Non-linear Three-component Model Research Articles

Elastic-viscoplastic behaviors of polymer-blend geocell sheets: Numerical and experimental investigations

Polymer-blend geocell sheets (PBGS) have been developed as substitute materials for manufacturing geocells. Various attempts have been made to test and predict the behaviors of commonly used geogrids, geotextiles, geomembranes, and geocells. However, the elastic-viscoplastic behaviors of novel-developed geocell sheets are still poorly understood. Therefore, this paper investigates the elastic-viscoplastic behaviors of PBGS to gain a comprehensive understanding of their mechanical properties. Furthermore, the tensile load-strain history under various loading conditions is simulated by numerical calculation for widespread utilization. To achieve this goal, monotonic loading tests, short-term creep and stress relaxation tests, and multi-load-path tests (also known as arbitrary loading history tests) are performed using a universal testing machine. The results are simulated using the nonlinear three-component (NLTC) model, which consists of three nonlinear components, i.e. a hypo-elastic component, a nonlinear inviscid component, and a nonlinear viscid component. The experimental and numerical results demonstrate that PBGS exhibit significant elastic-viscoplastic behavior that can be accurately predicted by the NLTC model. Moreover, the tensile strain rates significantly influence the tensile load, with higher strain rates resulting in increased tensile loads and more linear load-strain curves. Also, parametric analysis of the rheological characteristics reveals that the initial tensile strain rates have negligible impact on the results. The rate-sensitivity coefficient of PBGS is approximately 0.163, which falls within the typical range observed in most geosynthetics.

Prediction of creep behaviour from load relaxation behaviour of polymer geogrids

Evaluation of creep behaviour of polymer geosynthetic reinforcement is important for predicting the long-term performance of geosynthetic-reinforced soil (GRS) structures and determining the creep reduction factor of geosynthetic reinforcement for the design lifetime of a GRS structure. The inherent link between the creep behaviour and the stress relaxation behaviour was confirmed by performing a comprehensive series of sustained loading (SL) tests and stress relaxation (SR) tests and numerical simulations of SL and SR tests on several geogrid types. In the framework of the non-linear three-component (NTC) model, the creep strain in SL is entirely irreversible, while the tensile load decrement in SR is associated with the developed positive irreversible strain with zero total strain rate. Measured systematic relationships between the elapsed times necessary to reach the same irreversible strain rate in SL and SR tests and those between the irreversible strain increments necessary to reach the same irreversible strain rate in SL and SR tests are presented and simulated by the NTC model. It is shown that, based on these relationships, the time history of creep strain can be predicted from given results of SR tests performed for a much shorter period. This method is validated by successful simulations of experimental results.

Creep failure of natural gravelly soil and its simulation

In order to investigate creep failure behaviour of gravelly soils in the field, a series of triaxial compression tests was conducted on large-scale natural gravelly soil samples. The samples were retrieved by means of a new method using thick, water-soluble, polymer solutions from two tunnel excavation sites in Japan. Creep failure behaviour was evaluated by performing drained sustained loading at prescribed stress states during otherwise monotonic loading at a constant loading rate. Rate-dependent behaviour was also evaluated by stepwise changing vertical strain rate many times during otherwise monotonic loading at a constant strain rate. The observed viscous properties including creep failure behaviour were simulated by a non-linear three-component model taking into account the effects of particle characteristics on the viscous property parameters. The viscous property parameters evaluated for this simulation were compared with those of reconstituted granular materials obtained by previous studies. Shear moduli during the creep failure process, which were measured by the dynamic method, were also analysed.

Yielding of cement-mixed gravelly soil affected by viscous property, ageing and damage

The yielding of compacted moist cement-mixed gravelly (CMG) soil, subjected to arbitrary loading histories with two stress variables, is studied by means of non-standard drained triaxial compression tests. A non-linear three-component model is modified to describe the elasto-viscoplastic property affected by ageing and shear yielding-associated damage. The development of the inviscid yield locus (YL) is formulated based on the interactive double-yielding mechanism that comprises (i) the bounding mechanism controlled by “inviscid YL, YB” and (ii) the frictional mechanism controlled by “inviscid YL, YF”. Each inviscid YL is determined as an inner envelope of a given set of YB and YF that have developed by ageing and shear yielding and have been affected by damage. As the inviscid YL approaches the peak strength line, the shape changes in association with a decrease in the effect of YB and an increase in the effect of YF. The size and shape of the respective YLs in total stresses (i.e., measured effective stresses) are different from those of the corresponding inviscid YLs due to the viscous effects. The total stress–strain relation for a given loading history is obtained by accounting for the viscous effects from the inviscid stress–strain relation, which is obtained from the basic inviscid stress–strain relation accounting for the effects of ageing and damage. It is shown that this model can properly simulate the development of YL for a wide variety of loading histories applied along various stress paths.

Creep failure of sands exhibiting various viscosity types and its simulation

The creep failure behaviour of three reconstituted sands exhibiting various viscous property types was evaluated by large-, medium- and small-scale drained triaxial, and medium-scale drained unconfined compression tests. The creep characteristics were evaluated by performing sustained loading during otherwise monotonic loading at a constant loading rate. Creep failure and Isotach viscous stress–strain behaviour were observed with well-graded Miho sand compacted heavily under the optimum water content condition. Creep failure of saturated and air-dried Toyoura sand exhibiting TESRA viscosity was observed at the nearly peak stress state. Degradation of the shear modulus of Toyoura sand during creep failure process was measured by the dynamic method. Creep failure did not occur with air-dried Albany silica sand exhibiting P&N viscosity. It was experimentally shown that the stability against creep failure was higher in order of P&N, TESRA and Isotach viscosities. The creep behaviour of various viscous property types was well simulated by the non-linear three-component model taking into account the effects of particle characteristics on the viscous property parameters.

Simulation of geosynthetic load–strain–time behaviour by the non-linear three-component model

ABSTRACT: Polymer geosynthetic reinforcement materials exhibit significant elasto-visco-plastic load–strain behaviour that is controlled by, at least, current strain rate. For this reason, it is not possible to accurately evaluate the tensile load history only from a given tensile strain in a physical model test in the laboratory or with a full-scale soil structure in the field. A non-linear three-component model that can realistically simulate rate-dependent load–strain behaviour of polymer geosynthetic reinforcement is described with detailed explanations of the model framework together with the constitutive equations. The algorithms to simulate behaviours in three basic modes, constant strain rate monotonic loading, creep loading and load relaxation, are presented. A working example in Microsoft Excel with a user-defined Microsoft Visual Basic source code is provided in the appendices (which are available as supplementary data on the ICE Virtual Library website) so that readers can readily use the model.

Effects of loading rate on viscoplastic properties of polymer geosynthetics and its constitutive modeling

AbstractOn the basis of the special tensile test results under various loading histories, the rate‐dependent behaviors of three polymer geosynthetics due to their viscous properties have been investigated. All the investigated polymer geosynthetics show significant loading rate effects, creep deformation, and stress relaxation. Except for the polyester geogrid showing the combined viscosity, all the investigated polymer geosynthetics exhibit the isotach viscosity. An elasto‐viscoplastic constitutive model described in a nonlinear three‐component model framework is developed to simulate the rate‐dependent behaviors of polymer geosynthetics. The developed constitutive model is verified by comparing its simulated results with the experimental data of polymer geosynthetics presented in this study and those available from the literature. The comparison indicates that the developed model can reasonably interpret the rate‐dependent behaviors of polymer geosynthetics under arbitrary loading histories, including the step‐changed strain rate loading, creep, and stress relaxation applied during otherwise monotonic loading (ML). POLYM. ENG. SCI., 2010. © 2009 Society of Plastics Engineers

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

ABSTRACT 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.

Rate Effects on the Stress-Strain Behaviour of Eps Geofoam

The rate-dependency of the stress-strain behavior of EPS (Expanded Polystyrene) geofoam with densities of 19.3 and 28.0 kg/m 3 was investigated by performing unconventional unconfined compression tests. A set of monotonic loading (ML) tests were performed at different constant values of vertical (axial) strain rate, ε v . The ε v value was stepwise changed many times and several sustained loading (SL) tests were performed during otherwise ML at a constant ε v in other tests. A number of SL tests were performed during global unload and reload cycles to infer the stress-strain relation when ε v =0. The elastic properties were evaluated by applying minute unload/reload cycles during otherwise ML. The rate-dependent stress-strain behaviour observed in these tests was described by an elasto-viscoplastic model (i.e., a non-linear three-component model), for which the vertical (axial) stress, σ v , consists of inviscid and viscous components, σ v f and σ v v , while ε v consists of elastic and irreversible components, ε v e and ε v ir . It is shown that the viscous property of EPS geofoam is of Isotach type in that, under the loading conditions where ε v ir is always positive, the current σ v v value is a unique function of instantaneous ε v ir and ε v ir , therefore the strength increases with ε v . This viscous property was quantified based on the test results and incorporated into the model. The rate-dependent stress-strain behaviour, including the creep behaviour, observed in the experiment is simulated very well by the proposed model. In particular, the fact that the creep strain becomes significant when the sustained σ v value becomes larger than the inviscid yield vertical stress is well simulated.

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.

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.

Various Viscosity Types of Geomaterials in Shear and Their Mathematical Expression

ABSTRACT The viscous properties, or loading-rate effects on the stress-strain behaviour, of unbound and bound soils, in particular unbound granular materials, are summarised. The viscous properties were evaluated by stepwise changing the strain rate, e ˙ , and performing sustained loading during otherwise monotonic loading (ML) at a constant e ˙ and also by performing ML tests at different constant values of e ˙ . Four basic viscosity types, Isotach, Combined, TESRA (or Viscous Evanescent) and Positive & Negative (P & N), which were recently found are described. The Isotach type is the most classical one and, in the case of ML, the current viscous stress component is a function of instantaneous irreversible strain, eir and its rate, e ˙ ir . So, the strength during ML at a constant e ˙ increases with e ˙ . With the other three types, the viscous stress increment that has developed at a given moment, denoted as Δσv, decays with eir towards different residual values during subsequent ML. With the TESRAtype, Δσv decays eventually totally and the strength during ML at constant e ˙ is essentially independent of e ˙ . With the Combined type, Δσv decays with eir like the TESRA type, but it does not decay totally. So, the strength during ML at constant e ˙ increases with e ˙ like the Isotach type. With the P & N type, found latest, a positive value of Δσv decays towards a negative value. So, the strength during ML at constant e ˙ decreases with an increase in e ˙ . The viscosity type tends to change with eir: e.g., from Isotach toward TESRA and from TESRA toward P & N. A general mathematical expression that can describe these four viscosity types and transitions among them is proposed. Numerical simulations of typical drained triaxial compression tests of geomaterials based on a non-linear three-component model incorporating the general expression of the viscous stress are presented. The viscosity type is controlled by at least, grading characteristics and particle shape.

Rate-Dependent Load-Strain Behaviour of Geogrid Arranged in Sand Under Plane Strain Compression

A number of previous experimental studies showed that polymer geogrid reinforcement as well as sand exhibit significantly rate-dependent behaviour. The viscous properties of polymer geogrids and Toyoura sand were independently evaluated by changing stepwise the strain rate as well as performing sustained loading and load/stress relaxation tests during otherwise monotonic loading in, respectively, tensile loading tests and drained plane strain compression (PSC) tests. The viscous properties of the two types of material were separately formulated in the same framework of non-linear three-component rheology model. The viscous response of geogrid-reinforced sand in PSC is significant, controlled by viscous properties of geogrid and sand. Local strain distributions in the reinforced sand specimen were evaluated by photogrametric analysis and used to determine the time history of the tensile strain in the geogrid. The time history of tensile load activated in the geogrid during sustained loading of reinforced sand specimen was deduced by analysing the measured time history of geogrid strain by the non-linear three-component model. It was found that the tensile load in the geogrid reinforcement arranged in a sand specimen subjected to fixed boundary loads could decrease with time. In that case, the possibility of creep rupture of geogrid is very low.

Viscous Behaviour of Geogrids; Experiment and Simulation

The viscous properties of three types of geogrid polymer were evaluated by sustained loading tests lasting for 30 days at a load level about a half of its nominal rupture strength. The sustained loading tests were performed during otherwise monotonic loading (ML) at constant strain or load rate, unlike the conventional creep tests, in which the strain rate immediately before the start of sustained loading, which controls the creep strain rate, is not controlled or even not recorded. The following are presented in this study. The tensile rupture strength measured by ML that was started following a 30 day-long sustained loading was essentially the same as the one at the same strain rate at rupture obtained by continuous ML without any intermission of sustained loading. This fact indicates that creep is not a degrading phenomenon. Then, if free from chemical and mechanical degrading effects, the strength of a geosynthetic reinforcement (for a given strain rate at rupture) can be maintained until late in its service life. A non-linear three-component model is used to simulate the experimental results from the previous and present studies. The model can simulate very well not only the load-strain behaviour during ML with and without step changes in the strain rate and the one after sustained loading, but also the time histories of creep strain during sustained loading for short (one hour) and long (30 days) periods.

A theoretical framework to analyse the behaviour of polymer geosynthetic reinforcement in temperature-accelerated creep tests

A non-linear three-component model has been developed that can predict the strength and deformation of polymer geosynthetic reinforcement when subjected to arbitrary histories of strain, strain rate and temperature as encountered in the laboratory and in the field. An existing model framework assuming the elasto-viscoplastic property of material was modified to account for the effects of changes in ambient temperature on the load-strain relation. Tensile load-strain-time relations for typical geosynthetic reinforcement properties were obtained by direct simulations of long-term sustained loading (SL) tests at a fixed temperature as well as simulations of monotonic loading and sustained loading at different elevated temperatures in time-temperature superposition (TTS) and stepped isothermal method (SIM) tests. The procedures to obtain the master creep strain and modulus curves from the results of these three types of numerical analysis are presented and compared. Creep rupture curves constructed from the master curves obtained by direct simulations of long-term SL tests as well as the numerical TTS and SIM tests are compared. The creep rupture curves obtained by the three methods are similar for shorter creep rupture times, but they become different with an increase in the creep rupture time. The reasons for the difference are discussed. It is argued that the theoretical framework of the model is relevant and useful for analysing and interpreting results from TTS and SIM tests in a consistent manner.

A Modelling Procedure for Shear Yielding Characteristics Affected by Viscous Properties of Sand in Triaxial Compression

A series of triaxial compression (TC) tests were performed on Toyoura sand to evaluate the viscous effects on the stress-strain behaviour following the shear yielding mechanism. It is shown that very different shear stress and shear strain relations obtained from TC tests performed along different stress paths become rather unique when converted into relationships between the stress parameter Xst = (q/pa)/(p ' /pa)βsf, which is deemed to control the shear yield mechanism, and the normalized irreversible shear strain energy κs , which is the stress path-independent strain hardening parameter for shear yielding. Along each inviscid yield locus quantified based on the test results, with an increase in the effective mean principal stress p', the deviator stress q increases at a relatively large rate while the stress ratio q/p' decreases at a relatively small rate. According to the non-linear three-component model described in the paper, the stress parameter Xst is decomposed into the inviscid and viscous components, Xsf and Xsv. The inviscid shear yield loci are described in terms of Xsf and develop with an increase in Ks. The viscosity function gvκ̇s is introduced to relate Xsv to Xsf in the form of Xsv=Xsf⋅gvκ̇s based on the test results. It is shown that the viscous effects on the Xst − κs-Ks relations obtained from the TC tests performed along a wide variety of stress path could be simulated rather well by the model taking into account the decay of the viscous component Xsv with an increase in κs.

Time-dependent stress?strain behaviour due to viscous properties of geogrid reinforcement

A series of conventional and unconventional tensile tests were performed on six types of geosynthetic reinforcement to evaluate their viscous properties. It is shown that the isochronous model, according to which the load (or the stress) is a unique function of instantaneous strain and elapsed time, is unable to explain the major viscous aspects of the test results. In particular the model is unable to predict the stress–strain behaviour and rupture strength observed after loading is restarted at a constant strain rate following a creep loading or stress relaxation stage. It is argued that the widely prevailing concept that creep is a degrading phenomenon requiring the design strength to be reduced with an increase in the design lifetime is not realistic under typical field conditions where the stress–strain property does not deteriorate noticeably with time. It is also argued that this concept stems from the isochronous model. A non-linear three-component model is proposed to simulate the viscous aspects of the strength and deformation characteristics of the tested geosynthetic reinforcements. It is shown that this rheology model can simulate very well the experimental results obtained by the present study.

Time-dependent stress–strain behaviour due to viscous properties of geogrid reinforcement

A series of conventional and unconventional tensile tests were performed on six types of geosynthetic reinforcement to evaluate their viscous properties. It is shown that the isochronous model, according to which the load (or the stress) is a unique function of instantaneous strain and elapsed time, is unable to explain the major viscous aspects of the test results. In particular the model is unable to predict the stress–strain behaviour and rupture strength observed after loading is restarted at a constant strain rate following a creep loading or stress relaxation stage. It is argued that the widely prevailing concept that creep is a degrading phenomenon requiring the design strength to be reduced with an increase in the design lifetime is not realistic under typical field conditions where the stress–strain property does not deteriorate noticeably with time. It is also argued that this concept stems from the isochronous model. A non-linear three-component model is proposed to simulate the viscous aspects of the strength and deformation characteristics of the tested geosynthetic reinforcements. It is shown that this rheology model can simulate very well the experimental results obtained by the present study.