This paper presents an unconstrained stress updating algorithm for a critical state plastic model of clay soil, where the loading/unloading estimations and the consideration of the stress behaviour ...transition from elasticity to plasticity can be bypassed by using the Fischer–Burmeister smoothing function instead of the Kuhn–Tucker complementarity conditions. A smoothing tangent operator consistent with the unconstrained stress updating strategy is derived from preserving the quadratic convergence speed for the global solution. Specifically, the relationship and difference between the consistent and continuum tangent operators are analysed from the perspectives of algebra and geometry. In addition, the nonlinear constitutive equations obtained by the backward Euler integration scheme are solved by the double dogleg trust region method (improved by non-monotonic technology), where a larger strain increment than that of the newton method is allowed for the stress updating. Then, the modified Cam-clay model for soil is implemented in ABAQUS/Standard by the proposed algorithm. The results of numerical examples show that the algorithm has significant advantages in terms of computation efficiency and robustness in contrast to the ABAQUS/Standard default integration algorithm, especially for the condition of large load increments and cyclic loadings. More than twice the computational efficiency of the ABAQUS/Standard default integration algorithm can be observed in the representative numerical examples. The source code of the proposed algorithm is freely available at https://github.com/zhouxin615/NMTR_Method.
•Non-smoothness of MCC model is eliminated by unconstrained stress updating strategy.•Implicit integration equations is solved by non-monotonic region method.•Smoothing consistent tangent operator is derived.•Convergence of proposed algorithm is superior to that of ABAQUS algorithm.
This paper presents an exact semi-analytical analysis for cylindrical cavity expansion in modified Cam Clay critical state soil under the undrained condition. By assuming small-strain deformation in ...the elastic region and largestrain deformation in the plastic region, the formulation of the problem is reduced to solving a system of firstorder ordinary differential equations for the radial, tangential and vertical effective stresses in the plastic zone. The pore pressure distribution can subsequently be determined from the radial equilibrium equation in terms of the total stresses. The semi-analytical solution derived in this paper follows the rigorous definitions for the two effective stress invariants instead of approximate ones, as usually assumed in the existing literature, and applies to the more general case where the out-of-plane (vertical) in situ stress may be different from the in-plane (horizontal) one. The results show clearly that the stress history (overconsolidation ratio) has a significant influence on the stress and pore pressure distributions around the cavity. The present solution provides an exact and realistic theoretical framework for predicting the soil behaviour around the cylindrical cavity, with applications to the interpretation of pressuremeter tests and to pile installation problems. It also serves as a valuable benchmark for verifying various cavity expansion numerical methods involving the critical state plasticity model.
This study formulated the Cam-clay model, an elastoplastic constitutive model for fully remolded and normally consolidated clay, using the multiplicative decomposition of the deformation gradient and ...a hyperelastic body to correspond to the finite deformation theory. Finite deformation elastoplastic theory in this framework has been developed for metallic materials that do not yield plastic volume change. If this theory is directly applied to a model that yields plastic volume change, the Cauchy stress cannot be determined only from the current elastic deformation. Therefore, the existing multiplicative decomposition Cam-clay models cannot accurately reproduce the experimental facts underlying the core of critical-state soil mechanics. Through thermodynamic considerations that consider the volume changes occurring in the intermediate configuration, this study determined a common stress suitable for describing the elastic and plastic components, in addition to forms of hyperelastic body and plastic flow rule. Consequently, the proposed model can draw the state boundary surface in the Cauchy stress-specific volume space, which previous models could not achieve. In addition, an implicit stress-update algorithm for the proposed model was constructed, and a tangent modulus consistent with the algorithm was derived. The proposed model demonstrated the same numerical calculation convergence as that of existing models.
This work studies the response of a 2 x 2 pile group near a slope subjected to lateral load. Three-dimensional, non-linear finite element analysis is carried out. The entire code is developed in ...FORTRAN 90. Bending-dominated pile and pile caps are represented by 20 node elements with quadratic shape function, and shear-dominated soil elements are represented by eight-node elements with linear shape function. Sixteen node interface element of zero thickness is used for stress transfer between pile and soil. The outcome highlights the influence of slope parameters like slope angle and edge distance on the response of the 2 x 2 pile group near a slope. The lateral displacement and maximum bending moments are increased with an increase in slope. However, its effect reduces with an increase in slope distance. The point of zero-shear along the pile's depth shifts deeper with an increase in slope.
The effect of clay structure on the piezocone penetration test results and its mechanism are not very clear, the structured Cam-clay model is firstly program-implemented in the ABAQUS software. Then, ...the numerical model of piezocone penetration into structured clay is established, and the effect of clay structure on piezocone penetration test results is analyzed through numerical simulation. The numerical calculation results show that (1) the clay structure causes the increase of deviatoric stress of the soils surrounding the cone tip, and the maximum deviatoric stress appears at the lower right at some distance from the cone tip due to the structural damage of the soils near the cone tip. (2) The larger the parameter \begin{document}$p\text{'}_{ {\rm{yi}}} $\end{document} representing structural strength is, the larger the cone tip resistance qc, and the larger the parameter w representing structural damage speed, the smaller the qc value. (3) The larger the \begin{document}$p\text{'}_{ {\rm{yi}}} $\end{docu
AbstractThis paper presents a semianalytical solution for drained expansion of a cylindrical cavity in K0-consolidated clay. The solution is derived based on the K0-based anisotropic modified ...Cam-clay model (K0-AMCC), which can properly consider the initial stress anisotropy and the initial stress-induced anisotropy of natural soils. Parametric studies are carried out to investigate the effects of different overconsolidation ratios on the growth of plastic zone and cavity pressure, the distributions of the stress components and the specific volume around the cavity, and the effective stress path. The results are compared with the published solution based on the modified Cam-clay model to study the effects of the initial stress anisotropy and the initial stress-induced anisotropy on the cylindrical cavity expansion. The present solution provides a more realistic interpretation for practical geotechnical engineering problems such as pressuremeter tests and cone penetration tests.
Suffusion, one of the modes of internal erosion, occurs when fine particles are detached under hydraulic force. More fine particles are washed out with the void growth, which subsequently causes the ...failure of earthworks. At present, constitutive models considering suffusion are mostly established through DEM simulations and constitutive models that can capture the main features of eroded soils are quite limited. This study aims to establish constitutive equations to model the mechanical behaviour of soils subjected to suffusion by using drained triaxial experimental data. The modified subloading Cam-clay model incorporated with the normal yield surface for the eroded soil is proposed, which can express the variation of the normal yield surface with the loss of fine particles. The determination method of the erosion-related model parameters is also proposed. The erosion-related model parameters are estimated through empirical equations with curve-fitted parameters. Finally, the capability of this modified model is demonstrated through the comparisons with experimental results.
AbstractThis study proposes a new method to introduce the cementation effect into existing elastoplastic constitutive models for soils. The mechanical properties of cement-treated soil are evaluated ...via element tests and compared with those of naturally deposited clay. The similarities and differences between cement-treated soils and naturally deposited clays are studied, focusing on two states, the undisturbed and remolded states. The effective stress for cement-treated soils incorporating an internal state variable representing the cementation effect is newly defined to describe the mechanical properties of cement-treated soils. Moreover, by applying this extended effective stress to the super-subloading yield surface (SYS) Cam-clay model, which is an elastoplastic model for soils based on the skeleton structure concept, the scope of this constitutive model is extended to include cement-treated soils. The cementation effect introduced by the proposed method allows reproducing the mechanical behavior of the cement-treated soil. Finally, a brittle behavior not described at the element level can be obtained, leading to a soil–water coupled finite deformation analysis incorporating the proposed constitutive model.
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