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Abstract Mixtures of a fine sand with platy shell fragments have been tested under drained monotonic and high-cyclic loading. The content (0 to 40 %) and the size of the platy shell particles in the mixtures were varied. Comparative tests have been also performed on a mixture containing 40 % coarse sand and gravel particles instead of the shells. In the cyclic tests different stress amplitudes, initial relative densities and average stresses have been tested on the various mixtures. The strain accumulation rates were found to increase with growing content of shell particles. This can be primarily attributed to the more well-graded grain size distribution curves of the sand-shell mixtures. Particle breakage effects were almost absent in the cyclic tests as demonstrated by sieve analysis. Dependencies between the parameters of a high-cycle accumulation (HCA) model and the content of shell particles are analyzed. Amongst others, an extraordinary low dependence of the strain accumulation rate on strain amplitude (parameter C ampl < 1) has been observed for larger amounts of shell particles in the mixtures. Highlights • Mixtures of sand with different percentages of shell fragments have been produced. • They have been tested under drained monotonic and high-cyclic loading. • Strain accumulation rates increase with increasing content of shell fragments. • Direction of accumulation is almost independent of content of shell fragments. • No breakage of shell particles under high-cyclic loading has been observed. [ABSTRACT FROM AUTHOR]

In order to predict permanent deformations by means of a high-cycle accumulation (HCA) model, a random cyclic loading, i.e. a loading with frequently changing amplitudes, has to be grouped into packages of cycles each with a constant amplitude. Based on a series of drained triaxial tests on fine sand, in which the same cycles have been applied either in an order with frequently changing amplitudes or in packages of cycles, it is demonstrated that such bundling is conservative. Predictions by the HCA model of Niemunis et al. [19] are confronted with experimental data and with other approaches for the prediction of permanent deformations under packages of cycles, among them the frequently cited procedure of Stewart [26]. An effect not captured in the HCA model or in any other approach yet has been detected in another series of tests with a change of the average stress between bundles of cycles: The monotonic loading associated with this change can partially or fully erase the memory of the sand regarding its cyclic preloading history. [ABSTRACT FROM AUTHOR]

The present work is concerned with the analytical investigation of the effect of polydispersity on the elastic moduli of granular media. Empirical formulas are available for the estimation of elastic parameters of sands, especially for the shear modulus, usually as a function of the void ratio and the effective mean pressure. These relationships do not reflect the dependence of the small strain shear modulus on the granulometric material properties and especially on the non-uniformity index. This dependence is however strong as shown by experimental results. In the present work it is attempted to derive this qualitative dependence analytically, so as to provide a better understanding of the observations. Two different forms of granulometric curves are considered and the small strain moduli derived for isotropic and triaxial compression. In spite of the purely theoretical nature of the approach, the results are in good agreement with the experiments. A simplified formula is suggested, to facilitate application. [ABSTRACT FROM AUTHOR]

The high-cycle accumulation (HCA) model for sand proposed by Niemunis et al. (2005) [16] has been developed based on numerous drained cyclic triaxial tests with 100,000 cycles. In the present paper the validity of the HCA model, in particular its function f N and flow rule m , for larger numbers of cycles is inspected. For that purpose, drained long-term cyclic triaxial tests with 2 million cycles have been performed on 13 clean quartz sands with different grain size distribution curves. For all tested sands, the function f N , describing the shape of the strain accumulation curves ε acc ( N ) , has been found suitable up to 2 million cycles. The same applies to the cyclic flow rule m , determining the ratio of the volumetric and deviatoric strain accumulation rates. Based on the data from the long-term tests, correlations between the HCA material parameters entering f N and characteristics of the grain size distribution curve ( d 50 and C u ) have been improved for the application to 2 million cycles. These correlations are suitable for a simplified calibration of the HCA model and were validated up to 100,000 cycles only so far. [ABSTRACT FROM AUTHOR]

Depending on the boundary conditions a high-cyclic loading (=large number of cycles N ≥ 10 3 , small strain amplitudes ε ampl ≤ 10 − 3 ) may either lead to strain accumulation or stress relaxation in the soil. This paper concentrates on stress relaxation. For a cyclic loading applied under undrained triaxial conditions, the high-cycle accumulation (HCA) model of Niemunis et al. [23] predicts a relaxation of average effective stress until a stress ratio η av = q av / p av = M cc (triaxial compression) or M ec (extension) is reached. M cc and M ec are very similar to the critical stress ratios M c and M e known from monotonic shear tests. The average effective stresses finally reached after a sufficiently large number of cycles are called “stress attractors” herein. A zero effective stress state (liquefaction, p av = q av =0) is obtained as a special case of a stress attractor. However, up to now the stress attractors predicted by the HCA model were based on the data from drained cyclic tests only. In the present study they have been approximately confirmed by stress relaxation experiments, i.e. undrained cyclic triaxial tests with stress or strain control. These tests have been performed on a fine sand, varying the initial values of density, mean pressure and stress ratio as well as the stress or strain amplitude. [ABSTRACT FROM AUTHOR]

Abstract: Approx. 120 resonant column (RC) tests with additional P-wave velocity measurements using piezoelectric elements have been performed on 19 clean quartz sands with piecewise linear, gap-graded, S-shaped or other smoothly shaped grain size distribution curves. For each material different pressures and densities were tested. It is demonstrated that the extended empirical equations for the small-strain constrained elastic modulus proposed by the authors in an earlier paper work well also for most of the more complex grain size distribution curves tested in the present study. These equations considering the influence of the uniformity coefficient of the grain size distribution curve were developed based on the data from tests on linear gradations. A further improvement of the prediction for the more complex grain size distributions can be achieved if the correlation equations are applied with a specially defined average inclination of the grain size distribution curve. Such an improvement is demonstrated not only for the small-strain constrained elastic modulus, but also for small-strain shear modulus, modulus degradation and Poisson's ratio. [Copyright &y& Elsevier]

The modulus degradation curves, , and the damping ratio, , of 27 clean quartz sands with specially mixed grain size distribution curves were measured in approximately 280 resonant column tests. For each material, tests with various pressures and densities were performed. Based on the test data it is demonstrated that the shear modulus degradation is larger for higher values of the uniformity coefficient, , while it is rather independent of the mean grain size, . The observed dependence of curves is not adequately described by common empirical equations because these equations were developed based on tests on uniform granular materials. To consider the influence of the uniformity coefficient, the paper proposes correlations of the parameters of the common empirical equations with . Good agreement between the prediction of the extended empirical equations and the experimental data collected from the literature is demonstrated. Furthermore, the test data reveal that the curves of damping ratio, , and the threshold shear strain amplitude indicating the onset of residual deformation accumulation, , are rather independent of and . The threshold shear strain amplitude at the onset of modulus degradation, , slightly decreases with increasing values of and . [ABSTRACT FROM AUTHOR]

Although the hypoplastic models for sands have exhibited good predictive capability in monotonic loading, they are not able to reproduce memory effects and predict excessive plastic accumulation under cyclic loading. To overcome these issues, a loading surface has been incorporated into a hypoplastic model. This surface is capped and has two hardening variables. Notions from the bounding surface plasticity were borrowed in order to formulate the hardening functions. With this novel model, some salient features can be described: the model can account for the accumulation of plastic deformation, a memory effect is provided by the new surface, and stress-induced anisotropy effects observed in sands are successfully simulated. A short calibration guide of the parameters is given, and some simulations for Hostun RF loose sand and Toyoura sand are presented. [ABSTRACT FROM AUTHOR]

Abstract: The paper presents an experimental study on the influence of the grain size distribution curve on dynamic soil properties. More than 160 resonant column tests with additional P-wave measurements have been performed on 27 different grain size distribution curves of a quartz sand. While the small-strain shear modulus G max has been discussed by Wichtmann and Triantafyllidis the present paper focusses on P-wave velocity v P , on the small-strain constrained elastic modulus M max and on Poisson''s ratio . It is demonstrated that while v P and M max do not significantly depend on mean grain size d 50 in the investigated range, they decrease with increasing coefficient of uniformity C u =d 60/d 10 of the grain size distribution curve. Poisson''s ratio does also not depend on d 50 but increases with increasing C u . An empirical formula similar to Hardin''s equation has been developed for M max, considering the influence of the grain size distribution curve. It predicts quite well the experimental data. [Copyright &y& Elsevier]

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. [ABSTRACT FROM AUTHOR]

The influence of non-plastic fines on undrained monotonic behaviour of sand was investigated over a wide range of fines content (FC = 0–40%), global void ratio and initial mean effective stress ( p 0 ′ = 100 kPa to 500 kPa), by performing triaxial compression tests with isotropic and anisotropic consolidation. For the sand–silt mixtures, steady-state line in the e − log(p′) space was found to be dependent on fines content with the existence of a limiting fines content, which defines the transition from a "fines in sand" to a "sand in fines" soil fabric. It is demonstrated that by means of the concept of equivalent granular void ratio, e*, all steady-state/critical state data points can be well described by a unique relationship in the e* − log(p′) space called the equivalent steady-state line (EG-SSL), regardless of fines content. The equivalent granular state parameter (ψ*), defined in terms of e*, and the EG-SSL can be effectively adopted for predicting the undrained monotonic behaviour of sand–silt mixtures and the onset of static instability, irrespective of fines content and initial state of the sand–silt mixtures. [ABSTRACT FROM AUTHOR]

The prediction quality of three of the most sophisticated constitutive models for sands has been examined based on a comparison of results from element test simulations and laboratory tests. Hypoplasticity with intergranular strain, the Sanisand elastoplastic model in the version of 2004 and the recently proposed ISA (intergranular strain anisotropy) model have been inspected. The laboratory tests performed on Karlsruhe fine sand used in the present study are freely available on the homepage of the first author. The model predictions have been inspected for drained and undrained monotonic triaxial tests with various densities and pressures and for monotonic tests with a few number of un- and reloading cycles. The main focus, however, lies on undrained cyclic triaxial tests with either stress or strain control and with different densities, initial stresses and stress/strain amplitudes. The strengths and weaknesses of the different constitutive models for various test conditions are worked out. • The parameters of three models have been calibrated for the same fine sand. • Different sets of parameters are necessary for monotonic and cyclic loading. • No liquefaction with hypoplasticity in case of stress or large strain cycles. • Buttery predicted by Sanisand for large strain cycles contrasts experiments. • All models work well for certain test types and show deficits for others. [ABSTRACT FROM AUTHOR]

Correlations between “dynamic” (small-strain) and “static” (large-strain) stiffness moduli for sand are examined. Such correlations are often used for a simplified estimation of the dynamic stiffness based on static test data. The small-strain shear modulus G dyn = G max and the small-strain constrained modulus M dyn = M max have been measured in resonant column (RC) tests with additional P-wave measurements. Oedometric compression tests were performed in order to determine the large-strain constrained modulus M stat = M oedo , while the large-strain Young's modulus E stat = E 50 was obtained from the initial stage of the stress-strain-curves measured in drained monotonic triaxial tests, evaluated as a secant stiffness between deviatoric stress q =0 and q = q max / 2 . Experimental data for 19 sands or gravels with specially mixed grain size distribution curves, having different non-plastic fines contents, mean grain sizes and uniformity coefficients, were analyzed. Based on the present data, it is demonstrated that a correlation between M max and M oedo proposed in the literature underestimates the dynamic stiffness of coarse and well-graded granular materials. Consequently, modified correlation diagrams for the relationship M max ↔ M oedo are proposed in the present paper. Furthermore, correlations between G max and M oedo or E 50 , respectively, have been also investigated. They enable a direct estimation of dynamic shear modulus based on static test data. In contrast to the correlation diagram currently in use, the range of applicability of the new correlations proposed in this paper is clearly defined. [ABSTRACT FROM AUTHOR]

The dynamic response of an elastic continuously nonhomogeneous soil layer over bedrock retained by a pair of rigid cantilever walls to a horizontal seismic motion and the associated seismic pressure acting on these walls are determined analytically–numerically. The soil non-homogeneity is described by a shear modulus increasing nonlinearly with depth. The problem is solved in the frequency domain under conditions of plane strain and its exact solution is obtained analytically. This is accomplished with the aid of Fourier series along the horizontal direction and solution of the resulting system of two ordinary differential equations with variable coefficients by the method of Frobenius in power series. Due to the complexity of the various analytical expressions, the final results are determined numerically. These results include seismic pressures, resultant horizontal forces and bending moments acting on the walls. The solution of the problem involving a single retaining wall can be obtained as a special case by assuming the distance between the two walls to be very large. Results are presented in terms of numerical values and graphs using suitable dimensionless quantities. The effect of soil non-homogeneity on the system response is assessed through comparisons for typical sets of the parameters involved. [ABSTRACT FROM AUTHOR]

The dynamic response of a water-saturated linear poroelastic soil layer over bedrock retained by a pair of rigid cantilever walls to a horizontal seismic excitation is obtained analytically–numerically under plane strain conditions. Hysteretic damping in the soil skeleton may also be present. The problem is solved in the frequency domain and its exact solution is obtained analytically. This is accomplished with the aid of Fourier series along the horizontal direction and solution of the resulting system of ordinary differential equations to obtain the amplitudes of the soil skeleton displacements and the pore water pressure. Soil displacements and stresses, pore water pressure as well as wall pressures and resultant forces are explicitly presented. Their variation with frequency, hysteretic damping, porosity and permeability is numerically obtained and compared against an approximate solution, to assess the degree of validity of the assumptions. [ABSTRACT FROM AUTHOR]

The high-cycle accumulation (HCA) model proposed by Niemunis et al. [16] predicts permanent deformations due to a drained cyclic loading with many small cycles (i.e. N ≥ 10 3 cycles with strain amplitudes ε ampl ≤ 10 − 3 ). The strain amplitude is the most important influencing parameter of the rate of strain accumulation ε ̇ acc . Based on tests on a medium coarse sand, a square relationship ε ̇ acc ~ ( ε ampl ) 2 has been used in the HCA model so far. The new test results presented in this paper indicate, however, that the exponent of the amplitude-dependence may vary between 1.3 and 2.4, depending on the tested material. This comes out of 150 drained cyclic triaxial tests with 10 5 load cycles performed on 14 clean quartz sands with specially mixed grain size distribution curves. Consequently, an additional material constant C ampl has been introduced into the HCA model describing the amplitude dependence according to ε ̇ acc ~ ( ε ampl ) C ampl . The additional parameter requires a revision of the simplified calibration procedure proposed by Wichtmann et al. [24] which uses correlations between the HCA model parameters and granulometric ( d 50 , C u ) or index properties ( e min ). Furthermore, the new cyclic test data reveal that the existing correlations are inappropriate for well-graded granular materials ( C u ≥ 5 ). Enhanced correlations suitable also for more well-graded sands are proposed in the paper. The possible error of a HCA model prediction with parameters fully or partly determined from the correlations is discussed. [ABSTRACT FROM AUTHOR]

The influence of a non-cohesive fines content on small-strain shear modulus G max , small-strain constrained elastic modulus M max , shear modulus degradation G ( γ ) / G max , damping ratio D ( γ ) and threshold shear strain amplitudes γ tl and γ tv 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 < 0.063 mm according to DIN standard code) and uniformity coefficients ( 1.5 ≤ C u ≤ 50 ) have been tested at different relative densities and pressures. A significant decrease of G max and M max with increasing fines content was observed, while the modulus degradation curves G ( γ ) / G max were found rather independent of FC . A pressure-dependent decrease of the damping ratio and a slight increase of the threshold shear strain amplitudes γ tl and γ tv with fines content were measured. Extensions of several empirical equations for G max , M max , G ( γ ) / G max and D ( γ ) considering the influence of the fines content are proposed in the paper. [ABSTRACT FROM AUTHOR]

The paper presents a dynamic finite-element analysis of the deformation of saturated cohesionless soil in the vicinity of the toe of a vibrating cylindrical pile. The soil behaviour is described by a hypoplastic constitutive model with intergranular strain assuming locally undrained conditions for the pore fluid. Emphasis is placed on the detailed analysis of stresses and displacements in the soil. It is shown that, starting from a homogeneous stress state, the first several cycles of vibration lead to the formation of a permanent liquefaction zone with vanishing effective stresses at a certain distance from the pile. The displacement field reveals an accumulation of residual displacements in the soil in the form of rotation. The influence of the initial stress state, the pore fluid compressibility, the pile displacement amplitude and the soil density on the formation of a liquefaction zone, on the stress amplitude in the soil and on the intensity of the permanent rotation is investigated. [ABSTRACT FROM AUTHOR]

Abstract: An experimental validation of Miner''s rule for freshly pluviated sand is presented. Drained triaxial tests with four packages of 25,000 cycles applied in different sequences have been performed. It is demonstrated that an effect of the sequence of application on the “cyclic flow rule” and on the final value of the residual strain can be neglected for practical purposes. In contrast to the significant reduction in the rate of accumulation caused by a cyclic preloading, only a slight decrease of the intensity of accumulation was measured after a drained monotonic preloading. The cyclic flow rule remains unchanged by the monotonic preloading. These experimental findings are considered in the high-cycle accumulation (HCA) model proposed by the authors. Re-calculations of the laboratory tests with the HCA model confirm a good prediction. A change of and due to changes of the average stress needs further investigations. [Copyright &y& Elsevier]

Cyclic stresses due to passing wheels impose an accumulation of permanent strains in layers of unbound granular materials (UGMs) of flexible pavements. The hollow cylinder triaxial test would be the most appropriate test to simulate the in situ stress conditions but it is difficult to perform on UGMs due to their large maximum grain size. The simpler axisymmetric cyclic triaxial test does not consider the shear stress components. It can be performed with a constant confining pressure (CCP) or a variable confining pressure (VCP). CCP and VCP tests are commonly assumed to deliver similar residual and resilient strains as long as the average stress is the same. Thus, the simpler CCP test is mostly used in pavement engineering. However, this assumption is based on limited test data in the literature and may not be on the safe side. The present paper documents a comparative study of CCP and VCP tests on UGM. The study is mainly dedicated to the permanent deformations. The results show that only for some special stress paths do both types of tests deliver similar permanent axial or volumetric strains. For some other stress paths the CCP tests may underestimate the permanent axial strain in comparison to the corresponding VCP test. [ABSTRACT FROM AUTHOR]

A study on the influence of the sample preparation method on the cumulative strains in sand under high-cyclic loading is presented. Numerous drained cyclic triaxial tests with 10 5 cycles were performed on samples prepared by either air pluviation out of a funnel, air pluviation using a multiple sieve apparatus, water pluviation, moist tamping or dry loose deposition with a subsequent compaction by either vibration or tapping. The test results reveal a significant influence of the sample preparation method on the intensity of strain accumulation. While very loose samples prepared by moist tamping show much larger strain accumulation rates than their air-pluviated counterparts at same density, it is the other way around at medium and high densities. Samples prepared by procedures involving compaction in the dry state are more resistant against cumulative effects than samples directly prepared to the same relative density. The differences in the rates of strain accumulation are the result of a different initial fabric generated by the various constitution methods. A micromechanical explanation based on the distribution of contact normal orientations is provided. In contrast, the direction of strain accumulation (cyclic flow rule) and the elastic portion of deformation during the cycles (strain amplitude) are rather insensitive to the choice of the sample preparation method. • Samples prepared by di_erent methods have been tested under high-cyclic loading. • All tested pluviation techniques gave similar strain accumulation rates. • At loose state tamped samples showed higher cumulative rates than pluviated ones. • It is the other way around at medium dense state. • Flow rule and strain amplitude are insenstive to sample preparation method. [ABSTRACT FROM AUTHOR]

Correlations between the liquefaction resistance of sands in spreader dumps of lignite opencast mines on one side and the CPT tip resistance or the shear wave velocity on the other side have been developed based on an extensive experimental study on 10 different sands. The cyclic resistance ratio C R R (N f = 10) for a failure in 10 cycles, defined as the liquefaction resistance herein, was determined from undrained cyclic triaxial tests for all materials. The CPT tip resistance q c was measured in soundings performed in a calibration chamber. The shear wave velocity v S was obtained from measurements in a triaxial cell by means of bender elements. All three quantities C R R (N f = 10) , q c and v S were determined for different relative densities D r . In case of q c and v S also the pressure-dependence was examined in order to derive suitable equations for a pressure-normalization being necessary for the interpretation of field test data, giving values q c 1 and v S 1 for a mean effective stress of p ' = 100 kPa. The procedure for the development of the C R R (N f = 10) - q c 1 and C R R (N f = 10) - v S 1 correlations based on the experimental data is explained. The correlations derived for the various sands in the present study are analyzed with respect to the influence of the grain size distribution curve and compared to respective relationships for natural soils or uncompacted recent artificial fills from the literature. • CPT tip resistance qc of sands from dumps was measured in a calibration chamber • Shear wave velocity vS was measured with bender elements • Liquefaction resistance CRR was obtained from undrained cyclic triaxial tests • CRR-qc correlations for sands from dumps run atter than those from literature • CRR-qc and CRR-vS correlations for dumps depend on grain size distribution curve [ABSTRACT FROM AUTHOR]

Shear banding represents a local failure mechanism of a soil structure as a response to shear loading. In soil structures of different spatial scales systems of regularly spaced shear bands can be observed as a consequence of extensional loading. The phenomenon of single shear bands, defined as thin zones of localized deformation with a discontinuity of the strain field at its boundaries, is well understood. Inside the shear band the material undergoes inelastic strain softening accompanied by shearing and dilation, whereas the material outside the shear band unloads accompanied by elastic contraction in extension tests. Despite numerous experimental and numerical investigations, the physical mechanisms and parameters determining the spacing of parallel shear bands remained unknown. The paper in hand presents an analytical solution for the spacing of the shear bands and a comparison with a large base of experimental data gained from 1 g and ng (geotechnical centrifuge) model experiments. The analytical solution is based on the assumption that the elastic energy rate in the unloaded zone between the shear bands tends to a minimum value. The spacing was calculated as the energetically preferred solution for a broad range of cohesive-frictional granular materials. The dependency of the calculated spacing on initial and boundary conditions as well as on material parameters was found to be in good agreement with the experimental results. [ABSTRACT FROM AUTHOR]

Offshore wind turbines (OWT) are generally founded on piles or gravity base foundations. Up to now, there is a lack of validated and standardized analysis procedures for such foundations, especially for the serviceability limit state, i.e. for the prediction of accumulated deformations. In order to gain experience on the behaviour of a OWT gravity base foundation under typical offshore loading conditions, a full-scale test has been performed near the shore of the North Sea. The test foundation was subjected to about 1.5 million load cycles simulating several storm events. The foundation and the sandy subsoil have been extensively instrumented so that a large amount of measured data on the cyclic soil-structure interaction were collected. Meanwhile, a numerical procedure for the proof of the serviceability for OWT foundations was developed. The procedure is based on finite element (FE) calculations in combination with a high-cycle accumulation (HCA) model. The application of the HCA model in simulations of the full-scale test is described in this contribution. The essential simplification of the subsoil and the determination of the input parameters for the FE simulations are shown. The settlements, pore water pressures and soil pressures predicted by the HCA model are compared to the measurements. [ABSTRACT FROM AUTHOR]