Stress Path Dependency Research Articles

Analysis-oriented stress–strain models for ultra-high-performance concrete confined with fiber-reinforced polymer

The use of fiber-reinforced polymer (FRP) jackets or tubes as confining devices can significantly improve the compressive performance of ultra-high-performance concrete (UHPC). For FRP-confined UHPC, an analysis-oriented stress–strain model is essential for a comprehensive understanding of its compressive behavior and the development of design models. Although several analysis-oriented stress–strain models have been developed for FRP-confined normal-strength concrete (NSC), such models for FRP-confined UHPC are still lacking. In this study, an experiment is conducted to investigate the failure mechanism of UHPC confined with FRP under concentric compression, and the stress–strain behavior of the FRP-confined UHPC is analyzed using the stress–strain models of actively-confined UHPC. Results showed that the stress-path-independency assumption, which has been proven to apply to FRP-confined NSC, was inapplicable to FRP-confined UHPC. By modifying the confining pressure to consider the influence of stress-path dependency, an analysis-oriented model was proposed. The proposed model was verified using a collected test database. The results show that the proposed model accurately predicted the stress–strain behavior of FRP-confined UHPC.

An improved hypoplastic model incorporating intergranular strain for overconsolidated clay

Hypoplastic constitutive models are able to describe overconsolidated behaviors of clay with a single nonlinear tensor function using a set of parameters. For instance, an advanced hypoplastic model by Wang and Wu (2020) has successfully reproduced overconsolidated history by incorporating a structure tensor. To simulate the recent stress history effects and the stiffness variations at small strains of clay, the intergranular strain tensor is introduced by Niemunis and Herle (1997) to reproduce stress-path dependent stiffness of clay. The improved hypoplastic model is examined against experiments on overconsolidated Chicago clay. It is evidently concluded that the improved model is capable of replicating stress-path dependency on the small-strain behavior of overconsolidated clay.

Crushing and mechanical characteristics of coral sands under various stress paths

Coral sand is known to have stress path dependence and fragility. In this research, a series of drained triaxial tests were conducted to explore stress path effects on the mechanical and particle breakage characteristics of coral sands. Several mechanical characteristics, such as critical state, strength, and dilatancy characteristics were studied. The results revealed that the dilatancy behaviors, stress-strain responses, and crushing of coral sands were strongly affected by consolidation stress and stress path. The critical state lines of coral sands were straight in p‘-q space and e-(p‘/P a)0.44 plane regardless of stress path. Based on these characteristics, a dilatancy equation was derived and validated through test results. The developed dilatancy equation could predict the dilatancy relationships of coral sands under various stress paths.

Quantifying Particle Breakage and Its Evolution Using Breakage Indices and Grading Entropy Coordinates

Particle breakage in soils is a well-recognised behaviour. Conventional methods for quantifying the breakage process rely on calculating the area between the particle size distribution (PSD) curves produced before and after crushing. A key aspect of breakage is understanding the process across the different size/sieve fractions. Grading entropy coordinates allow for the representation of any PSD to be shown as a single point on a Cartesian plane and are able to track grading evolution with relative ease. In this study, grading entropy coordinates are compared to three commonly used breakage indices (Br, Br* and IG). It is shown that grading entropy coordinates are advantageous over the traditional indices in quantifying subtle changes in the PSD evolution and directly provide further insight with regards to the individual fraction sizes. It is also discussed that conventional breakage indices rely on relative measures and are dependent on assumptions of an initial and/or final PSD. In contrast, grading entropy coordinates depend only on the characteristics of the (current) PSD curve. It was also observed that the breakage evolution captured by the entropy coordinates is able to determine the rate at which differently sized particles break as differently sized particles take on stress. Moreover, it is suggested that entropy coordinates may also stress path dependency, a feature not present in conventional indices.

Comparison of two CDM-based models for necking and fracture limits of metal sheets under hot stamping conditions

A unified viscoplastic constitutive model based on continuum damage mechanics (CDM) has been recently developed for the prediction of forming limit curves (FLCs) and fracture forming limit curves (FFLCs). In this CDM model, two damage variables which are strain path dependent (so called strain-based model) have been introduced to model the necking and fracture limits in sheet metal forming. In this study, the two damage variables have been modified by replacing the strain components with stress components to model stress path dependence (so called stress-based model). Then the two sets of CDM models have been analysed and compared in respect to their computational accuracy and efficiency. For this purpose, all the material constants in the models have been calibrated using the recently published data of 22MnB5 boron steel sheet under hot stamping conditions. Subsequently, the two models together with the calibrated material constants have been implemented into the commercial software ABAQUS using a user subroutine VUMAT, and applied to biaxial tests for the computation of both the necking and the fracture limit strains at hot stamping temperatures. Computational results show that there is little difference between the two CDM models with respect to the computed limit strain values, but the strain-based CDM model is more time-efficient.

Stress path constraints on veined rock deformation

Although rock mechanical behaviour has a long record of study, attempts to understand the role of fractures on rock deformation still have unresolved issues. Due to technical and/or economic challenges, natural rock fractures are often dealt with crudely, without detailed consideration of fracture geometry and heterogeneity in many geoscience applications. Veined rocks that are ubiquitous in the upper Earth crust fall in that category where sustained efforts are needed to offer key information for rock mechanics and geomechanics applications. Following on from a recent study on the rupture of veined rocks (DOI: 10.1029/2019JB019052), we further examine stress path constraints on the deformation of veined rocks (i.e., stress-path-dependent behaviour of veined rocks) under polyaxial conditions. The Discrete Element Method is used to establish a calcite veined model where constant mean stress (σm) and constant least principal stress (σ3) paths that are representative in the subsurface activities are considered. The results reveal the stress-path dependency of brittleness for models under different loading paths. Models tested under constant-σm conditions exhibit no brittleness, compared to cases where constant-σ3 is applied. Sliding along the strike of an inclined vein is evident under constant-σm deformation, irrespective of the level of stress. Shear bands along the dominated (inclined) veins exhibit apparent particle trajectory anisotropy for the constant-σm deformations which is demonstrated by the evident colour contrast of the adjacent rock matrix and the displacement dispersion of the particles forming the shear bands. We envisage that the reactivation of veins is of relevance to Enhanced Geothermal Systems (EGS) development in terms of seismicity mitigation and multiphysics control of fracture and reservoir permeability.

A theoretical model for predicting mechanical properties of circular concrete-filled steel tube short columns

Circular concrete-filled steel tube (CCFST) short columns have superior mechanical properties and broad application prospects. To rapidly predict its mechanical properties, this paper introduced both the similarities and differences of existing models, evaluated the influence of debonding effect and radial stress on CCFST short columns, selected mechanical properties for materials, considered the stress-path dependence of concrete and the strain hardening of steel tubes, and proposed a theoretical model calculated by an incremental-iterative program. Results suggest that ignoring the radial stress and the de-bonding effect has little effect on the mechanical properties of CCFST short columns without local buckling. As the axial strain increases, the influence of the stress-path dependence on the concrete increases. The concrete in CCFST short columns has no stress-path dependence when the confinement factor is greater than 2.5. In the prediction of hoop strains, load components, load-axial strain curves, and axial load capacity, the proposed model is effective and accurate and is superior to the existing models.

Experimental Study of Yield Surface in Polypropylene Considering Rate Effect: Stress Path Dependence.

In order to investigate the yield surface evolution of polypropylene (PP) under dynamic impact and the relationship between yield surface parameters and the strain rate, five shear-compression specimens (SCSs) with different inclination angles are designed and produced to explore the yield behavior of PP under dynamic loading. Dynamic combined stress loading paths with different compression-shear ratios are achieved by the split Hopkinson pressure bar (SHPB). The evolution laws of the compressive stress and shear stress in the measurement region during the PP SCS compressive deformation process are analyzed. In terms of mechanical response, PP under combined compression-shear loading is of visco-elasticity plasticity and its deformation undergoes a three-stage transition, namely “unyield→yield→failure”. The yield characteristics of PP are found to be affected not only by the hydrostatic pressure but also by the stress path. According to the Hu–Pae yield criterion, the dynamic yield surface and model parameters of PP are obtained, and the relationship between the yield surface and the strain rate is ascertained. These findings contribute to deepening the research on the mechanical response characteristics of PP-based materials.

Unified modeling behavior of rockfill materials along different loading stress paths

Rockfill materials used for dam construction show obvious stress path dependency during construction process. The constitutive model for rockfill materials are mainly established based on conventional triaxial test. This brings some deviation to the numerical calculation for earth rockfill dam engineering, and it is necessary to develop a constitutive model considering stress paths effect. In the framework of generalized plasticity, plastic modulus can be expressed as the function of dilatancy equation and tangent modulus, hence the influence of stress paths on model can be transfer to the dilatancy equation and tangent modulus. This leads to a new method to describe stress-strain response of rockfill under various loading stress paths. Based on the analysis of large-scale triaxial experiments of rockfill materials with various stress paths, we proposed new dilatancy equation and tangent modulus to better describe stress paths effect and corresponding modified generalized plasticity model is established. Through the prediction and comparison of three groups of rockfill materials triaxial tests, the model established in this paper can simulate behaviors of rockfill materials under various stress paths, using only a set of parameters.

A division method for shallow tunnels and deep tunnels considering soil stress path dependency

Critical burial depth plays an important role in tunnel design and analysis. So, the division method for deep tunnels and shallow tunnels is perceived as a main concern. Considering the soil stress path dependency, this paper investigates the construction mechanical behavior of soil mass at different burial depths, and aims to explore a method for identifying critical burial depth. Firstly, using the Eulerian method and stress return mapping scheme, an elastoplastic algorithm applicable to double loading criteria was developed for a soil constitutive model considering complex stress paths. Then, the developed algorithm was implemented into a user-defined material subroutine (UMAT) and validated through numerical triaxial tests under different stress paths. Subsequently, the UMAT was used to model tunnel excavation in soils. The simulated results were compared with the results that from practical engineering, which shows that the UMAT could accurately predict the ground surface settlement. On the basis of this, the stress distribution and deformation performance in soil during tunneling at different burial depths were explored. Finally, the division method for differentiating shallow tunnels and deep tunnels in soil was discussed and a method for determining the critical depth was proposed.

Experimental Investigations of the Stress Path Dependence of Weakly Cemented Sand

AbstractCohesion between grains in a geological system is perhaps the simplest and ideal representation of a range of material systems including soft rocks, structured soils, mudstones, cemented sa...

Investigation of Lade‐Kim Plastic Potential Applicability under Various Stress Paths for Rockfill Materials

The dilatancy behavior of rockfill materials shows obvious stress path dependence. Lade‐Kim plastic potential equation has been proposed for a long time to model the mechanical behavior of sand and concrete materials. However, it lacks the verification of rockfill materials, especially under various stress paths. In this paper, the dilatancy performance of coarse‐grained materials under various stress paths is investigated, and then the dilatancy equation description and verification method based on Lade‐Kim plastic potential are given. The applicability of Lade‐Kim plastic potential for different stress path tests, such as conventional triaxial tests, constant P tests, and constant stress (increment) ratio tests, are verified and evaluated. It is found that Lade‐Kim plastic potential is difficult to consider the influence of stress path. Finally, the Lade‐Kim plastic potential, together with nonlinear dilatancy equation, is evaluated by changing the dilatancy equation in the framework of generalized plasticity. Lade‐Kim plastic potential is suitable for constant stress increment ratio loading experiments and special care should be taken when applied to other stress paths. These works are helpful to understand stress path dependence of dilatancy behavior for rockfill materials and is beneficial for the establishment of stress path constitutive model.

Stress-path-dependent effective medium model for granular media — Comparison with experimental data

Modeling velocity changes in response to stress changes plays an important part in understanding seismic responses from the subsurface. One branch of such modeling consists of treating an assemblage of grains as an effective medium and using established grain contact theories to determine the elastic moduli. Such models are commonly limited to hydrostatic or uniaxial strain scenarios, not capable of capturing the anisotropy induced by a general triaxial stress state. A new set of expressions is developed by extending an existing effective medium theory to a general stress state in which the radial (horizontal) stress is different from the axial (vertical) stress. The theory is valid at the limits of slip and no slip. Novel functions to combine the no-slip and slip limits are implemented to match the model to observed laboratory data on glass beads and sand grain assemblages loaded along different stress paths. The new expressions provide a good agreement between the modeled and measured stress and stress path dependence of the compressional wave (P-wave) and shear wave velocities and associated P-wave anisotropy. This stress dependence is of particular interest in rock-physics modeling workflows evaluating time-lapse feasibility for shallow or unconsolidated sand reservoirs or for characterizing burial history.

Experimental Study on Mechanical Properties of Soft Clay under Different Stress Paths

In actual engineering, when the soil element is subjected to load, the stress state will change accordingly. In this paper, undrained triaxial stress path tests for Ningbo reshaped saturated soft clay under different confining pressures are carried out. The test uses the GDS bidirectional vibrating triaxial instrument. The stress path dependence of saturated soft clay is studied. The stress-strain relationship and undrained shear strength under different stress path conditions are mainly analyzed. The test results show that the stress-strain relationship of the stress path test is obviously non-linear, basically strain hardening. The stress-strain curves of saturated remolded soft clay under different stress paths and consolidation pressures can be expressed in hyperbolic form. The initial stiffness E0 basically increases with the increase of the deflection angle of the stress path. The test results have certain reference significance for foundation pit and tunnel engineering.

Simplified analyses of stress induced anisotropy in remolded soft clay under undrained conditions

Purpose: The soil’s anisotropy induced by stress (i.e. stress induced anisotropy) has an important effect on the behavior of soil. This paper focuses on analyzing the anisotropy of remolded Shantou soft clay under compression stress path. Design/methodology/approach: Experiments were executed by using three axle experimental instruments. The data obtained from the plain strain tests were analyzed and the relationship between stress and strain was calculated by using the modified Duncan- Chang and Lade-Duncan models. The models were modified under the condition of plain strain and cohesion. Findings: It was concluded that in complex stress path conditions, the conventional triaxial tests may not fully reflect the actual stress of soil and its response in the Duncan-Chang and Lade-Duncan models. Research limitations/implications: The formulation of Mohr-Coulomb failure criterion in the plasticity framework is quite diffcult. As a result, dilatancy cannot be described. The properties of soil in unload or drained conditions remain to be part of further investigated. Practical implications: Based upon the two stiffness parameters, the modified Duncan- Chang model has captured the soil behaviour in a very conformable way and is recommened for practical modeling. These constitutive models of soil are widely used in the numerical analyses of soil structure such as embankments. Originality/value: Duncan-Chang and Lade-Duncan models widely used in engineering practices are modes based on conventional triaxial cases. Both models have have some inherent limitations to represent the stress-strain characteristics of soils, such as shear-induced dilatancy and stress path dependency and required corrections. In this investigation, the tests are carried out in undrained conditions. It is related to the properties of soil in load conditions.

Pre-failure behaviour of reconstituted peats in triaxial compression

This paper discusses the results of an experimental programme designed to investigate the deviatoric behaviour of peats. The results are obtained from triaxial experiments carried out on reconstituted peat samples. The interpretation of the experimental results follows a hierarchical approach in an attempt to derive the ingredients that an elastic–plastic model for peats should contain, including the yield locus, the hardening mechanism and the flow rule. The results obtained from stress tests along different loading directions show that purely volumetric hardening is not adequate to describe the deviatoric response of peat and that a deviatoric strain-dependent component should be included. The plastic deformation mechanism also depends on the previous stress history experienced by the sample. Stress and strain path dependence of the interaction mechanisms between the peat matrix and the fibres is discussed as a possible physical reason for the observed behaviour. This work offers a relevant set of data and information to guide the rational development and the calibration of constitutive laws able to model the deviatoric behaviour of peats.

Three-dimensional constitutive model for cyclic behavior of soil-structure interfaces

Many soil-structure interaction systems experience a three-dimensional loading condition (i.e. shear coupling) at their interfaces. In this study, an elasto-plastic constitutive formulation for interfaces in soil-structure interaction problems is proposed considering the effects of 3D shear coupling loading conditions. The proposed model is capable of simulating granular soil-structure interfaces for both monotonic and cyclic loading over a wide range of normal stress and normal stiffness using a single set of eleven calibration parameters. The model is capable of simulating a number of complex interface behaviour, including hardening and softening, compaction, dilation and phase transformation, stress path dependency, accumulative contraction and stabilization, stress degradation and particle breakage under monotonic and cyclic loading. The constitutive model performance is examined using available experimental data for gravelly and sandy soil-structure interfaces subjected to monotonic and cyclic loads involving shear coupling.

A path dependent stress-strain model for concrete-filled-steel-tube column

High-strength concrete (HSC) has higher strength-to-weight ratio and stiffness than normal-strength concrete (NSC), which can decrease the size and embodied carbon of columns in tall buildings. Because of the brittleness of HSC, the practical design strength limit of HSC is usually limited for providing minimum ductility. One feasible way to extend this limit would be to use concrete-filled-steel-tube (CFST) column, which has a better strength-ductility performance. There are two shortcomings in theoretical models predicting the stress-strain behaviour of CFST column: (1) Most of the models did not consider the imperfect steel-concrete interface bonding due to their different dilations under axial compression; (2) A stress-path independent confining stress-strain relationship was adopted, which ignored the progressive development of tensile splitting cracks in concrete leading to a more gradual building up of confining stress under passive confinement than active pressure. Herein, to better understand and simulate the behaviour of CFST column, a theoretical stress-strain model, which consists of the following four main components, has been developed: (1) Interaction between steel tube and concrete taken into account the de-bonding effect; (2) An accurate hoop strain equation; (3) A passively confined concrete model considering stress-path dependence; (4) A three-dimensional stress-strain model for steel tube. Comparing with the measured load-strain curves obtained by the authors and other researchers, the accuracy of the proposed model in predicting the axial behaviour of CFST columns has been verified.

A numerical study on the coupled hydro-mechanical behaviour of compacted bentonite

Understanding the mechanical behaviour of compacted bentonite upon re-saturation is of outmost importance in most designs of nuclear waste disposal repositories. The behaviour of bentonite is characterized by its stress-path dependency and it is typically interpreted on the basis of its microstructural interactions. Up to now, effective stress-based models have had limited success in reproducing consistently the main responses. Here a recently proposed model for the modelling of volumetric behaviour of compacted bentonites is extended to triaxial stress states. The model is formulated using a conventional effective stress expression and the degree of saturation. Because these two variables are directly related to the water retention, a suitable formulation for bentonites is used. The resulting equations are characterised by a high degree of hydro- mechanical couplings and a low number of material parameters, which can be obtained on the basis of well- established laboratory procedures. In order to demonstrate its capabilities, the model is used to simulate the behaviour of MX-80 bentonite for several stress paths under oedometric conditions. The emphasis is put on the process of parameter determination. The predictive capabilities of the model are also highlighted.

A 3D elastic-plastic-viscous constitutive model for soils considering the stress path dependency

In order to consider the stress path dependency of soils, this paper decomposes any arbitrary stress path into several infinitesimal stress paths. Then the infinitesimal stress path is further transformed into the superposition of two parts, i.e., a constant stress ratio part and a constant mean stress part, which are sufficiently close to the real stress path. The plastic strain increments under the transformed paths are determined separately, and then the plastic strain under any path is obtained. Based on the instantaneous loading line of normally consolidated soil, a reference state line is proposed to determine the overconsolidation ratio and creep time of soil. The overconsolidation ratio is introduced into the viscous flow rule to obtain the viscous strain increment. The stress-strain-time relationship for triaxial compression condition is extended to 3D stress condition by the transformed stress method. The proposed model adopts only seven material parameters and each of them has a clear physical meaning. Comparisons with test results demonstrate that the model can not only reasonably predict the plastic strain under typical stress paths of excavation, but adequately capture the time-dependent behaviours of soils, including creep, stress relaxation and strain rate effect.