the matrix crack density increases, with Poisson’s ratio appearing to be the most affected by transverse cracking. In cross-ply laminates with thick 90° layer strip-shaped delaminations begin to initiate and grow from the tips of matrix cracks at the 0°/90° interface. These delaminations contribute to further stiffness degradation of such laminates, and hence have to be taken into account in failure analysis models. The thickness of the 90° layer plays an important role; the thicker the 90° layer, the bigger stiffness reduction suggesting a size (volume) effect at ply level. In SiC/CAS cross-ply laminates reduction in the longitudinal modulus occurs mainly due to transverse cracks, while the shear modulus appears to be the most affected by the presence of longitudinal cracks. The shear modulus reduction ratio predicted previously by a semi-empirical formula is, in the most of cases, within 10% of the current ECM/2-D shear lag approach value. In some cases, though, the error of the semi-empirical finite element expression can be as big as 20% since it fails to capture damage mode interaction.

Evaluation of Shear Modulus and Damping Ratio of Granular Materials Using Discrete Element Approach

In this paper, an attempt has been made to highlight the influence of different parameters such as number of cycles, confining pressure, void ratio, gradation, initial anisotropy and stress path on the dynamic properties of granular materials using Discrete Element Method (DEM). A series of strain controlled cyclic triaxial numerical simulations using three dimensional DEM have been carried out on an assembly of spheres. Dynamic properties such shear modulus (G) and damping ratio (D) were determined from the typical hysteresis loop obtained during cyclic triaxial test simulation. It has been observed from the test results that the numerical simulation using DEM has captured the variation of dynamic properties over a wide range of shear strain values for different parameters considered for the current investigation. Maximum shear modulus (Gmax) was found to be influenced by initial confining pressure, void ratio, gradation and initial anisotropy. Whereas, the damping ratio (D) was found to be influenced by number of cycles, initial confining pressure, gradation and stress path. Further it has been shown that the variation of shear modulus with shear strain can be divided into three distinct zones such as Isotropic Zone (IZ), Anisotropic Zone (AZ) and Stable Anisotropic Zone (SAZ). A drastic reduction of shear modulus with shear strain has been observed in the Anisotropic Zone (AZ). In addition, the results obtained using numerical simulations have been compared with the laboratory experimental values.

Shear-induced gelation of associative polyelectrolytes

Copolymer of N,N-dimethylacrylamide (DMA) and acrylic acid (AA) was functionalized with pendant alkyl groups. Their dynamic mechanical properties in aqueous solution were investigated using continuous shear and oscillatory shear. Shear flow showed an abrupt divergence of the viscosity at a critical shear stress (σc). Oscillatory shear showed, with increasing applied stress, slight shear thinning followed by strong shear thickening above σc. The effect of the polymer concentration and the oscillation frequency (ω) was investigated. The behaviour at all concentrations and frequencies was fully determined by the product of the oscillation frequency and the terminal relaxation time (τ) of the systems at rest. Master curves of the data determined at different concentrations and frequencies were obtained if the reduced shear modulus was plotted versus the reduced applied stress at constant ω.τ. The effect of shear increased with decreasing value of ω.τ. At low frequencies the storage shear modulus crossed the loss modulus with increasing shear. A model is proposed for this phenomenon of shear-induced gelation.

Dynamic Properties of Municipal Solid Waste in Bioreactor Landfills with Degradation

Bioreactor landfills are operated to enhance refuse decomposition, gas production, and waste stabilization. The major aspect of bioreactor landfill operation is the recirculation of collected leachate back through the refuse mass. Due to the presence of additional leachate and accelerated decomposition, the characteristics of Municipal Solid Waste (MSW) in bioreactor landfills are expected to change. About 50% of the continental United States comes under the designated seismic impact zone. The federal regulations have focused increase attention on seismic design of solid waste fills, and have mandated that the solid waste landfills located in the seismic impact zones should be designed to resist the earthquake. Accordingly, assessment of dynamic properties of landfills is one of the major geotechnical tasks in landfill engineering. In order to understand the changes in dynamic properties of bioreactor waste mass with time and decomposition, four small scale bioreactor landfills were simulated in laboratory and samples were prepared to represent each phase of decomposition. The state of decomposition was quantified by methane yield, pH, and volatile organic content (VOC). A number of Resonant Column (RC) tests were performed to evaluate the dynamic properties (stiffness and damping) of MSW. The test results indicated that the normalized shear modulus reduction and damping curves are significantly affected by the degree of decomposition. The shear modulus increased from 2.11 MPa in Phase I to 12.56 MPa in Phase IV. The increase was attributed to the breakdown of fibrous nature of solid waste particles as it degrades. Therefore, considering MSW properties to be uniform throughout the bioreactor landfill is not a reasonable assumption and the shear modulus reduction curves should be evaluated based on the degree of MSW decomposition, rather than the sample composition itself.

Shear Stiffness of Neoprene Bearing Pads under Long-Term Loads

This research evaluated the interaction between the shear modulus of steel-reinforced neoprene bearing pads and the shear strain rate. The following interactions related to variations in the shear modulus were investigated for pads with various shape factors: product approval strain rates versus short-term field strain rates, short-term field strain rates versus long-term field strain rates, reduction in shear modulus due to load cycles, and compressive stress. Forty-two tests were performed with test equipment designed to apply a shear strain at a variety of rates (50% shear strain at rates from 45 s to 90 days) while applying a sustained compressive load. Test results indicated that the shear modulus was reduced on average by 7% when tests were performed with the short-term field strain rates of 50% over 12 h instead of the product approval strain rates of 50% over 30 to 60 s, that there was essentially no reduction in shear modulus with long-term field loading rates of 50% over durations up to 90 days versus short-term field strain rates, that the shear moduli for pads that had never been load-cycled were approximately 12% higher than those of cycled pads, and that the effect of compressive stress agrees with previous work (i.e., the shear modulus decreases with increased compression particularly for bearings with low shape factors).

Co-Seismic and Post-Seismic Behavior of an Alternately Layered Sand-Clay Ground and Embankment System Accompanied by Soil Disturbance

ABSTRACT In the evaluation of the damage caused by earthquakes, particular attention has been paid until now to the unstable behaviour (the phenomenon of liquefaction) of sandy grounds during tremors. However, studies of post-seismic damage and damage to clayey grounds have also been reported. In this paper, the behaviour of an actual alternately layered sand-clay ground and embankment-coupled system before, during, and after an earthquake is investigated. The investigations were carried out by soil-water coupled finite element analysis (GEOASIA), which is capable of handling inertial forces and utilizes the SYS Cam-clay model as the elasto-plastic constitutive model of the soil skeleton. By accounting for the effects of the soil skeleton structure (structure, overconsolidation, and anisotropy) at work, the above constitutive equation is capable of expressing the reduction of shear modulus, etc. caused by disturbance in loose sands and naturally deposited clays. In the analysis, (1) the effect of the rigidity of the embankment and (2) the effect of the penetration depth of the sheet pile in a strengthened ground with retaining walls and sheet piles joined by tie rods were examined. The main results are as follows: (1) If the embankment is soft, liquefaction of the upper sandy soil layer during the earthquake causes the embankment itself to collapse. In contrast, if the embankment is relatively hard, the shape of the embankment remains stable. However, a decrease in shear rigidity occurs in the lower clayey soil layer due to degradation (disturbance) of the soil structure, resulting in increased settlement both during and after the earthquake. (2) In the case of grounds strengthened by the sheet pile method, if the tips of the sheet piles are located in a soft soil layer with a high degree of structure, large disturbance may occur at such locations during an earthquake and cause increased settlement during and after the tremors.

Three-dimensional models of elastostatic deformation in heterogeneous media, with applications to the Eastern California Shear Zone

SUMMARY We present a semi-analytic iterative procedure for evaluating the 3-D deformation due to faults in an arbitrarily heterogeneous elastic half-space. Spatially variable elastic properties are modelled with equivalent body forces and equivalent surface traction in a ‘homogenized’ elastic medium. The displacement field is obtained in the Fourier domain using a semi-analytic Green function. We apply this model to investigate the response of 3-D compliant zones (CZ) around major crustal faults to coseismic stressing by nearby earthquakes. We constrain the two elastic moduli, as well as the geometry of the fault zones by comparing the model predictions to Synthetic Aperture Radar inferferometric (InSAR) data. Our results confirm that the CZ models for the Rodman, Calico and Pinto Mountain faults in the Eastern California Shear Zone (ECSZ) can explain the coseismic InSAR data from both the Landers and the Hector Mine earthquakes. For the Pinto Mountain fault zone, InSAR data suggest a 50 per cent reduction in effective shear modulus and no significant change in Poisson's ratio compared to the ambient crust. The large wavelength of coseismic line-of-sight displacements around the Pinto Mountain fault requires a fairly wide (∼1.9 km) CZ extending to a depth of at least 9 km. Best fit for the Calico CZ, north of Galway Dry Lake, is obtained for a 4 km deep structure, with a 60 per cent reduction in shear modulus, with no change in Poisson's ratio. We find that the required effective rigidity of the Calico fault zone south of Galway Dry Lake is not as low as that of the northern segment, suggesting along-strike variations of effective elastic moduli within the same fault zone. The ECSZ InSAR data is best explained by CZ models with reduction in both shear and bulk moduli. These observations suggest pervasive and widespread damage around active crustal faults.

Elastic properties of some bulk metallic glasses

The relationships between the elastic moduli, glass forming ability and response to deformation of bulk metallic glasses are investigated. Five bulk metallic glasses are prepared from high purity elements via suction casting. The results confirm that there exists a correlation between energy absorbed to failure during compression testing and the bulk to shear modulus ratio. This finding is developed such that it corresponds only to the elastic component of energy absorption, and that the bulk modulus dominates this. Plastic deformation appears to be favored by a reduced shear modulus, although it shows greater dependence on structural features that are frozen in during the glass transition, and so may well be dependent on the liquid fragility.

NONLINEAR BEHAVIOR OF COHESIVE SOILS ESTIMATED FROM STRONG MOTION RECORDS AT K-NET ANAMIZU AND JMA WAJIMA IN THE 2007 NOTO-HANTO EARTHQUAKE

Strain-dependent shear moduli of cohesive soils at K-NET Anamizu and JMA Wajima were estimated using the strong ground motions recorded in the 2007 Noto-Hanto Earthquake. The estimated shear moduli of the soils are in good agreement with those measured in the laboratory for the soil samples obtained from the sites, when the generated pore water pressure is taken into account. The pore pressure ratios induced by the main shock were estimated to be 0.4 at Anamizu and 0.3 at Wajima, suggesting that not only the cyclic shearing but also pore water pressure generated during earthquake shaking could have strong effects on the shear modulus reduction of cohesive soils.

An improved damaging model for structured clays

An improved damaging model formulated within the framework of bounding surface for structured clays was proposed. The model was intended to describe the effects of structure degradation due to geotechnical loading. The predictive capability of the model was compared with those of triaxial compression test on Tianjin soft clays. The results show that, by incorporating a new damage function into the model, the reduction of elastic bulk and shear modulus with elastic deformations and the reduction of plastic bulk modulus and shear modulus with plastic deformations are able to be appreciable. Before the axial strain reaches 15%, the axial strain computed from the model is smaller than that from the test under the drained condition. Under the undrained condition, after the axial strain reaches 1%, the axial strain increases quickly because of the complete loss of structure and stiffness; and the result computed from the model is nearly equal to that from the model without the incorporation of the damage function due to less plastic strain under undrained condition test.

Strengthening slabs using externally-bonded strip composites: Analysis of concrete covers on the strengthening

This study pertains to the experimental and theoretical behaviour of slabs strengthened by fibre reinforced polymer (FRP). The experimental results show that FRP significantly increases punching failure stress, resulting in a reduction of slab rotation around the loading column. The theoretical investigation presents a finite element model for the bending of strengthened slabs. The developed model considers the concrete as a 3D multi-layered non-linear material and explicitly takes into account the steel reinforcement and the FRP strips. The proposed model is then used to analyse the effects of a concrete cover on the reinforcement and repairs. In the analysed cases, the results show that an average reduction in the concrete shear modulus, between steel rod and FRP, of more than 30% leads to significant reductions of stress and slab stiffness.

Effect of a compliant fault zone on the inferred earthquake slip distribution

We present a new semi‐analytic method to evaluate the deformation due to a screw dislocation in arbitrarily heterogeneous and/or anisotropic elastic half plane. The method employs integral transformations to reduce the governing partial differential equations to the integral Fredholm equation of the second kind. Dislocation sources, as well as spatial perturbations in the elastic properties are modeled using equivalent body forces. The solution to the Fredholm equation is obtained in the Fourier domain using a method of successive over‐relaxation, and is mapped into the spatial domain using the inverse Fast Fourier Transform. We apply this method to investigate the effect of a soft damage zone around an earthquake fault on the co‐seismic displacement field, and on the earthquake slip distribution inferred from inversions of geodetic data. In the presence of a kilometer‐wide damage zone with a reduction of the effective shear modulus of a factor of 2, inversions that assume a laterally homogeneous model tend to underestimate the amount of slip in the middle of the seismogenic layer by as much as 20%. This bias may accentuate the inferred maxima in the seismic moment release at depth between 3–6 km suggested by previous studies of large strike‐slip earthquakes.

Induced Dynamic Nonlinear Ground Response at Garner Valley, California

We present results from a prototype experiment in which we actively induce, observe, and quantify in situ nonlinear sediment response in the near surface. This experiment was part of a suite of experiments conducted during August 2004 in Garner Valley, California, using a large mobile shaker truck from the Network for Earthquake Engineering Simulation (NEES) facility. We deployed a dense accel- erometer array within meters of the mobile shaker truck to replicate a controlled, laboratory-style soil dynamics experiment in order to observe wave-amplitude- dependent sediment properties. Ground motion exceeding 1g acceleration was pro- duced near the shaker truck. Thewave field was dominated by Rayleigh surface waves and ground motions were strong enough to produce observable nonlinear changes in wave velocity. We found that as the force load of the shaker increased, the Rayleigh- wave phase velocity decreased by as much as ∼30% at the highest frequencies used (up to 30 Hz). Phase velocity dispersion curves were inverted for S-wave velocity as a function of depth using a simple isotropic elastic model to estimate the depth depen- dence of changes to the velocity structure. The greatest change in velocity occurred nearest the surface, within the upper 4 m. These estimated S-wave velocity values were used with estimates of surface strain to compare with laboratory-based shear modulus reduction measurements from the same site. Our results suggest that it may be possible to characterize nonlinear soil properties in situ using a noninvasive field technique.

Shear modulus and material damping of municipal solid waste based on large-scale cyclic triaxial testing

Representative dynamic properties of municipal solid waste (MSW) are required to perform reliable seismic analyses of MSW landfills. A comprehensive large-scale cyclic triaxial laboratory testing program was performed on MSW retrieved from a landfill in the San Francisco Bay area to evaluate the small-strain shear modulus, and strain-dependent normalized shear modulus reduction and material damping ratio relationships of MSW. The effects of waste composition, confining stress, unit weight, time under confinement, and loading frequency on these dynamic properties were evaluated. The small-strain shear modulus depends primarily on waste composition, confining stress, unit weight, and time under confinement. The normalized shear modulus reduction and material damping curves for MSW depend on waste composition and confining stress. Based on the results of this study and a review of literature, strain-dependent shear modulus reduction and material damping relationships are recommended for use in landfill design.

Seismic Properties of Anita Bay Dunite: an Exploratory Study of the Influence of Water

As a pilot study of the role of water in the attenuation of seismic waves in the Earth’s upper mantle, we have performed a series of seismic-frequency torsional forced-oscillation experiments on a natural (Anita Bay) dunite containing accessory hydrous phases, at high temperatures to 13008C and confining pressure (Pc )o f 200 MPa, within a gas-medium high-pressure apparatus. Both oven-dried and pre-fired specimens wrapped in Ni^Fe foil within the (poorly) vented assembly were recovered essentially dry after 50^100 h of annealing at 13008C followed by slow staged cooling. The results for those specimens indicate broadly similar absorptionband viscoelastic behaviour, but with systematic differences in the frequency dependence of strain-energy dissipation Q � 1 , attributed to differences in the small volume fraction of silicate melt and its spatial distribution. In contrast, it has been demonstrated that a new assembly involving a welded Pt capsule retains aqueous fluid during prolonged exposure to high temperaturescallowing the first high-temperature torsional forced-oscillation measurements under high aqueous fluid pore pressure Pf. At temperatures 410008C, a marked reduction in shear modulus, without concomitant increase in Q � 1 , is attributed to the widespread wetting of grain boundaries resulting from grain-scale hydrofracturing and the maintenance of conditions.

Structure and mechanical properties of faults in the North Anatolian Fault system from InSAR observations of coseismic deformation due to the 1999 Izmit (Turkey) earthquake

We study the structure and mechanical properties of faults in the North Anatolian Fault system by observing near‐fault deformation induced by the 1999 Mw 7.4 Izmit earthquake (Turkey). We use interferometric Synthetic Aperture Radar (InSAR) and Global Positioning System observations to analyze the coseismic surface deformation in the near field of the Izmit rupture. The overall observed coseismic deformation is consistent with deformation predicted by a dislocation model assuming a uniform elastic crust. Previous InSAR studies revealed small‐scale changes in the radar range across the nearby faults of the North Anatolian fault system (in particular, the Mudurnu Valley and Iznik faults) (e.g., Wright et al., 2001). We demonstrate that these anomalous range changes are consistent with an elastic response of compliant fault zones to the stress perturbation induced by the Izmit earthquake. We examine the spatial variations and mechanical properties of fault zones around the Mudurnu Valley and Iznik faults using three‐dimensional finite element models. In these models, we include compliant fault zones having various geometries and elastic properties and apply stress changes deduced from a kinematic slip model of the Izmit earthquake. The best fitting models suggest that the inferred fault zones have a characteristic width of a few kilometers, depth in excess of 10 km, and reductions in the effective shear modulus of about a factor of 3 compared to the surrounding rocks. The characteristic width of the best fitting fault zone models is consistent with field observations along the North Anatolian Fault system (Ambraseys, 1970). Our results are also in agreement with InSAR observations of small‐scale deformation on faults in the Eastern California Shear Zone in response to the 1992 Landers and 1999 Hector Mine earthquakes (Fialko et al., 2002; Fialko, 2004). The inferred compliant fault zones likely represent intense damage and may be quite commonly associated with large crustal faults.