Small-Strain Stress-Strain Properties of Expanded Polystyrene Geofoam

The small-strain stress-strain properties of expanded polystyrene (EPS) geofoam with densities of about 20 kg/m³ and 30 kg/m³ were evaluated by laboratory unconfined compression tests on specimens of 75 mm in diameter and 150 mm in height. Two series of tests were conducted, which were continuous monotonic loading (ML) tests and ML tests intervened by sustained creep loading and minute cycles of unload and reload. Relatively small vertical and horizontal strains were locally measured by means of a pair of local deformation transducers (LDTs) and a set of three clip gauges, respectively. The paramount importance of measuring local strains in compression tests on EPS to reliably evaluate its stress-strain properties, in particular those at relatively small strains, is demonstrated. The initial modulus, E₀, and Poisson's ratio, ν₀, were evaluated from initial stress-strain relations at small strains obtained by these ML tests. The tangent parameters, E_tan and ν_tan, were also evaluated from the ML stress-strain behaviour. The equivalent parameters, E_eq and ν_eq, were evaluated from the stress-strain behaviour during minute cycles of unload and reload. The stress-strain behaviour is essentially linear only at small strains, and it becomes highly non-linear and a significant drop of stiffness occurs as observed in the overall stress-strain behaviour. The Poisson's ratio for inelastic deformation is found to be negative.     

Small Strain Stiffness and Non-Linear Stress-Strain Behaviour of Cement-Mixed Gravelly Soil

The stiffness at small strains and non-linear stress-strain relation of compacted cement-mixed well-graded gravelly soil as well as the ageing effects were evaluated by drained triaxial compression tests on compacted moist specimens cured for different periods at isotropic and different anisotropic stress states. In all the tests, the initial stress-strain relation at small strains less than about 0.001% was essentially elastic and the initial Young's modulus, E₀, was essentially the same as the E_eq value evaluated by applying unload/reload cycles under otherwise the same conditions. The E_eq values were rather independent of strain rate. The E_eq value from the first unload/reload cycle applied during otherwise continuous ML became noticeably lower than the elastic modulus evaluated at the same stress state, more as approaching the peak stress state. After a number of small unload/reload cycles and long sustained loading, the E_eq value became closer to the elastic modulus due to a decrease in the viscous effects. The ratio of E₀ to the compressive strength (q_max) was similar to that of concrete but noticeably larger than those of uncompacted cement-mixed soil, sedimentary softrock and unbound gravelly soil. Both E₀ and q_max increased with time by ageing, while the E₀/q_max ratio decreased with time. When ML was restarted at a constant strain rate after ageing with a shear stress, the tangent stiffness became very high for a large stress range with a substantial change in the non-linearity of stress-strain relation.     

Time-Dependent Shear Deformation Characteristics of Geomaterials and their Simulation

The viscous aspects of the stress-strain behaviour of saturated and air-dried clean sands in drained plane strain compression (PSC) and saturated clean sand and soft clays in undrained triaxial compression (TC) are presented. Common as well as different viscous features among the different geomaterials are addressed. The general three-component model is used as the framework for constitutive modelling, in which the total strain rate ε is decomposed into elastic and irreversible components ε^e and ε^ir while the stress σ is decomposed into inviscid (non-viscous) and viscous components σ^f and σ^v. In the simplest model (called the new isotach model) among those described in the paper, σ^f is a nonlinear function of ε^ir, while σ^v is a non-linear function of ε^ir and always proportional to σ^f for primary loading. This model is relevant to kaolin for the full pre-peak range and a reconstituted low-plasticity clay (Fujinomori clay) at small strains, both in undrained TC. The model is modified to simulate the viscous effect that decays with ε^ir, as observed with clean sands and a natural soft clay. It is shown that the second type of model (called the viscous evanescent model and the TESRA model) simulates well the above-mentioned behaviour, not only during primary loading, but also at unloaded conditions. The model is further modified to simulate the behaviour of Fujinomori clay whereby the rate at which the viscous effect decays gradually increases with ε^ir (the general TESRA model). The viscous components σ^v of the three models can be represented by a set of common equations, and the other models are specifically simplified versions of the general TESRA model.     

Effects of Particle Characteristics on the Viscous Properties of Granular Materials in Shear

The viscous properties of a wide variety of unbound granular materials (GMs) were evaluated by drained shear tests. The specimens were reconstituted ones that were loose or dense and air-dried or moist or saturated, of mostly natural sands and gravels, having different mean particle diameters, uniformity coefficients, fines contents, degrees of particle angularity and particle crushabilities. The tests were mostly triaxial compression (TC) tests and partly plane strain compression tests, both at fixed confining pressure, and direct shear tests at fixed normal pressure. The viscous properties of GMs were evaluated by stepwise changing the loading rate and performing sustained loading (SL) tests during otherwise monotonic loading (ML) at a constant loading rate. The viscous properties are characterised in terms of the rate-sensitivity coefficient (β), the viscosity type parameter (θ=β_r/β) and the decay parameter (r₁). Correlations among these parameters and effects of particle characteristics on these parameters are analysed. Creep strains are compared with residual strains by cyclic loading under otherwise the same TC conditions. As the particles become less angular, as the grading becomes more uniform and as the particles become less crushable, the viscosity type deviates more from the Isotach type (i.e., θ=1.0) changing toward the P & N type (i.e., θ<0) associated with a decrease in β and r₁, while creep strains by SL decreases and residual strains by many unload/reload cycles increases. It is shown that the loading rate effects observed in the experiments can be simulated well by the three-component model taking into account the effects of particle characteristics on the viscous property parameters.     

Modelling and Simulation of Rate-Dependent Stress-Strain Behaviour of Granular Materials in Shear

A constitutive modelling of the elasto-viscoplastic stress-strain behaviour of geomaterials in shear that has been developed within a non-linear three-component model framework is validated by simulating a comprehensive series of drained triaxial compression (TC) and direct shear (DS) tests on a wide variety of granular materials. Illustrative simulations of rate-dependent stress-strain behaviour of geomaterial under typical laboratory test conditions were performed to analyse the structure of the model. The versatility of the proposed model and its applicability to a wide variety of shear loading histories is examined and demonstrated by these simulations. The following results are shown. Commonly with different basic viscosity types, Isotach, TESRA and P&N, the viscous stress component has a positive component that increases with an increase in the irreversible strain rate, which makes feasible stable and realistic simulations of rate-dependent stress-strain behaviour, including creep deformation, based on the proposed model. With different unbound granular material types having similar relative densities, the creep strain in TC tests and creep shear displacement in DS tests that develop by sustained loading at a given shear stress level for a given period tends to decrease with an increase in the particle roundness. This trend of behaviours is explained by a decrease in the viscosity type parameter, θ, associated with an increase in the particle roundness based on the simulations of these tests.     

Viscous Property of Toyoura Sand Over a Wide Range of Shear Deformation Rate and its Model Simulation

As part of a long-term research program to evaluate the rate effects on the stress-strain behaviour of geomaterials, the viscous properties of a poorly-graded relatively angular quartz-rich sand, Toyoura sand, under air-dried conditions, were investigated by performing a comprehensive series of direct shear (DS) tests at a fixed normal stress equal to 50 kPa. The tests were performed on loose and dense specimens subjected to the following different loading histories: a) monotonic loading (ML) at constant shear displacement rate (s) differing by a factor up to 100,000; b) ML at constant s including otherwise a number of step changes in s by a factor of 100; and c) a number of sustained loading (SL) stages during otherwise ML at constant values of s differing by a factor up to 1,000. Tests a) revealed that, with dense specimens, the peak shear strength is remarkably independent of s while the residual shear strength noticeably decreases with an increase in s. That is, the viscous property is the so-called TESRA type at the peak stress state, while it is the so-called Positive & Negative (P&N) type at the residual state. With loose specimens, both peak and residual shear strengths decrease with an increase in s, indicating that the viscous property is already the P&N type at the peak stress state and definitely so at the residual state. These results are qualitatively and quantitatively consistent with those from tests b), by which the viscosity properties were quantified in terms of the rate-sensitivity coefficient. The results from tests c) showed that creep shear displacement, Δs, increases with a decrease in the tangent stiffness at the immediately preceding ML phase or with an increase in the shear stress level during the SL stage. The value of Δs for a given period steadily increases with an increase in s during the immediately preceding ML phase. These trends of viscous behaviour are simulated all very well by a non-linear three-component model incorporating a general expression of viscous stress.     

A Simple Pneumatic Loading System Controlling Stress and Strain Rates for One-Dimensional Compression of Clay

A simple but automated pneumatic loading system that can control the stress and strain rates for one-dimensional (1D) compression of clay was developed. The rate-dependency of stress-strain behaviour due to the viscous property of clay was investigated by 1D compression tests on standard-size specimens by various loading methods: 1) Standard Consolidation Tests (SCTs), stepwise increasing the axial stress two times every one day; 2) ordinary Constant-Rate-of-Strain (CRS) tests at different strain rates; 3) special CRS tests including unloading and reloading cycles with different stress amplitudes at strain rates of which the absolute value was either kept constant throughout respective tests or changed at the start of reloading; and 4) special CRS tests including a number of sustained loading (SL) during otherwise primary loading or unloading or reloading at constant strain rate. Sufficiently low strain rates were employed to ensure essentially fully drained condition. The followings were found. Despite that the newly developed pneumatic loading system is rather simple, 1D compression tests following such various loading histories as above can be performed on four types of clay rather accurately. The stress-strain behaviour of clay is significantly rate-dependent, exhibiting significant creep strains at SL stages. The creep strain rate is significantly different whether SL starts during otherwise primary loading or unloading or reloading, controlled by the magnitude and sign of the initial strain rate at the start of SL. The whole observed trends of rate-dependent stress-strain behaviour can be qualitatively explained by the non-linear three-component elasto-viscoplastic model extended to cyclic loading conditions.     

Viscous Behaviour of Unbound Granular Materials in Direct Shear

The viscous properties of a variety of poorly graded unbound granular materials were investigated by direct shear tests on 12 cm-cubic specimens. A number of natural sands having different particle shapes and sizes as well as uniform glass beads having different particle sizes were used. The viscous properties were evaluated by changing the shear displacement rate many times during otherwise monotonic loading (ML) at constant shear displacement rate and normal pressure. Creep loadings were performed in two tests. Different types of viscous properties, which are affected by the particle shape but essentially independent of the particle size, are reported. The viscosity type varies as the shear displacement increases from the pre-peak regime towards the residual state. A new viscosity type, called “Positive & Negative”, was found with relatively round granular materials in the pre-peak regime and with relatively angular granular materials in the post-peak softening regime and at the residual state. Peculiar “rate-independent unstable behaviour” is observed with round natural sands and glass beads in the post-peak regime, which is more significant and frequent with glass beads. Controlled by the particle size, this behaviour is caused by the so-called stick/slip phenomenon. The viscous properties observed in the DS tests are quantified by the rate-sensitivity coefficient defined in terms of the shear and normal stresses, which are then converted to those defined in terms of the major and minor principal stresses, β₁₃. These β₁₃ values are consistent with those directly obtained by the triaxial and plane strain compression tests. The effects of particle size on the β₁₃ value are negligible and the β₁₃ value tends to decrease as the particle shape becomes more round.     

Effects of Viscous Property and Wetting on 1-D Compression of Clay and Model Simulation

A series of one-dimensional (1D) compression tests on compacted kaolin powder were performed to evaluate the combined effects of the viscous property and wetting on the elasto-viscoplastic deformation of soil. In the tests, both creep deformation and collapse deformation due to wetting were allowed to take place at various fixed stress states during otherwise monotonic loading at a fixed strain rate. Combined effects of the viscous property and wetting on the stress-strain behaviour observed during 1-D compression were described by incorporating the wetting effects into a non-linear three-component elasto-viscoplastic model (a 3C model). Based on the experimental results, the effects of wetting on the inviscid stress and the irreversible strain relation of the plastic component of the 3C model and the property of the viscous component, having an Isotach property, are formulated as a function of the degree of saturation. Complicated rate- and time-dependent stress-strain behaviour observed during saturation at a fixed stress state and subsequent monotonic loading at a constant strain rate were successfully simulated.     

Large-Scale Plane Strain Compression Tests on Compacted Gravel with Active and Passive Controls

Large-scale plane strain compression tests were performed to study the effect of compaction on strength and deformation properties of gravel. The specimen is rectangular prismatic with dimensions of 50 cm in height and 22 cm times 25 cm in cross-section. By employing well-graded crushed sandstone called as Chiba gravel, five sets of plane strain compression tests were conducted on partially saturated specimens having dry densities in the range of 1.80-2.15 g/cm³ that were prepared using manual or automatic compaction techniques. For each set of tests, one specimen was tested by following the conventional approach called as “passive control” of &epsilon;₂, while the second specimen was tested by following a new approach called as “active control” in which one of the two confining plates was allowed to move forward and backward for keeping the locally measured value of &epsilon;₂ almost zero. As a result, no significant effect of the active control was found on the stress-strain behavior as compared to the passive control, except for the beginning of shearing. The maximum deviator stresses in the two kinds of plane strain compression tests were about 20% larger than those in the relevant triaxial compression tests under the employed range of the compaction levels.     

Short- and long-term behavior of EPS geofoam in reduction of lateral earth pressure on rigid retaining wall subjected to surcharge loading

Retaining walls are subjected to dead loads from backfill and adjacent structures, live loads and other loads from the vicinity of the structure. Retaining walls need to withstand earth pressure generated from above mentioned loads satisfactorily throughout their service life. Lateral earth thrust on retaining walls can be minimized by placing a compressible inclusion, such as, EPS geofoam, between the backfill and retaining wall. The present study is aimed at understanding both short- and long-term influence of EPS geofoam on surcharge induced lateral earth pressures on retaining walls through 1-g model studies. Four densities of geofoam in the range of 10–25 kg/m³ and three thicknesses of geofoam in the range of 25–75 mm were used in the present study. Lateral earth pressure at several locations along the height of the wall were monitored using earth pressure cells. Geofoam compression and backfill settlements under the surcharge load were also quantified using image analysis. From the series of model tests, it was observed that with the use of geofoam, lateral earth pressure on retaining wall was reduced under both short- and long-term loading conditions. However, higher reduction was observed under long-term loading.     

Stress–strain relations of cement-mixed gravelly soil from multiple-step triaxial compression test results

The peak compressive strengths at different confining pressures of cement-mixed gravel (CMG) that are very similar to those obtained by single-step loading (SL) drained triaxial compression (TC) tests using multiple specimens can be obtained by a multiple-step loading (ML) test using a single specimen. However, only the unload/reload stress–strain relations at different confining pressures (except for the primary loading pressure at the first step) can be obtained from an ML test, and the reloading relations become softer with the increases in negative irreversible axial strain increments that have taken place during the respective immediately preceding unloading regimes. This phenomenon is formulated by a unique empirical equation for the CMG tests. Undamaged reloading stress–strain curves (URCs) were inferred by removing the damage effects from measured reloading curves (MRCs) in the ML TC test based on this correlation. A method was developed within the framework of the proportional rule to infer primary loading curves (PLCs) at different confining pressures from the URCs and the PLC at the first step obtained from a given ML TC test. A procedure was formulated to modify the PLCs obtained by this procedure based on the PLCs measured at stresses exceeding the yield stress for large-scale yielding during reloading at different confining pressures in the ML test. This method was validated by comparing the PLCs obtained from the results of a pair of ML tests, increasing and decreasing the confining pressure, with those obtained from a set of SL TC tests at different confining pressures.     

Coupled Measurements of Water Content and Electrical Conductivity in Dielectrically Lossy Clay Slurry Using a Coated TDR Probe

Although time domain reflectometry (TDR) has been widely accepted as a non-destructive in-situ method with high reliability, the effective use of TDR for water content (w) and electrical conductivity (EC) measurements in clay slurry has not been established. We developed a Teflon-coated (TC) probe with a 0.05-mm thick fluorocarbon resin coating, and conducted a calibration experiment for kaolinite slurry to indicate its applicability to the measurements. The TC probe could estimate w from the observed effective dielectric constant (&epsilon;_eff) in the range of w≥47% with a ±6% error range. The &epsilon;_eff includes dielectric constant of two components: material under test (&epsilon;_m) and coating material (&epsilon;_tef). The relationship between &epsilon;_eff and w for this particular probe design cannot be directly applied to other coated probes because each probe has its own specific dielectric characteristic. We defined a function expressing the characteristic, that is &epsilon;_eff vs. &epsilon;_m, according to the testing in various fluid media. By applying the function, the observed data sets of &epsilon;_eff were transformed for a soil specific value (&epsilon;_m). Owing to the sufficient agreement of the &epsilon;_m values with those for the uncoated probe, we obtained the data sets of &epsilon;_m vs. w and its empirical expression for kaolinite slurry.     

Fem Simulation of the Viscous Effects on the Stress-Strain Behaviour of Sand in Plane Strain Compression

A stress-strain model called TESRA (Temporary Effects of Strain Rate and Acceleration), described in a non-linear three-component framework, has been proposed to simulate the effects of viscous property on the stress-strain behaviour observed in drained plane strain compression (PSC) tests on clean sands. According to the TESRA model, the current viscous stress component is obtained by integrating for a given history of irreversible strain increments of viscous stress component that developed by respective instantaneous irrecoverable strain increment and its rate and have decayed with an increase in the irreversible strain until the present. The TESRA model was implemented into a generalized elasto-plastic isotropic strain-hardening non-linear FE code. The integration scheme to obtain the viscous and inviscid stress components according to the TESRA model in FEM analysis needs some specific considerations including the relevant choice of the suitable rate parameter. The shear stress—shear (or axial) strain—time relations from five drained PSC tests on saturated Toyoura sand and air-dried Hostun sand were successfully simulated by the FE code embedded with the TESRA model. It is shown that the FE code can simulate the time-dependent stress-strain behaviour of sand accurately without spending any significant extra computational time or storage. The results of simulation using one element and multi-element are essentially the same.     

Modelling of Ageing Effects on the Elasto-Viscoplastic Behaviour of Geomaterial

The time effects on the stress-strain behaviour of geomaterial consist of effects of loading rate and ageing. The positive ageing effects are analysed based on the results from drained triaxial compression (TC) tests on cement-mixed kaolin and well-graded gravelly soil and incorporated into a non-linear three-component model that can simulate the elasto-viscoplastic behaviour of geomaterials. The inviscid yielding is controlled by the inviscid yield stress that develops basically by irreversible straining and time elapsing following, respectively, a basic inviscid strain-hardening function and an ageing function. The inviscid yield stress may develop additionally by positive interaction between ageing and inviscid yielding following an interaction function, which expresses an additional strength gain by longer ageing at higher shear stress levels. Positive interaction effects are damaged by subsequent irreversible straining following a damage function. These functions are formulated based on experimental results. Illustrative model simulations are presented to describe the structure of the proposed model. The model is validated by simulating drained TC tests exhibiting significant effects of loading rate and ageing.     

Ageing Effects on the Yielding Characteristics of Cement-Mixed Granular Materials

Ageing effects on the elasto-viscoplastic property of compacted moist cement-mixed granular material (GM) were evaluated by performing a series of non-standard drained triaxial compression (TC) tests. Two types of GM, crushed gravelly soil from a quarry and crushed concrete aggregate (i.e., a recycled material), were used. The specimens were produced by moist-compaction and then cured at constant water content under unstressed conditions for seven days. They were re-cured basically for two days under different stress states during otherwise drained TC loading at a constant strain rate. Yielding characteristics upon the restart of drained monotonic loading (ML) at a constant strain rate toward ultimate failure at the same or increased or decreased confining pressure were evaluated. The stress-strain behaviour before the stress state reaches the current yield locus is very stiff and highly reversible. Unlike elasto-plastic materials exhibiting no ageing effects, the yield locus expands during sustained loading at a fixed effective stress state due to not only yielding associated with creep deformation, controlled basically by the viscous property, but also ageing, controlled basically by time-elapsing. The shape and location of current yield locus depends on the location of the current stress state relative to the current ultimate failure envelope. The observed yield characteristics were analyzed based on a newly introduced interactive double-yield concept while in the framework of the non-linear three-component elasto-viscoplastic model that takes into account ageing effects as well as an interaction between ageing and inviscid yielding (and its potential decay by irreversible straining). The trends of stress-strain-time behaviour observed with the two types of cement-mixed GMs are essentially the same.     

Viscous Properties of Granular Materials Having Different Particle Shapes in Direct Shear

The viscous properties of air-dried relatively poorly-graded granular materials having different particle shapes were evaluated by performing a series of direct shear (DS) tests. The applied loading histories include repeated step changes in the shear displacement rate (s) or repeated sustained loading stages during otherwise monotonic loading (ML) at a constant s under constant vertical stress. Test results of an angular gravelly soil (i.e., Chiba gravel-a) obtained from the present study and those of a wide variety of poorly-graded granular materials (i.e., glass beads and natural sands including Toyoura, Hostun, Silica No. 6a, Ticino, Silver Leighton Buzzard, Ottawa, Albany and Monterey sands) previously obtained by the authors are analysed. The viscous properties of granular materials can be adequately described by three basic parameters: i.e., the rate-sensitivity coefficient, the residual rate-sensitivity coefficient (or their ratio, i.e., the viscosity-type parameter) and the decay parameter. These parameters, as well as the viscosity type (i.e., Isotach, Combined, TESRA and P&N), are strongly affected by particle shape as quantified in terms of the degree of particle angularity while being rather independent of particle size. The creep deformation that takes place by sustained loading increases with an increase in the shear stress level, and it also increases with changes in the viscosity type associated with an increase in mainly the particle angularity and partly the coefficient of uniformity. The various viscous property types and transitions among them can be described by a single general equation incorporating these parameters. A non-linear three component model incorporating this general equation can simulate very well all of the various viscous responses observed in the DS tests referred to in the paper.     

The influence of a cyclic loading history on soil-geogrid interaction under pullout condition

The knowledge of soil-geosynthetic interface behaviour is a key point in the design of geosynthetic-reinforced soil structures. The pullout ultimate limit state can be reproduced conveniently by means of pullout tests performed with large-size laboratory apparatuses, which allow studying the interaction mechanisms that develop in the anchorage zone. During the service life of geosynthetic-reinforced soil structures, reinforcements may be subjected to long-term cyclic vehicular loads or short-term seismic loads in addition to dead loadings, such as the structure's self-weight and other sustained loads. In order to study the influence of a cyclic loading history (a sinusoidal function with fixed amplitude A, number of cycles N and frequency f) on the post-cyclic peak pullout resistance, the writers carried out a series of multi-stage pullout tests on a high density polyethylene extruded uniaxial geogrid embedded in a compacted granular soil for different vertical effective stress σ′_v values. Moreover, the stability of the soil-geosynthetic interface from a point of view linked to the cyclic loading application has also been investigated. Test results showed that the design pullout resistance parameters are affected by the applied cyclic loading history for specific combined conditions (A, N and σ′_v) and it should be taken into account for designing geosynthetic reinforced soil structures.