Resonant Column Research Articles

Macro- and Micromechanical Assessment of the Influence of Non-Plastic Fines and Stress Anisotropy on the Dynamic Shear Modulus of Binary Mixtures

Resonant column tests were carried out on Hostun sand mixed with 5%, 10% and 20% non-plastic fines (defined as grains smaller than 0.075 mm) in order to quantify the combined influence of the void ratio (e), anisotropic stress state (defined as σv′/σh′) and fines content (fc) on the maximum small-strain shear modulus Gmax. A significant reduction in the Gmax with increasing fc was observed. Using the empirical model forwarded by Roesler, the influence of e and σv′/σh′ on Gmax was captured, although the model was unable to capture the influence of varying fines content using a single equation. From the micro-CT images, a qualitative observation of the initial skeletal structure of the ‘fines-in-sand’ grains was performed and the equivalent granular void ratio e* was determined. The e was henceforth replaced by e* in Roesler’s equation in order to capture the variation in fc. The new modification was quantified in terms of the mean square error R2. Furthermore, the Gmax of Hostun sand–fine mixtures was predicted with good accuracy by replacing e with e*. Additionally, a micromechanical interpretation based on the experimental observation was developed.

Experimental Study on Dynamic Modulus and Damping Ratio of Rubber–Sand Mixtures Over a Wide Strain Range

This paper systematically investigates the dynamic behavior of sandy soils mixed with recycled tire rubber over a wide strain range in the order of 10[Formula: see text]–10[Formula: see text], using combined resonant column and cyclic triaxial tests for measurement of the shear modulus and damping ratio. The experiment integrates small-strain tests using a resonant column apparatus and large-strain tests using a cyclic triaxial apparatus. The results demonstrated that the addition of rubber particles significantly enhances the linear elastic properties of the host sandy soils and improves the critical shear strain from which the rubber–sand mixtures change from linear to nonlinear stress–strain behavior. The critical shear strain is therefore introduced as the function of rubber content (RC), to identify the influence of RC on the strain-dependent dynamic properties of the host sandy soils. Then, a well-calibrated prediction formula is applied in conjunction with the concept of binary packing material to describe the behavior of the host sandy soils with various RC. Remarkably, the obtained normalized shear modulus and damping ratio vs. shear strain relationships address the limitations of existing testing methods to simultaneously capture the soil dynamic properties at low-strain (stiffness) and the large-strain (energy dissipation) regimes. The model constants can be simply determined through a unique set of explicit expressions which incorporate some basic index properties of the host sand and recycled tire rubber. In this regard, the proposed procedure provides a significant advantage in the evaluation of strain-dependent dynamic properties of rubber–sand mixtures in practice.

Effects of specimen size and inertia on resonant column tests applied to sands

The availability of a Stokoe type resonant column apparatus adapted to accommodate specimens of different size motivated a closer look into the details of the calibration procedure, with the aim to refine it so as to ensure that the derived shear moduli are independent of the specimen size. The starting point for the investigation is the experimental evidence reported by previous studies that the effective drive head inertia depends on the measured resonant frequency. In the paper, the theoretical background of the data reduction procedure is re-visited, and two calibration approaches are analyzed and applied for three distinct specimen sizes: i) the common technique using added masses, and ii) one without added masses relying on the system response with presumed calibration bar dynamic properties. The geometry of the calibration bars is varied, and the effects of non-planar torsion are assessed. The first approach, with frequency and specimen size dependent drive head inertia, is subsequently implemented in test series on three sands with different grain size distribution curves. The specimen size is varied. The experimental results in terms of shear modulus and damping ratio at small and intermediate shear strains yield almost coinciding curves for all specimen sizes considered, thus confirming the adequacy of the data reduction procedure. Known features of the dynamic soil behavior are well reproduced. The agreement with results for similar sands reported in the literature is also very good. • Theoretical background of evaluation and data reduction procedure are revisited. • Calibration techniques with/without added masses are analyzed and assessed. • Necessity of drive head inertia dependent on frequency and specimen size is shown. • Range of eigenfrequency in calibration must comply to that anticipated in the soil tests. • Proper calibration yields modulus and damping largely independent of specimen size.

Dynamic Characteristics of Coral Sand in the Condition of Particle Breakage

To study the influence of coral sand particle breakage on its dynamic characteristics, taking the South China Sea coral sand as the research object, one-dimensional consolidation test was conducted to prepare different particle breakage degree samples, and then, the GCTS resonant column test was carried out on these samples. The results show that with the degree of coral sand particle breakage increases, the maximum dynamic shear modulus of coral sand first increases and then decreases, and the minimum damping ratio also shows a similar trend. In addition, based on Hardin’s theory of the relative breakage, this study proposes a new modified relative breakage B r ′ for describing particle breakage and establishes a relationship between the maximum dynamic shear modulus and the modified relative breakage B r ′ .

Low-frequency seismic responses during microbial biofilm formation in sands

This study investigates changes in low-frequency attenuation responses of sands during microbial formation of soft viscous biofilms, or extracellular polymeric substances (EPS). The resonant column experiments were conducted with two model bacteria Shewanella oneidensis MR1 and Leuconostoc mesenteroides, while monitoring changes in the wave velocities and damping ratios associated with EPS formation in sands. The results show that the accumulation of soft, viscous EPS hardly changes the wave velocities, both the shear and flexural modes. By contrast, the low-frequency attenuations, both torsional and flexural damping ratios, show significant increases with the accumulation of highly viscous EPS. It is found that the contribution of EPS to seismic responses of water-saturated sands is mainly limited to the pore fluid component, causing additional energy dissipation during wave propagation, but with no or minimal impact on skeletal stiffness or no involvement in seismic stress transfer. With these unique and unprecedented low-frequency seismic data of biofilm-associated sands, the results suggest that the formation and accumulation of soft, viscous EPS or biofilms by bacterial activities can be detected by monitoring seismic attenuation and can also alter the seismic attenuation responses of sands, such as the case under earthquake loading or blast-induced compaction.

Effect of the driving system on Hardin-type resonant columns

Resonant column (RC) devices have been widely used for estimating the shear modulus and damping ratio over a broad range of shear strain amplitudes. Although RCs significantly improve the assessment of soil dynamic properties, some challenges mainly associated with the calibration process still exist. This paper discusses the effect of the driving system rigidity on the measurements performed on a Hardin-type RC. It is shown that the use of a rigid connection between the soil specimen and the driving mass could significantly influence the obtained results. The findings of this study indicate that the apparatus resonant frequency of the Hardin-type RC device should be lower than the resonant frequencies likely to be measured during testing of the specimens.

Effect of different fibers on small-strain dynamic properties of microbially induced calcite precipitation–fiber combined reinforced calcareous sand

Microbially induced calcite precipitation (MICP)–fiber combined reinforcement through the addition of fibers during the MICP process is a novel, natural, and green technique for foundation improvement, which can effectively enhance the mechanical properties of cemented soil. However, the small-strain dynamic properties of this method remain unexplored. The effects of different polyester fiber and hemp fiber contents (0%, 0.1%, 0.2%, and 0.4%) on the dynamic properties of the MICP–fiber combined reinforced calcareous sand under small-strain conditions were studied using resonant column tests, scanning electron microscopy (SEM), and atomic force microscopy (AFM). The maximum dynamic shear modulus of the MICP–fiber combined reinforced calcareous sand under small-strain increases with the fiber content; the stiffness degradation rate of the dynamic shear modulus ratio of the test sample increases with the addition of two types of fibers, and the addition of hemp fibers greatly boosts the increase rate of the damping ratio. The SEM results indicate that excessive fibers distributed between the sand particles occupy the nucleation sites of bacteria, hinder the bonding between sand particles, and ultimately affect the dynamic shear modulus parameters of the sample. The AFM results show that the hemp fiber has much greater surface roughness than the polyester fiber. Therefore, the change rate of the damping ratio of the hemp fiber-doped MICP–fiber combined reinforced calcareous sand is much greater than that of the polyester fiber-doped sample. This is the first report on the basic mechanism of the small-strain dynamic properties of the MICP–fiber combined reinforced calcareous sand with different fiber contents and types. Furthermore, it provides a new theoretical basis for related research on improving the dynamic properties of sand thus reinforced.

Effect of Mean Grain Size on the Small‐Strain Dynamic Properties of Calcareous Sand

Calcareous sand was selected as the prior material for island reclamation in many coastal regions. The mechanical properties of the granular materials are greatly affected by their grain size distribution conditions. The shear modulus and damping ratio are two important parameters for earthquake ground response analysis and liquefaction evaluation. A series of resonant column tests had been performed on calcareous sands with varying median grain diameter and uniform coefficient. The dependence of the shear modulus and damping ratio of the calcareous sand on grain size has been confirmed in this examination. The test results reveal that the shear modulus decreases with a rise in shear strain for calcareous sand samples at a given confining pressure and relative density. The maximum shear modulus tends to increase with confining pressure and relative density. On the maximum shear modulus and void ratio plane, the trend lines of the measured results shift toward up and right position with a rise in grain diameter. The measured results indicate that the influence of uniform coefficient on the maximum shear modulus is neglectable. A revised empirical equation based on the Hardin model had been proposed considering the influence of grain diameter to estimate the maximum shear modulus of calcareous sand. The predicted values show satisfactory agreement with the measured results. The results manifest that the effect of grading condition on small‐strain dynamic properties of calcareous sands cannot be neglected for the evaluation of seismic safety for reclamation engineering sites.

Small strain stiffness for granite residual soil: effect of stress ratio

Most previous studies have focused on the small strain stiffness of sedimentary soil, while little attention has been given to residual soils with different properties. Most studies also neglected the effects of the deviator stress, which is extensively involved in civil engineering. This note considers the effects of the deviator stress on the small strain stiffness of natural granite residual soil as established from resonant column tests performed under various stress ratios. Although increasing the stress ratio results in a greater maximum shear modulus for both natural and remolded residual soils, remolded soil is more sensitive to changes in the stress ratio, which highlights the effects of soil cementation. The data herein offers new insights to understand the stiffness of residual soil and other weathered geomaterials.

The effect of particle size and hydrate status on dynamic mechanical properties of hydrate‐bearing sediments

AbstractDynamic mechanical properties of natural gas hydrate (NGH) reservoirs are extremely important owing to their critical role in drilling safety and reservoir stability during NGH development. However, the comprehensive influence of reservoir skeleton and hydrate status on the dynamic mechanical properties of hydrate‐bearing sediments (HBS) has rarely been reported. In this study, three types of sandy sediments with different particle size were simulated. A customized resonant column system was used to synthesize HBS and to test the dynamic mechanical properties of the HBS under the conditions of different confining pressures and shear strains. In addition, the dynamic mechanical responses of the hydrate‐free and hydrate‐dissociated specimens were comprehensively studied to further demonstrate the dominant role of hydrate status and skeleton‐hydrate interactions on the dynamic mechanical properties of HBS. The results show that the shear moduli of the HBS specimens increase exponentially with an increase in confining pressure and decrease in amplitude strain. However, the damping ratios decreases with an increase in confining pressure and decrease in amplitude strain. With an increase in the median particle size (D50) of the simulated sediments, the shear moduli tend to increase, whereas the damping ratios decreas. In addition, the hydrate occurrence decreases differences in moduli between fine‐, medium‐ and coarse‐skeleton specimens, and the enhancement effect of hydrate on the mechanical properties of the specimen is the maximum for the fine sediment specimens. Interestingly, we find that the modulus of the hydrate‐dissociated specimen is relatively smaller than that of the hydrate‐free specimen, which implies that the structure of the sediments could be rearranged and weakened due to the hydrate formation‐dissociation processes.

Evaluation of the damping ratio of soils in a resonant column using different methods

This paper addresses the differences between two approaches of damping estimation in the resonant column testing: Steady-State Vibration (SSV) and Free Vibration Decay (FVD) method, at small (<0.005%) to medium (0.07%) strain range. The tests were conducted on “two types of reconstituted sands” and “two types of clayey soils” at different relative densities and confining pressures. The test results suggested to use the SSV method in small strain damping measurement and the FVD method (two or three successive cycles) in medium strain damping measurement. A systematic decrease in the damping with the increasing number of cycles was observed up to a certain strain level in the FVD method. Furthermore, the effects of relative density, confining pressures, soil types on the damping ratio derived from the two methods for the chosen soils were studied. The results showed that the damping ratio of clayey soils exhibits a little higher value than those of sandy soils.

Characterizing the Effect of Water Content on Small-Strain Shear Modulus of Qiantang Silt

Due to the impact of natural and artificial influence, such as waves, tides, and artificial dewatering, the small-strain shear modulus of soils may vary with the water content of soil, causing deformation of excavations and other earth structures. The present study used a resonant column device to investigate the effects of water content, void ratio, and confining pressure on the small-strain shear modulus of a silt extracted from an excavation site near Qiantang River in Hangzhou, China. The test results revealed that the effects of the three factors are not coupled and can be characterized by three individual equations. In particular, the small-strain shear modulus decreases with increasing water content under otherwise similar conditions, which can be characterized by a power function. The classical Hardin’s equation is modified to consider the effect of water content by introducing an additional function of water content.

Inspection of various grain morphology parameters based on wave velocity measurements on three different granular materials

In this study, correlations between the shear wave velocity of granular materials and various descriptors of grain morphology are investigated. Based on a comprehensive study of the literature different shape descriptors used in previous studies are summarized. The suitability of the various grain shape descriptors to describe the shear wave velocities of three materials with significantly different grain shape, crushed glass, natural sand and glass beads, is analyzed. The shear wave velocities are obtained from a series of torsional resonant column tests under different confining pressures. Recommendations regarding the suitability of certain morphological parameters are given. Lastly, a novel graphical presentation by means of the grain shape distribution curve is proposed, which eases the comparison of various granular materials and provides an information about the range of a certain grain shape descriptor which can be quantified by a shape uniformity coefficient. Correlations of this coefficient with the shear wave velocity data are also explored and found to yield comparable trends like the mean grain shape which has been employed in past studies.

In-situ properties of Poisson's ratio based on KiK-net seismic observations

Poisson's ratio has been considered as an important parameter for the analysis of a geotechnical structure under both static and dynamic loads by many researchers. However, most of the studies have been performed using laboratory test such as resonant column and bender element, or the field test without seismic data such as suspension logging, seismic cross-hole and seismic cone penetration, the studies using the geophysical method based on seismic observations are rare. In this study, in-situ properties of Poisson's ratio are investigated based on KiK-net seismic data. The methods for extracting the in-situ Poisson's ratio and describing its variation with shear strain considering effect of groundwater are firstly introduced. Then, an empirical model for the in-situ assessment of small-strain Poisson's ratio is proposed based on the studies of the effects of vertical effective stress, groundwater and rock layer type. Moreover, it is found that the change threshold of the in-situ Poisson's ratio is larger than the laboratory test results. The results of the study are verified in part based on the fact that they are generally consistent with the theoretical and experimental relationships in many ways, and they can be employed as the reference to the engineering practice and related studies, such as site response analysis and specifying material constitutive relationships for the numerical analysis.

Effect of Slenderness Ratio of the Specimen on Resonant Column Test Results

Abstract To investigate the effect of the slenderness ratio (L/d) of the specimen, resonant column (RC) tests were conducted on dry sand specimens by using three different values of L/d, namely 2, 3, and 4, keeping the same diameter (d = 50 mm) to measure the shear moduli and material damping associated with the shear strain varying approximately from 0.0004 to 0.03 %. For the sake of the comparison, bender element (BE) tests were also performed on the same specimens to examine the effect of L/d on the shear moduli. Different combinations of relative densities and isotropic confining pressures were employed. The current experimental findings based on the simplified theory, which is widely used for analyzing the RC test results, reveal that the measured shear moduli of the specimens become higher for a slender specimen. On the other hand, the damping values were found to be only marginally affected with the changes in L/d. For greater L/d, generally the damping values were found to be slightly higher, especially with greater relative densities. The BE tests, on the other hand, hardly illustrate any variation in shear moduli with the changes in L/d. The shear wave velocities (Vs) from the BE tests were found to be a little greater as compared with the RC tests, and the difference between two sets of results becomes narrower with an increase in L/d. This study reveals that it will be more appropriate to use a L/d equal to 4 rather than 2, especially when testing at isotropic confining pressure ≥ 500 kPa.

DEM analysis of small and small-to-medium strain shear modulus of sands

Despite the significant progresses in discrete-based numerical studies of granular materials, most efforts have been placed in the study of large deformation problems and there are many unresearched areas in the multi-scale analysis and the influence of grain-scale parameters on the bulk behavior of granular systems in the regime of small strains. In this work, we present a numerical investigation into the small and small-to-medium strain shear modulus of sands performing DEM analyses, exploring the influence of grain-scale parameters, and attempting to link micromechanical-based quantities with the macroscopic behavior of granular materials. For the calibration, we used real experimental grain-scale data for the contact stiffness and interparticle friction, and resonant column macroscopic test results on a quartz sand were used as the benchmark model sample. Subsequently, a parametric DEM study was carried out investigating the influence of Young’s modulus (and contact stiffness) as well as the interparticle friction on macroscopic stiffness and stiffness reduction curves, and additional insights were obtained based on the inferred contact forces and force networks, coordination number and fabric anisotropy. The numerical results contribute to understand the differences between different sand types as reported in the literature in the regime of small-to-medium strains.

Geomechanical property evolution of hydrate-bearing sediments under dynamic loads: Nonlinear behaviors of modulus and damping ratio

Understanding dynamic mechanical properties of hydrate reservoirs is essential for ensuring safety and economic hydrate production. The modulus, damping ratio, and Poisson's ratio are critical parameters in interpreting seismic surveys and well logging data and the stability prediction of hydrate reservoirs during production or under earthquake conditions. In this paper, the shear and Young's moduli and damping ratios were evaluated by conducting resonant column tests on the synthetic hydrate-bearing specimens with respect to hydrate saturation, stress state, strain range, void ratio, pore pressure, and stress history. Regardless of the test conditions, a distinct increase in the damping ratio with an increase in the modulus of hydrate-bearing specimens could be used to identify the hydrate occurrence. The stress and hydrate improve the modulus of hydrate-bearing specimens; however, the exponent enhancement of stress on the modulus of hydrate-bearing specimens is suppressed by high hydrate saturation. In addition, a rapid nonlinear decrease in the normalized modulus of hydrate-bearing specimens with high hydrate saturation occurred under identical strain increments, and the corresponding damping ratio also increased rapidly. Along with the modulus data of other synthetic and natural hydrate-bearing specimens determined using various methods, a definite exponential relationship between Eh = E0 ∗ en∗Sh and different parameter settings was established to satisfy various application conditions. In contrast, the Poisson's ratio of hydrate-bearing sediments should be determined with caution because of its relationship with specimen deformation or damage.

A Modified Resonant Column Device for In-Depth Analysis of Vibration in Cohesive and Cohesionless Soils

With the accelerating progression of global climate change, switching to renewable energy sources is inevitable. Wind energy is a fast-growing branch of this industry, and according to the 2021 Global Wind Report, this trend must continue in order to limit the increase in global average temperature. While onshore wind turbines still dominate and account for most recent growth, offshore wind turbines are becoming a promising alternative for geographical, power density-related or even aesthetic reasons. Offshore wind turbines are subjected to more complex loading conditions and proper foundation design is very challenging, however, this is crucial for ensuring and maintaining the structure’s reliability. Soil dynamic tests are one of the bases for wind turbine foundation design. Technical regulations in many countries require such tests to be carried out in a Resonant Column (RC). In this study, a modification of the RC sensors and data acquisition system was introduced in order to conduct in-depth analysis of vibrating soil specimens. The new set of sensors contained five additional accelerometers (Analog Devices ADXL345) attached to the surface of a soil specimen that was subjected to dynamic loading. These accelerometers sent the data to a new data acquisition system, an ARM microcontroller with software developed by authors. The software was able to process test results synchronously with the original software of the RC device. Additionally, the load control system was supplemented with a current pulse generator, which makes it possible to observe the propagation of high-frequency mechanical waves in the tested materials. The modified dynamic testing equipment allowed for the measuring of accelerations and displacements at specific selected points located along the height of the sample, with sampling frequency more than three times higher than that offered by the sensors originally built into the RC device. As a result, some additional dynamic phenomena (i.e., disturbances in the uniformity of vibrations of non-cohesive materials, specimen–device contact imperfections) were observed in the tested soil specimens which remained undetected in standard RC test.

Effect of Confining Pressures on the Dynamic Response Characteristics of Niger Delta Clay Soils

The study investigated the earthquake potential in Niger Delta region of Nigeria. A series of resonant column and bender element test was performed on compacted clay soil samples across the investigated Niger Delta States, which showed the influence of confinement on frequency, shear modulus, shear velocity and damping ratio. The confinement in clay was high. The frequency response increases with pressure increase. Also, the resonance column test at various confinements revealed changes in shear modulus, accelerometer output and damping ratio. Thus, there was high variation in the test parameters as confinement pressure was increased. Similarly, the bender element tests also showed that pressure has effect on shear wave-velocity, shear modulus and damping ratio confinement. Although, unlike Resonance Column tests, the shear modulus and shear wave-velocity generally increased as confinement pressure was increased, while for damping ratio it decreases as confinement pressure was increased. The variations in resonance column/binder element test parameters showed that the Niger Delta region, as an oil and gas area, is susceptible to earthquake. Therefore, continuous monitoring of oil exploration activities must be put in place.

Nonlinear stiffness and damping characteristics of gravelly crushed rock: Developing generic curves and attempting multi-scale insights

Gravelly soils and aggregates composed of crushed rock are commonly encountered in a variety of applications in geotechnical, transportation and infrastructure engineering projects, while gravel-sized materials, often in the form of soil mixtures, are also found in natural deposits in alluvial, glacial and shoreline environments. Despite the significant amount of research being conducted on the dynamic properties of soils, less attention has been given on the assessment and modeling of the behavior of gravel-sized materials, particularly in the range of medium strains, where stiffness and damping have a nonlinear relationship with strain amplitude. In the present study, laboratory data stemming from resonant column tests published in the literature are re-analyzed with emphasis on gravel-sized crushed rock of strong and hard grains and the range of small-to-medium strain amplitudes. The test samples had a mean grain size in the range of 1.5–10 mm and a coefficient of uniformity from 1 to 13. The stiffness reduction curves are studied by means of the Oztroprak-Bolton hyperbolic model and from the data analysis, correlations are developed for the reference strain, the linear threshold strain and the curvature coefficient, which are then incorporated as model parameters into the hyperbolic expression. For the damping increase curves, a correlation is proposed with respect to the stiffness values, taking into account normalizations for small-strain material damping. The analysis led to the development of generic stiffness reduction and damping increase curves which are compared with previous data and models published in the literature for a variety of soils. These comparisons show that for crushed rock of irregular-in-shape grains (i.e., elongated and angular grains), significant differences are observed on the stiffness reduction and damping increase curves between gravels and sands with the gravels displaying higher non-linearity with shifted reference strain and linear threshold strain to smaller values. This was particularly highlighted for uniform gravels compared with uniform sands, whereas a convergent of the generic curves between sands and gravels was observed for high values of the coefficient of uniformity. Thus, existing relationships developed on the basis of granular materials of rounded particles and specifically expressions on the basis of sand-sized materials should be cautiously used in the deformation analysis of problems involving gravelly crushed rock and natural soils of irregular-in-shape grains, particularly for uniform to poorly graded materials.