Small-strain Shear Modulus Gmax Research Articles

The small-strain stiffness of frozen clay soils at different temperatures and initial water contents: Experimental study and predicted model

The small-strain stiffness of frozen soils is important for the constructions of geotechnical structures in cold regions and artificial ground freezing engineering. The variation in the small-strain shear modulus Gmax of frozen soils with decreasing temperature T was studied in detail through temperature-controlled bender element tests, and the effect of initial water content w0 on the changes was detected. A double-upscaling mechanism, involving the compaction of pore ice and bonded contact of solid particles, is proposed to interpret the changes in Gmax and then a predicted model of Gmax is proposed. In this model, the void ratio e and cryogenic suction ψ in frozen soils are the indictors of the double-upscaling mechanism, which can be determined for frozen soils with any T and initial water content w0 with the assistance of SFCC and the Clapeyron equation. The void ratio function and suction function on Gmax incorporated in this model are borrowed or slightly revised from the models for unsaturated soils reported in several relevant literature sources. The good performance of model is found via our own tests and two independent experimental datasets on two frozen clays, and the comparison results show that the predicted results are in reasonable agreement with the measured data.

Hierarchical Bayesian model for predicting small-strain stiffness of sand

This paper develops a hierarchical Bayesian model (HBM) that integrates the physical knowledge and the test data to predict the small-strain shear modulus Gmax for a target sand type. The limited target-specific data are combined with the abundant generic data through a hierarchical structure so that the variability of Gmax within one sand type and across different sand types can be captured. The hyperparameters that characterize the same underlying distribution of physical model parameters across all the sand types are first estimated from the abundant generic data. The model parameters for the new sand type are then updated as the limited site-specific data become available. The approach is illustrated using a generic database and two real examples not covered by the generic database. Multiple possible hierarchical models are compared in terms of model complexity and goodness-of-fit. The results show that the hierarchical modeling of small-strain shear modulus data is reasonable and necessary. The hierarchical model can provide less biased and more accurate predictions of Gmax compared to the commonly used complete pooling model, especially in cases where the site-specific data are quite different from the overall average of the generic database.

Effect of particle size on small strain stiffness of biotreated sands

Particle size is critical for the engineering behavior of sand. For biocemented sand, the studies concerning particle size and small strain stiffness are rare. In this study, particle size is seen as the main grain characteristic contributing to the change of small strain shear modulus Gmax. Isotropic consolidation tests with shear wave velocity measurement were performed to investigate Gmax and Gmax anisotropy of biocemented sand. The test results showed that for the uncemented sands, Gmax increases with the increase of particle size. The constants n and A in Hardin equation decrease and increase with the increase of particle size, respectively, when D50 is larger than around 1.5 mm. For biocemented sand, biocementation is more effective for the sands with smaller diameters. For smaller grain sizes, the contribution of stress increase to stiffness increment is higher than that of biocementation. For coarse sand, biocementation could inhibit the stiffness increase induced by stress increase and at a higher stress level, Gmax of uncemented sand is even higher than that of the biocemented sand. Particle size has no impact on the small strain stiffness anisotropy of uncemented and biocemented sand for the rounded glass beads.

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.

Characterization on the correlation between SPT-N and small strain shear modulus Gmax of Jiangsu silts of China

Small strain shear modulus plays a fundamental role in the evaluation of site response parameters. Only few authors used measured density and shear wave velocity (Vs) to estimate small strain shear modulus. In this study, an attempt has been made to develop the regression relationship between standard penetration test (SPT) N values and the small strain shear modulus (Gmax). For this purpose, field investigations SPT and seismic piezocone penetration test (SCPTU) data from locations in Su-Xin Expressway of China, have been used, which were also used for ground improvement project. The in situ density of soil layer was estimated using undisturbed soil samples from the boreholes. The Vs profiles with depth were obtained for the locations close to the boreholes. The values for small strain shear modulus have been calculated by measured Vs and in situ soil density. About 50 pairs of SPT-N and Gmax values were used for regression analysis. The differences between measured and corrected values which were used in fitted regression relations were analyzed. Most of the existing correlations were developed based on the studies carried out in Japan and in India, where N values are measured with hammer energy of 78%, which may not be directly applicable for other regions because of the variation in SPT hammer energy which in China is about 55%. A new correlation has been generated using the measured values in silts of China. From this study, it is found that uncorrected values of N and modulus gives the best fit regression relations when compared to corrected N and corrected modulus values. With most equation was used for sand and clay, the regression relations between corrected values of N and modulus gives the equation of silts in China.

Predicting the small strain shear modulus of coarse-grained soils

Coarse-grained soils are important geotechnical materials widely used in construction. The contribution of particle size distribution on the small strain shear modulus Gmax of coarse-grained soils has not yet been fully recognized. This paper presents an experimental investigation into the effects of the uniformity coefficient Cu and the mean particle size D50 on the small strain shear modulus of coarse-grained soils. To this end, a series of shear wave velocity tests were conducted at different confining stresses and void ratios on reconstituted specimens covering a wide range of particle size distributions. All tests were performed by taking advantage of a custom-developed measurement device in a large-scale triaxial apparatus. The results demonstrate that Cu and D50 have pronounced but opposite effects on Gmax. Specifically, Gmax decreases with Cu and increases with D50. The effects of Cu and D50 were then quantified to generate two types of empirical equations, type-A and type-B, that are representative of a broad family of Gmax equations accounting for the influence of particle size distribution. The equations are tuned based on model parameters A, x and n. In both equations, n is a function of Cu. The difference between the two types of equations is that x is the function of Cu and D50 and A is the function of Cu in the type-A equation, while x is constant and A is the function of Cu and D50 in the type-B equation. The proposed equations for predicting Gmax were used to produce acceptable estimates for both coarse-grained soils in this study and from existing literature. The findings acquired from this study are expected to provide a reference for estimating the small strain shear modulus of coarse-grained soils at the beginning of the project when the test data have not yet been obtained.

Experimental study to evaluate the effect of particle size on the small strain shear modulus of coarse-grained soils

Abstract Coarse-grained soils are found commonly in nature and are extensively used for a wide range of engineering applications, such as slopes, earth dams, and railway foundations. This study presents an experimental investigation on the effect of mean particle size D50 on the small strain shear modulus Gmax of coarse-grained poorly-graded and well-graded soils. Combined with particle morphology analysis, a series of shear wave velocity tests were performed on pure sand, pure gravel and sand-gravel mixture specimens by taking advantage of a torsional vibration measurement device in a large scale triaxial apparatus. The results demonstrate that Gmax is insensitive to D50 for uniform sand and gravel specimens. On the other hand, Gmax increases gradually with D50 for well-graded sand-gravel mixture specimens. The discrepancy in the relationship between Gmax and D50 for poorly- and well-graded soils is related to the degree of size polydispersity in the specimens.

Study on the small strain shear modulus of saturated sand-fines mixtures by bender element test

The small strain shear modulus Gmax is an important parameter in geodynamic calculation and earthquake response analysis of site. To have a better fundamental understanding of the deformation behaviour of sand-fines mixtures, a total of 105 bender element tests have been performed. It is found that the Gmax is significantly dependent on fines content FC, initial effective confining pressure σ′3c and void ratio e. Furthermore, FC has an obvious influence on the trend of Gmax – e curve, but the impact decreases as σ′3c increases. According to Hardin’s equation, a modified model and an evaluation method of Gmax of sand-fines mixture are proposed and verified. Tests results and example of application indicate that the modified equation accounting for the influence of FC can predict the Gmax of sand-fines mixture satisfactorily.

Suction-Induced Hardening Effects on the Shear Modulus of Unsaturated Silt

AbstractThe small-strain shear modulus Gmax is a key material parameter in modeling the behavior of soils subjected to dynamic loading. Recent experimental results indicate that seasonal weather interaction with near-surface soils causes Gmax to change by up to an order of magnitude in some climates, with a hysteretic response upon drying and wetting. The increase in Gmax during drying and the stiffer response during subsequent wetting have been postulated to be due to plastic hardening during drying. To further understand this behavior, a series of isotropic compression tests were performed on compacted silt specimens at different values of matric suction to evaluate changes in the preconsolidation stress with suction. The Gmax values obtained previously on this silt matched well with a model using a hardening parameter independently derived from the isotropic compression tests, as well as the parameters of the soil water retention curve (SWRC). The model showed an increase in Gmax during drying from an ...

Dynamic properties of dense sand-rubber mixtures with small particles size ratio

In this study, the small strain shear modulus Gmax and the damping ratio Dmin of sand–rubber mixtures with a small particles size ratio Sr (D50rubber/D50sand = .36) are characterised by shear wave propagation using bender elements inserted in a modified triaxial cell. The influence of addition of less than 50% rubber volume fractions Rf in a range of confining pressures varying from 50 to 500 kPa was investigated. The results showed that, for all confining pressures, the shear modulus decreases with increasing rubber volume fractions, while the damping ratio linearly increases. A quasi-conservation of shear modulus up to a volume fraction Rf = .2 and sharp decrease beyond this content is observed. The shear modulus decay and the damping enhancement with addition of rubber fractions are mitigated by increasing confining pressures. An optimal increase of the damping ratio without significant loss of rigidity and a minimal sensitivity to confining pressure for mixtures containing about 10% rubber is highlighted. The shear modulus and damping ratio are power function of the mean effective stress within the range studied.

Effect of A Void Ratio On the Small Strain Shear Modulus Gmax for Coarse - Grained Soils

This article discus about the small strain shear modulus Gmax and the shear wave velocity vs of coarse-grained soils, depending on their state parameters such as the void ratio e. Bender elements installed in a triaxial apparatus were used as a technique for measuring the small strain properties of the soil tested. Gmax and vs are the basic parameters for evaluations of soil responses due to seismic/dynamic loading and for descriptions of the non-linear behaviour of soil in a wide range of strains. The current designs of shallow foundations (settlement, bearing capacity) are discussed. The review of this topic includes previously published empirical equations for Gmax and a description of measurement techniques for bender elements and their evaluation. Sand from the Danube from the locality of Győr was chosen for the testing. A general description of the material is given. A time domain technique was used for the evaluation of the tests. Various input signals and frequencies were used. The samples were tested in a vacuum confinement. The results are compared with the empirical equations proposed in the reviewed literature. Some issues about the testing method and sample preparation observed during the testing are discussed. The type and frequency of input signals, methods for the interpretation of test results, and measurement discrepancies are analysed. Finally, the authors arrive at conclusions from the current laboratory testing. The effect of the void ratio on Gmax and consequently on vs was confirmed.

On the influence of a non-cohesive fines content on small strain stiffness, modulus degradation and damping of quartz sand

The influence of a non-cohesive fines content on small-strain shear modulus Gmax, small-strain constrained elastic modulus Mmax, shear modulus degradation G(γ)/Gmax, damping ratio D(γ) and threshold shear strain amplitudes γtl and γtv has been studied in approx. 130 resonant column (RC) tests with additional P-wave measurements by means of piezoelectric elements. Specially mixed continuous grain size distribution curves of a quartz sand with varying fines contents (0≤FC≤20%, defined as the mass percentage of grains with size d<0.063mm according to DIN standard code) and uniformity coefficients (1.5≤Cu≤50) have been tested at different relative densities and pressures. A significant decrease of Gmax and Mmax with increasing fines content was observed, while the modulus degradation curves G(γ)/Gmax were found rather independent of FC. A pressure-dependent decrease of the damping ratio and a slight increase of the threshold shear strain amplitudes γtl and γtv with fines content were measured. Extensions of several empirical equations for Gmax, Mmax, G(γ)/Gmax and D(γ) considering the influence of the fines content are proposed in the paper.

Influence of cyclic loading history on small strain shear modulus of saturated clays

Small strain shear modulus Gmax is an essential parameter in soil dynamics, and it is usually estimated based on the Hardin and Richart equation. However, many previous researches on sands have indicated that the Hardin and Richart equation does not consider the influences of cyclic loading history on Gmax. In this paper, effects of cyclic loading history on Gmax of saturated clays under undrained conditions are studied using a combination device of piezoelectric-ceramic bender element system and cyclic triaxial apparatus. The dynamic pre-loading includes both relatively high amplitudes of cyclic stresses and cyclic strains. Gmax without cyclic loading history is also investigated for the comparison purpose. Test results show that, at the same effective stress, both cyclic strain history and cyclic stress history will induce reduction of Gmax compared to the corresponding Gmax values with non-cyclic loading effects. In strain-controlled tests, the reduction of Gmax is slight and relatively stable; while in stress-controlled tests, the reduction of Gmax increases suddenly and remarkably when the effective stresses degrade to a certain degree. The comparison between double amplitude axial strain and residual excess pore water pressure behaviors show that the remarkable reduction of Gmax can demonstrate the cyclic failure of saturated clays.

On the interpretation of seismic cone penetration test (SCPT) results

Abstract The paper deals with the methodology of performing and interpretation of seismic cone penetration test (SCPT). This type of test is used to determine velocity of the seismic wave in the soil medium. This study is focused on shear wave. The wave is triggered on the ground surface by hitting an anvil with a sledgehammer. Then, vibrations induced at different depths are measured. Based on recorded measurements wave velocity (Vs) and thus also small strain shear modulus Gmax may be calculated. An interpretation of exemplary seismic test results is presented. Crossover and cross-correlation methods are discussed and another, more adequate one is featured and then applied in the interpretation example. Conditions for correct test performance and interpretation are discussed.

Role of Particle Angularity on the Mechanical Behavior of Granular Mixtures

AbstractParticle shape affects the mechanical behavior of soils, including packing density, stiffness, volume change during shear, and strength. Laboratory experiments conducted to study the mechanical response of sand mixtures made of round and angular grains show an increase in void ratio, small strain shear modulus Gmax (constant fabric), oedometric compressibility CC (fabric changes), and friction angle but a decrease in lateral stress coefficient k0 as the mass fraction of angular particles increases. These results reflect variations in particle mobility and highlight the relative role of contact stiffness versus fabric changes.

Resonant Column Test for Unsaturated Soils With Suction–Saturation Control

Abstract Comprehensive characterization of the small strain shear modulus Gmax of an unsaturated soil specimen during hydraulic hysteresis requires precise control of the stress state, matric suction, degree of saturation, as well as knowledge of the void ratio. This paper describes the details and typical results from a test method which incorporates the axis translation technique for suction control, a flow pump for degree of saturation control, and a vertically oriented proximeter to infer changes in void ratio into a fixed–free resonant column setup. A unique aspect of this test method is the operation of the flow pump to reach equilibrium points on the hysteretic soil–water retention curve (SWRC) for measurement of Gmax. The flow pump, which controls water flow to or from the soil specimen through a high air-entry ceramic disk, is guided using a feedback loop involving the matric suction measured at the boundary of the specimen. Values of Gmax were measured at different equilibrium points on the primary drainage path of the SWRC up to the point of water occlusion, then along a scanning imbibition path of the SWRC. The results indicate a greater shear modulus during imbibition, consistent with trends and magnitudes noted in the technical literature.

Influence of the Grain-Size Distribution Curve of Quartz Sand on the Small Strain Shear Modulus Gmax

The paper presents a study of the influence of grain-size distribution curve on the small strain shear modulus Gmax of quartz sand with subangular grain shape. The results of 163 resonant column tests on 25 different grain-size distribution curves are presented. It is demonstrated for a constant void ratio that while Gmax is not influenced by variations in the mean grain-size d50 in the investigated range, it significantly decreases with increasing coefficient of uniformity Cu=d60/d10 of the grain-size distribution curve. Well-known empirical formulas (e.g., Hardin’s equation with its commonly used constants) may strongly overestimate the stiffness of well-graded soils. Based on the RC test results, correlations of the constants of Hardin’s equation with Cu have been developed. The predictions using Hardin’s equation and these correlations are in good accordance with the test data. Correlations of the frequently used shear modulus coefficient K2,max with Cu and empirical equations formulated in terms of relative density, are also given in the paper. A comparison of the predictions by the proposed empirical formulas with Gmax-data from the literature and a micromechanical explanation of the experimental results are provided. Correction factors for an application of the laboratory data to in situ conditions are also discussed.

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

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

Use of Piezocone to Predict Maximum Stiffness of Venetian Soils

A comprehensive geotechnical in situ and laboratory investigation into the soils forming the Upper Quaternary basin of the Venetian Lagoon has been carried out. In addition to standard tests, measurements of shear wave velocity were performed using crosshole, seismic piezocone, bender element system, and resonant column tests. Despite the incompatible strain levels of the seismic and piezocone tests, it is shown that piezocone tip resistance and excess pore pressure can be used for a preliminary estimate of the small-strain shear modulus Gmax for the Venetian soils.

Laboratory and field determinations of small-strain shear modulus for a structured Champlain clay

Values of small-strain shear modulus Gmax, for a Champlain Sea clay deposit were obtained both under an embankment built 18 years ago, and outside of the area influenced by this embankment. The small-strain shear moduli Gmax were measured in the laboratory by using resonant column tests and in the field by spectral analysis of surface waves. In addition to verifying the two methods, comparison of the in situ and laboratory values allowed evaluation of the influence of the sampling and the need to correct the laboratory values to account for the age of the deposit. The test program also made it possible to verify the influence of the deposit's consolidation and the existing models predicting small-strain shear moduli in clay deposits. Key words : shear modulus, shear-wave velocity, resonant column, in situ test, surface waves, soft clay.