Fig 5 - uploaded by Yang-Ping Yao
Content may be subject to copyright.
Proposed yield curve (fine solid line), failure state lines (bold solid line) and characteristic lines (dotted line) in triaxial stress.
Source publication
The Sekiguchi–Ohta model is extended to be a unified three-dimensional elastoplastic model for clays, silts and sands by introducing a transformed stress tensor and a new hardening parameter H. The model can describe the negative and positive dilatancy of soils with an initially stress-induced anisotropy in three-dimensional (3D) stress. An elastop...
Contexts in source publication
Context 1
... the proposed model, the associated flow rule is adopted in the transformed stress ~ r ij space [6], i.e., where K is the proportionality constant, and can be determined from the consistency condition. Fig. 5 shows the proposed yield curve (Eq. (9), fine solid curve), failure state lines (~ g k ¼ M f , bold solid line) and characteristic lines ~ g ¼ M, dotted line) in triaxial compression and triaxial extension stresses. From Eq. (12), it is known that when M f ¼ M the failure state line becomes the same as the characteristic state line, ...
Context 2
... proposed model is incorporated into the FEM program DACSAR coded by Iizuka and Ohta in Japan [17]. As shown in Figs. 2 and 5, when the stress path is along the K 0 -line, the plastic flow at the singular point of non-smooth yield surface is unable to be correctly evaluated due to an unpredictable gradient at the corner. A very simple handling method adopted in the FEM code is that K 0 is assumed to be slightly smaller than the stress ratio (r 2 =r 1 ¼ r 3 =r ...
Similar publications
![Validation of the anisotropic yield criterion (after [27]).](publication/334199410/figure/fig1/AS:1086041586958337@1635943900033/Validation-of-the-anisotropic-yield-criterion-after-27_Q320.jpg)
![Validation of the anisotropic yield criterion (after [27]).](publication/334199410/figure/fig2/AS:1086041586958351@1635943900076/Validation-of-the-anisotropic-yield-criterion-after-27_Q320.jpg)
![Display of the non-coaxial plastic flow rule [24, 27].](publication/334199410/figure/fig3/AS:1086041586962434@1635943900116/Display-of-the-non-coaxial-plastic-flow-rule-24-27_Q320.jpg)
![Display of the non-coaxial plastic flow rule [24, 27].](publication/334199410/figure/fig4/AS:1086041586958362@1635943900144/Display-of-the-non-coaxial-plastic-flow-rule-24-27_Q320.jpg)
Soil strength isotropy and coaxiality of the principal axes of stress and plastic strain rate tensors are often assumed in modelling the soils around tunnels, in the conventional plastic theory. However, the complexity of the soil response during the excavation of tunnelling cannot be well exhibited. In this paper, a recently developed two-dimensio...
Boom Clay is extensively studied as a potential candidate to host underground nuclear waste disposal in Belgium. To guarantee the safety of such a disposal, the mechanical behaviour of the clay during gallery excavation must be properly predicted. In that purpose, a hollow cylinder experiment on Boom Clay has been designed to reproduce, in a small-...
The mechanical behaviour of rubber materials is known to be incompressible or nearly incompressible and hyperelastic with non-linear load-extension behavior. Another complexity is added when the rubber is reinforced with fibers. Prediction of such a complex behavior of elastomers subjected to general strain histories is a task that requires extensi...
In this work, we have brought to light the effect of material orientation on void growth. For that purpose, we have performed finite element calculations using a cubic unit-cell model with a spherical void at its center and subjected to periodic boundary conditions. The behavior of the material is described with an elastic isotropic, plastic orthot...
Background
Finite element is an effective tool to simulate stent expansion inside stenotic arteries, which provides an insightful understanding of the biomechanical behaviour of the whole stent-artery system during the procedure. The choice of balloon type, system constraint and artery constitutive model plays an important role in finite element si...
Citations
... Numerous anisotropic plastic models and damage models have been used to predict the mechanical response of anisotropic soil and rock [1][2][3][4][5][6]. Based on the framework of critical state soil mechanics (CSSM) for the triaxial space, Dafalias et al. [1] have presented an anisotropic clay plasticity constitutive model. ...
The fabric anisotropy and anisotropic parameters have great effect on the mechanical property of sand. Based on the existing anisotropic model, a modified anisotropic hypoplastic model is developed by incorporating the relation between fabric tensor and anisotropic parameters into the nonlinear part of the constitutive model. The applicability of the improved anisotropic hypoplastic model is validated by comparing with the existing model and experimental data. As a result, it is found that the modified model can well predict the mechanical response of anisotropic sand.
... The filling of the embankment is accomplished through the keywords '*MODEL CHANGE REMOVE' and '*MODEL CHANGE ADD' of ABAQUS package, which are designed for remove and add elements to simulate the excavation and filling problems. The S-CLAY1 model parameters of the sand layer and the uniform marine clay layer used in the FEM model are listed in Table 4, which are summarized and extended by Iizuka and Ohta (1987) and Sun et al. (2004) from extensive in-situ and laboratory tests on the soil samples extracted from the site. Since the parameters of the surface clay layer are not provided in the source literature of Iizuka and Ohta (1987), the surface clay layer is approximately assumed as an elastic mass with typical parameters of E = 20 MPa and v ' = 0.2 in the simulation. ...
The stress correction, which prevents stresses drifting from the yield surface, is a key step in the explicit scheme for integrating elastoplastic constitutive models in finite element analyses. In this paper, a simple, robust, and efficient stress correction method is proposed for improving the well-established explicit modified Euler scheme of Sloan et al. (2001). The method subtly proposes a single correction coefficient assuming that the stress components are proportional to the corrected stress components on the yield surface. The expression of the correction coefficient can be explicitly determined with the current stress state and the yield function, which allows the correction procedure to be easily and conveniently accomplished through multiplying the stress components by a single coefficient without resorting to the Newton iteration algorithm. The proposed method is applied to develop a user defined material (UMAT) subroutine for the advanced anisotropic elastoplastic model S-CLAY1 (Wheeler et al. 2003), which is subsequently used to simulate triaxial tests, the collapse of a rigid smooth square footing and a natural ground under embankment loading. The comparisons with other stress correction methods, the exact results from MATLAB, and the field measured values demonstrate the stability, robust, efficiency and validity of the proposed method.
... Significantly different shear strengths have been obtained when the major principal stress acts perpendicular to and parallel to the depositional plane, respectively (Lam and Tatsuoka, 1988;Oda et al., 1978;Tang et al., 2020;Yang et al., 2016). Potential hazards might be encountered if the shear strength of TI-soils is not well understood and captured in practical engineering (Gao et al., 2021;Sun et al., 2004;Zdravkovic et al., 2002), which is why the failure criteria for TI-soils have been the focus of research in geotechnical engineering. The difference between the shear strengths under the above two conditions is usually used to indicate the anisotropy degree. ...
The remarkable effect of the depositional angle δ on the shear strength of transversely isotropic soils (TI-soils) has long been experimentally confirmed. However, the δ-effect under the true triaxial conditions is still difficult to be well described by existing strength criteria. This paper presents a new perspective to determine the mobilized plane based on the characteristic stress, i.e., the Characteristic Mobilized Plane (CMP), and the CMP criterion is proposed according to the strength conditions on the CMP. In order to incorporate the δ-effect into the CMP criterion, the distribution of the microstructure of the TI-soil and stress, as well as the relative orientation between the depositional plane and the CMP, are analyzed. Based on the projection of the microstructure tensor onto the normal vector of the CMP, and combined with the δ-dependence strength variation rule, a CMP-based strength parameter is proposed, which can be used to improve the CMP criterion into one for TI-soils, i.e., TI-CMP criterion. The features of the TI-CMP criterion in capturing the coupling effects of b and δ are demonstrated by analyzing the variation rule of the strength curves. The validation performed against the test results examines the excellent predictive capability of the TI-CMP criterion.
... By substituting Eqs. (34,36) and ...
... By substituting Eq. (34,36) into (26,27,31), applying plane strain conditions, i.e. de z ¼ 0, and following the approach used by Chen and Abousleiman [8], the change of specific volume can be obtained from Eqs. (2,34,37), and the following eight partial differential equations in terms of the auxiliary variable n are found (three corresponding to stress increments, one to specific volume change, three to rotation of the yield surface and one to destructuration) ...
This paper presents a novel, exact, semi-analytical solution for the quasi-static drained expansion of a cylindrical cavity in soft soils with fabric anisotropy and structure. The assumed constitutive model is the S-CLAY1S model, which is a Cam clay-type model that considers fabric anisotropy that evolves with plastic strains, structure and gradual degradation of bonding (destructuration) due to plastic straining. The solution involves the numerical integration of a system of eight first-order ordinary differential equations, three of them corresponding to the effective stresses in cylindrical coordinates, other three corresponding to the components of the fabric tensor and one corresponding to the amount of bonding and another corresponding to the specific volume. The solution is validated against finite element analyses. When destructuration is considered, the solution provides slightly lower values of the effective radial and mean stresses near the cavity wall. Besides, the specific volume is further reduced due to loss of bonding. Parametric analyses and discussion of the influence of soil overconsolidation, expansion of the cavity and initial amount of bonding are presented.
... Sekiguchi and Ohta (1977) proposed an elastoplastic model for the initially anisotropic clays, which remains limited in its description of anisotropic soil behavior. The K 0 -AMCC model was presented by Sun et al. (2004), which accounts for the initial stress anisotropy, and is used to simulate the problem of cavity expansion. The yield function in the K 0 -AMCC model is expressed as ...
Cavity expansion is a classical problem in the field of solid mechanics with a wide range of applications in
geotechnical and petroleum engineering. A drained solution is developed for cylindrical cavity expansion in anisotropic soils
under biaxial in-situ stresses using a K0-based anisotropic modified Cam-clay model (K0-AMCC). The problem is formulated by solving differential equations using an auxiliary variable, which provides analytical expressions for the volume and four stress
components of the soil around the cylindrical cavity. The solution is validated by comparisons with existing well�developed solutions. The results show that the present solution well captures the cavity expansion responses in anisotropic soils under biaxial in-situ stresses, and removes limiting assumptions that the cylindrical cavity expands under uniform in-situ stress in isotropic soils. The elastic-plastic boundary of the expanding cylindrical cavity in K0-consolidated anisotropic soils under biaxial in-situ stresses is a circle rather than an ellipse in isotropic soils, and the mathematical proof is provided in detail.
... Therefore, the hardening parameter should be reconstructed. Several hardening parameters and hardening modulus have been proposed and used for modelling dilatancy behaviours of sand that is related to density and stress state [29][30][31][32], anisotropy [33][34][35] and even fabric evolution [36][37][38]. However, they are all formulated based on orthogonal plastic flow conditions. ...
A non-orthogonal elastoplastic constitutive model for sand with dilatancy is presented in the characteristic stress space. Dilatancy of sand is represented by the direction of plastic flow, which can be directly determined by applying the non-orthogonal plastic flow rule to an improved elliptic yield function. A new hardening parameter is developed to describe the contractive and dilative volume change during the shear process, which is co-ordinated with the non-orthogonal plastic flow direction. The combination of the non-orthogonal plastic flow rule and the proposed hardening parameter renders the proposed model with the ability to reasonably describe the stress-strain relationship of sand with dilatancy. The model performance is evaluated by comparing with the experimental data of sand under triaxial stress conditions.
... This simplistic treatment performs well for undrained triaxial extension tests, but fails to predict the volumetric strain responses under various loading paths (Pestana and Whittle 1999;Yang et al. 2015b). This model has been improved by employing a bounding parameter χ, which is supposed to be a constant initially (Dafalias 1986) and subsequently have been modified as a stress-state-dependent variable (Anandarajah 2000;Anandarajah et al. 1996;Dafalias et al. 2004Dafalias et al. , 2006Gajo and Muir Wood 2001;Hu et al. 2012;Inel and Lade 1997;Jiang and Ling 2010;Li and Dafalias 2002;Liang and Ma 1992a, b;Ling et al. 2002;Sun et al. 2004;Wheeler et al. 2003;Yin et al. 2010;Zdravkovic and Carter 2008;Zhou et al. 2005). The main strengths and limitations of these rotational hardening rules have been discussed and evaluated deeply by Dafalias and Taiebat (2013), with three representative models (Dafalias 1986;Wheeler et al. 2003) being chosen to simulate experimental tests. ...
An anisotropic plasticity model for the description of nonisotropic mechanical behaviors of porous media is presented. This model is developed using bounding surface plasticity theory within the critical state framework. The inherent and stress-induced an-isotropy has been accounted for by an anisotropic variable, which is employed with the consideration of both irrecoverable deformation and stress state. The evolution of anisotropy has been described by both rotational and distortional hardening rules. The rotational hardening rule is proposed for the consideration of bounding surface inclination induced by inherent or induced anisotropy. The distortional hardening rule is developed to capture the varying shape of bounding surface associated with the accumulation of irrecoverable deformation and anisotropy. This model has been validated through modeling the stress-strain responses of porous media under various loading conditions, including triaxial drained/undrained compression/extension tests on both isotropically and anisotropically consolidated samples. Good agreement between model simulation and experimental results has been achieved for all cases taken into consideration , demonstrating the capability of the proposed model.
... Since the deformation mechanism of the soil around the pile shaft is similar to the expansion of a cylindrical cavity, the pile installation effects on the surrounding soils could be properly assessed by the cylindrical cavity expansion theory [23,47,51,74]. Given the fact that the initial stress state of most natural clay deposits is anisotropic due to their deposition and K 0 consolidation [17,60,67], the elasto-plastic solution for cylindrical cavity expansion, presented by Li et al. [32] based on an anisotropic modified Cam-clay (AMCC) model, is employed in this study to evaluate the pile installation effects. Taking pile installation as undrained expansion of a cylindrical cavity from zero initial radius to the pile radius, the excess pore water pressure, Du pile , induced by pile installation and the mean effective stress of the soil, p 0 f , in the vicinity of the pile immediately after pile installation can be approximately evaluated by the cavity expansion solution of Li et al. [32], respectively, as follows: ...
In this paper, a simple but feasible approach is proposed to predict the time-dependent load carrying behaviours of jacked piles from CPTu measurements. The corrected cone resistance, which considers the unequal area of the cone rod and the cone, is used to determine the soil parameters used in the proposed approach. The pile installation effects on the changes in the stress state of the surrounding soil are assessed by an analytical solution to undrained expansion of a cylindrical cavity in K0-consolidated anisotropic clayey soil. Considering the similarity and scale effects between the piezocone and the pile, the CPTu measurements are properly incorporated in the shaft and end resistance factors as well as in the load-transfer curves to predict the time-dependent load carrying behaviours of the pile. Centrifuge model tests are conducted and the measured load carrying behaviours of the model piles are compared with the predictions to validate the proposed approach. The proposed approach not only greatly saves the time of conducting time-consuming pile load tests, but also effectively avoids solving the complex partial differential equations involved in the consolidation analysis, and hence is feasible enough to determine the time-dependent load carrying behaviours of jacked piles in clay.
... This paper aims to develop a generic similarity solution to undrained contraction of a cylindrical cavity in anisotropic modified Cam-clay model soils. The K 0 -AMCC model by Sun et al. [32] is employed to consider the effects of the initial stress anisotropy and stress-induced anisotropy on the cavity contraction responses. The spatially mobilized plane (SMP) criterion is adopted in the solution by making use of the stress transform method to capture the three-dimensional strength of the soils during cavity expansion. ...
... An elastoplastic model proposed by Sekiguchi and Ohta [34] for initially anisotropic clays, which is an extension of the original Cam-clay model to normally K 0 -consolidated clays, and cannot reasonably describe the three-dimensional mechanical behaviour. Therefore, a SMP criterion based K 0 -AMCC model by Sun et al. [32], which could consider the initial stress anisotropy, stress-induced anisotropy and the three-dimensional strength of natural soils, was employed in this study to formulate the cavity contraction problem. The yield function of the model is expressed as follows: ...
... The angle of inclination from the p′-axis reflects the degree of stress anisotropy in the soils. It should be noted that the SMP criterion revised K 0 -MCC model of Sun et al. [32] used in the similarity solution is an extension of MCC model, which was developed for predicting the mechanical behaviour of natural clayey soil and soft rock under various loading conditions. Hence, the proposed solution is only applicable to undrained cavity extraction in clayey soils and soft rock. ...
... Therefore, the hardening parameter should be reconstructed. Several hardening parameters and hardening modulus have been proposed and used for modelling dilatancy behaviours of sand that is related to density and stress state [29][30][31][32], anisotropy [33][34][35] and even fabric evolution [36][37][38]. However, they are all formulated based on orthogonal plastic flow conditions. ...
A non-orthogonal elastoplastic constitutive model for the sand with dilatancy is presented in the characteristic stress space. Dilatancy of sand is represented by the direction of plastic flow, which can be directly determined by applying the non-orthogonal plastic flow rule to an improved elliptic yield function. A new hardening parameter is developed to describe the contractive and dilative volume change during the shear process, which is coordinated with the non-orthogonal plastic flow direction. The combination of the non-orthogonal plastic flow rule and the proposed hardening parameter renders the proposed model with the ability to reasonably describe the stress-strain relationship of sand with dilatancy. The model performance is evaluated by comparing with the experimental data of sand under triaxial stress conditions.
