Shear Modulus Degradation Research Articles

An analytical shear modulus degradation model for carbonate sand supporting marine geostructures

The shear modulus degradation curve in normalized shear modulus vs. shear strain plane presents crucial information about the cyclic and/or dynamic response of soil, especially for undrained conditions. This study introduces an analytical shear modulus degradation model specifically for carbonate sand subjected to high-amplitude cyclic loading associated with marine geostructures. Unlike hard-grain siliceous sand, carbonate is soft and crushable under low confining conditions. To address this, we utilize a generic analytical shear modulus degradation model and enhance it for carbonate sand. The model coefficients are first calibrated based on existing cyclic experiments on carbonate sand collected from various offshore regions around the world, without taking into account the particle crushing effect. Later, cyclic undrained tests are numerically simulated, accounting for the particle-crushing effect using a bounding surface plasticity soil model. The simulation results show a noticeable shift in the shear modulus degradation curves while accounting for the particle breakage compared to non-crushable sands, irrespective of cyclic stress ratio conditions. Based on the numerical simulations, the analytical model is further refined through evolving characteristics of sand gradation (i.e., coefficient of uniformity). The proposed model is validated with separate experimental results of carbonate sand subjected to different confining pressures.

Ballast stiffness estimation based on measurements during dynamic track stabilization

Ballast compaction with the Dynamic Track Stabilizer (DTS) is known to improve the lateral track resistance by increasing the stiffness of the ballast. This paper presents two approaches for estimating the strain dependent ballast shear modulus G based on measurements during dynamic track stabilization. One approach uses the Hardin equation with its enhancement for coarse-grained soils to estimate the small strain shear modulus for a given grain size distribution curve. Since different shear strains are induced on an observed sleeper (with fixed location) by a bypassing DTS, the measurement of ballast shear strains with accelerometers on the top and the bottom edge of the ballast layer yield shear modulus degradation curves G/Gmax. It is shown for data from a regular maintenance operation, that these shear modulus degradation curves are in accordance with previous research. For the second approach, a SDOF model for the track-ballast interaction under harmonic loading (caused by the dynamic track stabilizer) is developed. Influence lines are used to estimate the mass, the mass moment of inertia and the geometry of an equivalent machine foundation (with spring and dashpot coefficients according to the Hall analog). An optimization algorithm is used to fit the model response to the measured data from field tests with the DTS. The resulting shear moduli show plausible values for loose and compacted ballast conditions, which proves the potential of the presented method as a basis for a future system for Intelligent Compaction (IC) with the DTS.

Contribution to micromechanical modeling of the shear wave propagation in a sand deposit

The object of study is the vertical wave propagation in a sand deposit. This paper is aimed at analyzing the vertical wave propagation in a sand deposit through micromechanical modeling that inherently takes account of intergranular slips during deformation. Such a problem, which is part of the general framework of wave propagation in the soil, has long been analyzed using continuum models based on approximate behavior laws. For this purpose, a 2D Discrete Element Method (DEM) model is developed. The DEM model is based on molecular dynamics with the use of circular shaped elements. The intergranular normal forces at contacts are calculated through a linear viscoelastic law while the tangential forces are calculated through a perfectly plastic viscoelastic model. A model of rolling friction is incorporated in order to account for the damping of the grains rolling motion. Different boundary conditions of the profile have been implemented; a bedrock at the base, a free surface at the top and periodic boundaries in the horizontal direction. The sand deposit is subjected to a harmonic excitation at the base. Using this model, the fundamental and resonance frequencies of the deposit are first determined. The former is determined from the low-amplitude free vibration and the latter by performing a variable-frequency excitation test. It is noted that there is a significant gap between the two frequencies, this gap could be attributed to the degradation of the soil shear modulus in the vicinity of the resonance. Such degradation is well proven in classical soil dynamics. The effects of deposit height and confinement on resonance frequency and free-surface dynamic amplification factor are then investigated. The obtained results highlighted that the resonance frequency is inversely proportional to the deposit’s thickness whereas the dynamic amplification factor Rd increases with the deposit’s thickness. In the other hand, when the confinement increases the deposit becomes stiffer, which results in reducing the amplification. Such result is in accordance with theoretical knowledge which states that the most rigid profiles such as rocks do not amplify seismic movement.

Shear modulus of sand-rubber mixtures: element testing and constitutive modeling

In this study, a series of resonant column tests was conducted to measure the shear modulus of sand-rubber mixtures at small strain amplitudes (i.e. between 10−4% and 10−2%), considering different rubber percentages and confining stress levels. The results were then combined with data obtained by dynamic hollow cylinder tests to investigate shear modulus degradation of the mixtures over a wider shear strain range. Based on the test results, a new expression was proposed to improve the prediction of maximum shear modulus of sand-rubber mixtures using the modified equivalent void ratio concept. A new constitutive model was also developed for estimation of strain-dependent shear modulus of the mixtures based on the modified hyperbolic framework. The shear modulus of the mixtures was found to be a function of rubber percentage, confining stress, the modified equivalent void ratio and the relative shear stiffness of rubber and sand. The experimental data and the developed models showed that the shear modulus decreased with rubber percentage and increased with confining stress. Moreover, the reference shear strain of the modified hyperbolic model increased with both rubber percentage and confining stress while its curvature coefficient increased more considerably with rubber percentage compared to the confining stress.

Influence of the curing stress effect on the stiffness degradation curve of a silt stabilized with lime and cement

This study investigated the shear modulus degradation curves of reconstituted stabilized soil specimens and their evolution during curing up to 270 days. An experimental protocol is proposed to get as close as possible to the in situ curing conditions of a chemically (lime and hydraulic binder) and mechanically (compaction) improved soil placed in a high-rise geotechnical structure. Innovative solutions now make it possible to build high embankments (> 10 m) in stabilized soil. In the laboratory, a silty soil stabilized with 1% lime and 5% hydraulic binder, which is a classic treatment for linear projects, was cured with a pressure of 300 and 500 kPa, corresponding to a depth in the embankment of 15 and 25 m. These structures are expected to have high mechanical performance and must be able to withstand very small deformations (earthquakes, traffic loads). Experimental campaigns are performed in laboratory using torsion tests with a resonant column apparatus (RCA) to obtain the shear modulus G as a function of distortion. A comparison was made between normalized curing conditions (temperature of 20 °C and atmospheric pressure) and curing with confining pressure (temperature of 20 °C and 300 or 500 kPa pressure). For this aim, 74 torsional RCA tests were conducted on 16 compacted soil specimens. These showed that the curing pressure, applied just after compaction, brings the expected properties more quickly and confers superior properties of around 15% in the long term. A power law was proposed to estimate the Gmax of a stabilized silt specimen as a function of time, based on the Gmax measured during the first two days of curing. This empirical law gives the Gmax over the long term (270 days) for curing with or without confining pressure. Pioneering a combined curing-testing RCA approach, this study elucidates the short and long-term behavior of stabilized silts under realistic curing conditions.

Effect of complex-grain-size curves on shear modulus degradation of calcareous sand

The dynamic shear modulus G and its degradation tendency G / G max are essential parameters for characterizing the dynamic properties of soil. Coastal facilities constructed on calcareous sand foundations are subjected to multiple types of cyclic loadings. To investigate the effects of the uniformity coefficient C u , effective confining pressure σ 0 ′ , relative density D r , and median grain size d 50 on the dynamic G and its degradation rule for calcareous sand, a set of resonant column tests is conducted on calcareous sand with different grain-size-distribution curves. The experimental results clearly show that the G degrades faster for calcareous sand with a lower σ 0 ′ and a larger C u . By contrast, the degradation of the G is affected less by D r and d 50 . The G / G max values decreased slightly as γ increased but remained less than 10 − 5 , whereas the G / G max curve descended rapidly as γ increased beyond 10 − 5 . Based on the test results obtained in this study and previously published data, a new mathematical model characterizing the degradation tendency of G / G max with respect to the shear strain level of calcareous sands with different gradation conditions is proposed. The relevant parameters associated with the proposed model are correlated with C u and σ 0 ′ .

Small Strain Shear Modulus of the Ljubljana Marsh Soil Measured with Resonant Column and Bender Elements under Isotropic and Anisotropic Stress Conditions

The increasing use of finite element analysis in modern infrastructure design emphasizes the importance of determining soil stiffness at small strains. This is usually represented by the normalized shear modulus degradation curve, which is crucial for accurate design. In the absence of specific measurements on the local soil, engineers often rely on empirical correlations and assume comparable behavior of soils with similar intrinsic properties. However, the application of this approach leads to uncertainties, especially for unique geological formations such as the soft cohesive soils of the Ljubljana Marsh. The main objective of this study was to determine the small strain shear modulus of Ljubljana Marsh soil with a plasticity index between 11 and 35%. Isotropic and anisotropic stress conditions were investigated as part of an extensive laboratory test program that included 45 bender element and 89 resonant column tests on 20 soil samples. By emphasizing the importance of measuring soil stiffness at small strains, this study not only provides reliable data for the development of the built environment in the Ljubljana Marsh and similar areas, but also underlines its necessity.

State-dependent dilatancy of sand based on hollow cylinder laboratory tests under shear strain cycles

The present study is devoted to the investigation of the dilatancy behaviour of a fine sand based on hollow cylinder tests. Medium and dense samples were tested at a constant average γ = 1, 2, 3 and 4%. Dilatancy curves along with shear wave velocity measurements to investigate the influence of the shear strain amplitude γampl in the shear modulus degradation curve are presented and discussed. The measured stress and strain paths were used to compare the performance of four advanced constitutive models especially in describing the dilatancy behaviour of sand. From the perspective of their constitutive equations, the differences between the simulations with various material models are examined. It may be concluded that all four models allow a proper prediction of torsional shear tests as long as a proper calibration of the material parameters is secured.

The threshold value of ground motion acceleration characterizing the nonlinear response of sites

Assessing the nonlinearity of a site plays a crucial role in earthquake engineering. For some building structures and lifeline projects that need safety assessment after earthquakes, the analysis of nonlinear degree of sites can help accurately revealing the amplification effect of sites and evaluating the damage degree of buildings which is convenient for subsequent reinforcement and demolition work. The quantitation of nonlinear threshold of sites is an important method to evaluate the degree of site nonlinearity. In this paper, a nonlinear characteristic index reflecting the degradation of shear modulus is proposed based on the instantaneous frequency of the site calculated by using the vector auto-regression moving average (VARMA) model. Then, seismic records of class Ⅰ, Ⅱ, Ⅲ and Ⅳ sites specified as per code for seismic design of buildings in China are selected from the KiK-net network in Japan, and the threshold value of ground motion acceleration characterizing the nonlinear response of sites are provided. Finally, the variation of the nonlinear characteristic index (shear modulus degradation) vs. different (peak ground acceleration) PGA for four types of sites are presented.

Effect of the particle’s shape on the dynamic shear modulus and compressibility of diatomaceous soils

Diatomites are unicellular algae fossils that can be found worldwide. This paper studies the diatom's shape effect on diatomaceous soil mixtures' dynamic and compressibility properties. Physical characteristics of six diatomite samples with variable shapes and taxonomies are presented. Among these six samples, three diatomites of similar grain size distribution were mixed with kaolin, and the mechanical properties (i.e., shear modulus and damping ratio from small to large strains) were analysed. The results showed that diatom frustules increased the mixtures' compressibility and reduced the maximum shear modulus compared with pure kaolin samples. Moreover, the diatom's shape influenced the normalised shear modulus degradation curve and the damping ratio. Overall, the presence of diatomites reduces the energy dissipation capacity in soils. This research evidenced the importance of distinguishing the shape of diatom in soil mixtures when mechanical properties are analysed, a situation that has yet to be explored.

Effect of a Fine Fraction on Dynamic Properties of Recycled Concrete Aggregate as a Special Anthropogenic Soil.

The literature confirms that fine recycled concrete aggregate (fRCA) can be used as a replacement for natural soil in new concrete, offering many advantages. Despite these advantages, there are also critical barriers to the development of fRCA in new mixes. Among these, the first challenge is the variability of fRCA properties, in both physical, chemical, and mechanical terms. Many individual studies have been carried out on different RCA or fRCA properties, but little investigative work has been performed to analyze their dynamic properties. Therefore, the influence of the non-cohesive fine fraction content of RCA on the dynamic properties of this waste material, when used as a specific anthropogenic soil, has been studied in laboratory conditions, employing a standard resonant column apparatus, as well as piezoelectric elements. In the present research, special emphasis has been placed on the dynamic shear modulus, dynamic damping ratio, small-strain shear modulus, and small-strain damping ratio, as well as shear modulus degradation G(γ)/Gmax, the damping ratio increase D(γ)/Dmin, and the threshold shear strain amplitudes γtl and γtv. Artificially prepared fRCAs with varying fine fraction contents (0% ≤ FF ≤ 30%, within increments of 5%) have been tested at different pressures (p' = 90, 180, and 270 kPa) and relative densities of Dr > 65%. This study also examined the effect of two tamping-based sample preparation methods, i.e., dry and wet tamping. The results presented herein indicate that the analyzed anthropogenic material, although derived from concrete and produced by human activities, behaves very similarly to natural aggregate when subjected to dynamic loading. The introduction of a fine fraction content to fRCA leads to changes in the dynamic properties of the tested mixture. Concrete material with lower stiffness but, at the same time, with stronger damping properties can be obtained. A fine fraction content of at least 30% is sufficient to cause a significant loss of stiffness and, at the same time, a significant increase in the damping properties of the mixture. This study can serve as a reference for designing fRCA mixtures in engineering applications.

A generalized elastoplastic load-transfer model for axially loaded piles in clay: Incorporation of modulus degradation and skin friction softening

The softening behavior of skin friction is commonly observed from load-displacement responses of axially loaded piles in stiff clay, sensitive clay, and dense sands at a large loading level. This paper presents a generalized and novel elastoplastic load-transfer model to predict the load-displacement response of axially loaded piles in clay considering the degradation of skin friction. In this model, the soil around piles is divided into the shear band immediately adjacent to piles and the soil outside shear bands. An elastoplastic model in terms of the critical state theory-based modified Cam-clay model is developed to describe the mechanical behavior of shear bands. The elastoplastic model can explicitly consider both hardening and softening behaviors of skin friction. The elastic behavior of the soil outside shear bands is represented by a modulus degradation model, which captures the shear modulus degradation with the shear strain. Subsequently, an elastoplastic load-transfer model possessing generalized ability to describe both hardening and softening behaviors is developed by combining these two theoretical models. Predictions of the load-settlement curves are compared with the measured values from three well-documented cases to verify the proposed model. Good agreements demonstrate that the proposed load-transfer model provides reasonable and effective prediction for bearing performance of piles.

Response of cohesive–frictional soils at small to medium shear strain levels from thermo-controlled resonant column testing

The shear modulus and damping ratio are arguably the two most crucial soil parameters to be used in seismic site-response analyses and a wide variety of other geotechnical engineering applications involving soil materials subjected to dynamic loading. The dependency of these parameters on the level of load-induced shear strains in the field has been investigated rather extensively for different types of soils. Most experimental studies, however, have relied on a limited set of controlled environmental factors and stress variables, mainly soil moisture and confinement. The present work is an attempt to gain further insights into the possible impact of an additional critical factor: soil temperature. A resonant column apparatus was upgraded to assess the dynamic response of three types of cohesive–frictional soils as they transitioned from linear to nonlinear behavior under thermo-controlled cyclic torsional loading. Emphasis was placed on shear modulus degradation, and hence variation in damping ratio, with increasing shear strain amplitude (cyclic torque magnitude). Results showed a mostly detrimental effect of increasing soil temperature on the normalized shear modulus, damping ratio, and threshold shear strain of clayey, silty, and sandy soils when subject to small to medium shear strain levels.

Velocity structure above seismological bedrock estimated from earthquake recordings: an application of diffuse wave-field concept to strong motions in Iran

We present velocity structure inversion for three stations of Iranian Strong Motion Network (ISMN), and one KiK-net station that is used as a benchmark, for the application of diffuse wave-field concept in tectonic and geological setting of the west of Iran. This study compares the results of two existing computer codes for the velocity structure inversion at these sites. The computer codes use different search space parameterization, and error-minimization algorithms. Firstly, the available information on subsurface structure and surface geology from the strong motion stations is introduced. Then, ground motions of MW larger than 4, with PGA of all components less than 50 cm/s2 are used to calculate horizontal-to-vertical spectral ratios of earthquakes (eHVSR) at each station. The observed eHVSR curves are inverted for the velocity structure of the stations, and the results are compared with each other and the information of previous studies. Finally, the eHVSR curves of the mainshock records of the recent MW 7.3 earthquake at two ISMN sites are investigated. The velocity inversion is repeated by considering the shear modulus degradation of several shallow layers. Empirical nonlinear site amplification functions are calculated based on the modified VS structure and the VS structure of the linear ground response for two ISMN stations.Graphical

Effect of particle size on the dynamic properties of tire derived aggregates (TDA)

This paper investigates the dynamic properties of tire derived aggregate (TDA) as a recycled material used in civil engineering applications. The effect of TDA type A particle size on the dynamic response is studied experimentally in detail, and the effects of hysteresis loop asymmetry, shear strain, and confining pressure on the shear modulus and damping ratio are also examined. Undrained strain-controlled cyclic triaxial tests with consolidation stresses ranging from 25 to 200 kPa and shear strains ranging from 0.1 to 10% are used to compare a granulated rubber (GR) specimens and TDA specimens with different maximum particle sizes. The dynamic response of TDA type A differs from that of granulated rubber, because of the larger particle sizes of TDA type A. Although TDA stiffness increases with increasing particle size, the damping ratio is insensitive to TDA particle size in the particle size range considered in this study. However, at all consolidation stresses, the damping capacity of GR is significantly lower than that of TDA. In particular, due to hysteresis loop asymmetry, conventional equations can significantly underestimate the shear modulus and damping ratio of TDA type A. Furthermore, a generalized MKZ model is proposed to estimate the maximum shear modulus at small strains (Gmax) and to predict shear modulus degradation curves for TDA type A with maximum particle sizes ranging from 19.1 mm to 50.8 mm. Comparisons of these shear modulus degradation curves to data reported in the literature and to the experimental results of a TDA sample with a random particle size distribution show that the proposed generalized MKZ model can provide reasonable estimates of the shear modulus of TDA type A.

Maximum shear modulus and modulus degradation curves of an unsaturated tropical soil

The maximum shear modulus (G0) and the modulus degradation curve (G/G0 versus γ) are important information in the evaluation of the soil mechanical behavior, both for dynamic and static loads. Dynamic tests (resonant column and cyclic triaxial tests) are not routinely performed in geotechnical practice in Brazil, and the geotechnical literature on the dynamic behavior of unsaturated tropical soils is limited. This paper presents and discusses seismic dilatometer (SDMT), resonant column, and triaxial test with bender elements and internal instrumentation to determine G0 and the modulus degradation curve in an unsaturated tropical sandy soil profile. It was observed that G0 tends to increase non-linearly with soil suction and net stress (σ - ua). It was also observed that the in situ G0 values determined with the SDMT were higher than those from laboratory tests (bender elements and resonant column). The modulus degradation curves determined with resonant column were used to define the reference curve via SDMT for the studied site. Soil suction influence in shear modulus degradation curves determined with unsaturated triaxial compression tests with local instrumentation is also presented and discussed.

Shear stiffness of sand-fines binary mixtures: Effects of sand gradation and fines content

In this study, a comprehensive experimental programme was carried out on five clean sands of different gradations mixed with low plastic fines using an apparatus that incorporates both resonant column (RC) and bender element (BE) functions. The sand gradation is characterized by uniformity coefficient of host sand (Cus) and grain size ratio (Rd), which is defined as the ratio of the mean grain size of sand to that of fines. The effects of fines content (FC) and sand gradation on small strain shear modulus G0 are analyzed from the experimental results. Both RC and BE test results show that G0 continuously decreases in a non-linear manner as FC increases to 30% and becomes as low as nearly 50% of that of clean sand at the highest FC. The reduction rates with respect to FC are similar regardless of the testing type and the stress dependence of G0 is insensitive to FC. Meanwhile, G0 decreases as Cus or Rd increases at a given FC and void ratio or at a fixed equivalent skeleton void ratio e*. A new predictive model in terms of e* is proposed to evaluate the G0 of sand-fines mixtures to account for the effects of void ratio, confining pressure, FC, and sand gradation within ±20% deviation. Moreover, the rate of shear modulus degradation with shear strain and the damping ratio are higher for sand-fines mixtures with higher FCs.

Resonant Column Calibration and Dynamic Torsional Shear Testing Using Stepped Frequency Sweeps

Abstract This article introduces a new apparatus calibration procedure along with testing protocols, data acquisition, and reduction procedures for a fixed-free resonant column test in which a fixed amplitude sinusoidal torque is applied to the specimen at discrete frequencies over a wide bandwidth that encompasses the resonant frequency. Recently developed resonant column theory, consistent with ASTM D4015-21, Standard Test Methods for Modulus and Damping of Soils by Fixed-Base Resonant Column Devices, is shown to hold for all frequencies in this bandwidth and enables determination of shear modulus, damping, and shear strain amplitude at each frequency. For off-resonant frequencies, shear strain amplitudes are much lower than those at resonance; hence, under a constant applied torque, the method measures values over a range of shear strains. These procedures are facilitated using a spectrum analyzer. The new and more robust approach for apparatus calibration relies on conducting stepped frequency sweeps (SFS) on calibration rods and allows concurrent determination of all apparatus calibration factors, which apply to the full frequency bandwidth for testing soils. Test results on sand are used to illustrate the developed procedures and recommendations are provided for determining shear modulus and damping over the full shear strain range of the apparatus. If the fixed amplitude applied torque is low, the test provides shear modulus and damping at very low strains. For sufficiently high values of the applied torque, a single SFS allows semicontinuous characterization of the shear modulus degradation and shear damping increase behavior. The article provides recommendations for selecting frequency bandwidth, frequency step values, and spectrum analyzer settings. For testing with large input torques, SFS should be from high frequency to low frequency to more accurately capture the response function for strain softening behavior. The total time for SFS is on the order of 10 min, and the number of applied loading cycles can be controlled.

Fatigue properties of a structural rotor blade adhesive under axial and torsional loading

AbstractAxial and torsional fatigue tests at different stress ratios were performed on a structural adhesive designed for wind turbine rotor blades. By employing previously optimized specimens, fatigue properties were recorded without influences of manufacturing‐induced defects such as pores. The Stüssi S–N model was an excellent fit to the data and was combined with a Haibach extension line to account for uncertainties in the gigacycle fatigue regime. A comparison of the results with hand‐mixed specimens revealed significant and load level‐dependent differences, indicating that manufacturing safety factors should be applied to the slope of the S–N curve. The experiments were accompanied by stiffness degradation measurements, which enabled an analysis of Young's and shear modulus degradation interactions. The degradation was modeled using power law fits, which incorporated load level‐dependent fitting parameters to allow for a full description of the stiffness reduction and a prediction of the residual fatigue life of run‐out specimens.

Experimental and numerical investigations on the micro-damage behaviour of glass fibre-reinforced plastics

The formation and influence of micro-damage in glass fibre-reinforced plastics (GFRP) is carried out by numerical and experimental investigations. A quasi-static material characterisation is performed and the stiffness and strength of unidirectional, undamaged material in longitudinal and transverse direction as well as in the 23-plane are determined. Since the desired micro-damage could not be generated in unidirectional laminates due to abrupt failure, a [0∘/90∘]s layup has been identified to be most suitable to generate micro-damage in a reproducible way in the 90° layers, which is done using a tension–tension fatigue test program. During these experiments, micro-damage is detected optically and by means of ultrasonic birefringence, where the latter method shows a reduction in shear modulus due to fibre–matrix debonding prior to final inter-fibre failure. The shear modulus degradation is indirectly measured by the change in the velocity of sound. Since this method is limited to measurements in the 13- and 23-plane, all experiments are accompanied with microstructural simulations with detailed statistical volume elements (SVE), to study the influence of micro-damage under various loading conditions and directions. For loading in fibre direction, no influence on the mechanical properties is observed for the investigated fibre–matrix debonding. However, this is different for transverse loading, where a transverse shear stiffness loss of around 8% results in a decrease of transversal stiffness of around 18%, if the load direction is perpendicular to the damage plane. A similar behaviour is observed for the strength, which is reduced by a factor of 2 for the same configuration.