Micromechanical modelling for effect of inherent anisotropy on cyclic behaviour of sand

The inherent anisotropy more or less exists in sand when preparing samples in laboratory or taking from field. The purpose of this paper is to model cyclic behaviour of sand by means of a micromechanical approach considering inherent anisotropy. The micromechanical stress–strain model developed in an earlier study by Chang and Hicher (2005) is enhanced to account for the stress reversal on a contact plane and the density state-dependent dilatancy. The enhanced model is first examined by simulating typical drained and undrained cyclic tests in conventional triaxial conditions. The model is then used to simulate drained cyclic triaxial tests under constant p′ on Toyoura sand with different initial void ratios and different levels of p′, and undrained triaxial tests on dense and loose Nevada sand. The applicability of the present model is evaluated through comparisons between the predicted and the measured results. The evolution of local stresses and local strains at inter-particle planes due to externally applied load are discussed. All simulations have demonstrated that the proposed micromechanical approach is capable of modelling the cyclic behaviour of sand with inherent and induced anisotropy.     

砂土初始孔隙比空间变异性对其力学特性及破坏模式的影响分析

现有研究大多采用简单的摩尔库伦模型针对土的空间变异性对边坡或基础的安全系数或失效概率做计算分析.事实上临界状态本构模型,如SIMSAND,能更准确地反映土的应力-应变关系.为此,本文采用SIM-SAND模型,针对砂土初始孔隙比的空间变异性对其力学特性及破坏模式的影响做详细分析,算例采用简单的室内平面应变双轴试验,分为松砂排水、密砂排水、松砂不排水和密砂不排水四种情况.每一种情况均采用蒙特卡罗方法进行初始孔隙比的随机分布生成,并做大量计算,以此来分析初始孔隙比的不均匀性对剪切带生成和破坏模式和竖向承载力发展及其概率密度分布的影响.     

Micromechanical modeling for behavior of silty sand with influence of fine content

Silty sand is a soil mixture with coarse grains and fine grains. Experimental observations have shown that small amount of fines may reduce the undrained shear strength significantly. The purpose of this paper is to propose a micromechanical model for the stress–strain behavior of silty sand influenced by fines under drained and undrained conditions. The micromechanical stress–strain model accounts for the influence of fines on the density state of the soil mixture, thus consequently affect the critical state friction angle and the amount of sliding between particles. The present model is examined by simulating typical drained and undrained tests in conventional triaxial conditions. The simulated stress–strain curves are compared with the measured results on samples made of Ottawa sand and Foundry sand with various amounts of fines. The predictive ability of the present model for simulating the behavior of silty sand is discussed.     

Unified modeling of the monotonic and cyclic behaviors of sand and clay

In this study, we aim to investigate a unified modeling method for the monotonic and cyclic behaviors of sand and clay. A simple double-yield-surface model, with plastic hardening modulus and dilatancy relation being dependent on density state unlike in existing approaches,is developed by considering the location of the critical state line. The model is used to simulate the drained and undrained tests of various sands and clays under monotonic and cyclic loadings.Prediction results are compared with experimental results, which show that the proposed approach is capable of modeling the monotonic and cyclic behaviors of sand and clay.     

饱和砂土的循环边界面本构模

饱和砂土在循环加卸载过程中,土体发生显著的组构变化和塑性变形的累积。试验现象分析表明,循环过程中,砂土的首次与再循环塑性模量既有区别又有联系。因此,论文引入考虑组构变化的剪胀内变量,并提出循环塑性模量的关系式,真实描述上述两种现象;进而基于已有本构模型的基础上,建立饱和砂土的循环边界面本构模型。最后,将饱和砂土的模型预测结果与三轴试验结果进行验证对比,得到较好地吻合,这表明该模型能够合理反映饱和砂土循环加卸载的变形行为。     

Unified sand modeling using associated or non-associated flow rule

A constitutive model for unified modeling of sand behavior was formulated in this study. The model is based on generalized plasticity and critical state mechanics. It incorporates a unique flow rule and a unique hardening modulus. The flow rule is a function of the void ratio and its deviation from an associated flow rule reduces with an increase in sand density. The hardening modulus allows the model to simulate a wide range of sand behavior even with an associated flow rule. With 13 material constants, most of which have definite physical meanings and are straightforward to calibrate using conventional element tests, the model can simulate the drained and undrained responses of sand over a large range of initial void ratios and confining pressures. In addition, the model can be readily degenerated to follow an associated flow rule. The associated-flow-model, which requires 11 material constants, can also reproduce the responses of medium-loose to dense sands when the confining pressure is modest. Although the associated-flow model is not capable of describing the bifurcation of sand responses before the failure surface is reached, it may have advantage in the numerical simulation of well-compacted earth structures like earthdams, embankments and retaining walls.     

Mechanical Behaviors of Saturated Sand under Complicated Loading

The different physical states of saturated sand, including shear elasticity, positive dilatancy, and negative dilatancy (preliminary negative dilatancy, secondary negative dilatancy and reversal negative dilatancy) are revealed based on the pore water pressure response of saturated sand in undrained dynamic torsional tests of thin cylinder samples and also checked by the drained cyclic triaxial tests under a given mean effective normal stress. According to the effective stress path of different physical states under the undrained cyclic torsional tests the physical state transformation surface, stress history boundary and yield surface are determined, and the state boundary surface is also determined by the range of effective frictional stress state movement. Based on the moving yield surface without rotation, and the expanding stress history boundary surface relevant to the stress path variations under different physical states in 3D stress space, a physical state model is proposed to provide a new app     

剪胀性砂土边界面模型的研究

剪胀性对于砂土,尤其是中密以及密实砂土,是一个非常显著的特性。相变线是剪胀性砂土的特征曲线,能够反映砂土的围压以及初时孔隙比对变形特性的影响。本文在边界面塑性理论的框架内,把相变状态参量引入到剪胀方程以及塑性硬化模量中,建立了一个能够描述砂土剪胀性以及循环特性的本构模型。本模型采用一套参量可以模拟不同初时孔隙比、不同围压、排水(或不排水)条件下单调(或循环)加载的应力-应变特性。验证表明本模型数值计算与试验结果相吻合。     

Elasto-plastic stress-strain theory for cohesionless soil with curved yield surfaces

An elasto-plastic stress-strain theory for cohesionless soil with curved yield surfaces is developed on the basis of soil behavior observed in laboratory tests. This theory is applicable to general three-dimensional stress conditions, but the parameters required to characterize the soil behavior can be derived entirely from results of isotropic compression and conventional drained triaxial compression tests. The theory is shown to predict soil behavior under various loading conditions with good accuracy. Of special interest is its capability of predicting soil behavior under drained as well as undrained conditions over a range of confining pressures where the behavior changes from that typical of dense sand to that typical of loose sand. Work-hardening as well as work-softening is incorporated in the theory.     

Discrete simulation and micromechanical analysis of two-dimensional saturated granular media

In this study, a novel approach to incorporate the pore water pressure in the discrete element method (DEM) to comprehensively model saturated granular media was developed. A numerical model was constructed based on the DEM by implanting additional routines in the basic DEM code; pore water pressure calculations were used with a two-dimensional (2D) model to simulate the undrained behavior of saturated granular media. This model coupled the interaction of solid particles and the pore fluid in saturated granular media. Finally, several 2D undrained shear tests were simulated. The test results showed that the model could predict the response of the saturated granular soil to shear loading. The effect of initial compaction was investigated. Biaxial tests on dense and loose specimens were conducted, and the effect of the initial density on the change in shear strength and the volume change of the system was investigated. The overall behavior of loose and dense specimens was phenomenologically similar to the real granular material. Constant volume tests were simulated, and the results were compared to those from the coupled model. Induced anisotropy was micromechanically investigated by studying the contact force orientation. The change in anisotropy depended on the modeling scheme. However, the overall responses of the media obtained using the coupled and constant volume methods were similar.     

Discrete simulation and micromechanical analysis of two-dimensional saturated granular media

In this study, a novel approach to incorporate the pore water pressure in the discrete element method （DEM） to comprehensively model saturated granular media was developed. A numerical model was constructed based on the DEM by implanting additional routines in the basic DEM code; pore water pressure calculations were used with a two-dimensional （2D） model to simulate the undrained behavior of satu- rated granular media. This model coupled the interaction of solid particles and the pore fluid in saturated granular media. Finally, several 2D undrained shear tests were simulated. The test results showed that the model could predict the response of the saturated granular soil to shear loading. The effect of initial compaction was investigated. Biaxial tests on dense and loose specimens were conducted, and the effect of the initial density on the change in shear strength and the volume change of the system was inves- tigated. The overall behavior of loose and dense specimens was phenomenologically similar to the real granular material. Constant volume tests were simulated, and the results were compared to those from the coupled model. Induced anisotropy was micromechanically investigated by studying the contact force orientation. The change in anisotropy depended on the modeling scheme. However, the overall responses of the media obtained usinz the couoled and constant volume methods were similar.     

Study of modeling unsteady blade row interaction in a transonic compressor stage part 1: code development and deterministic correlation analysis

The average-passage equation system (APES) provides a rigorous mathematical framework for accounting for the unsteady blade row interaction through multistage compressors in steady state environment by introducing deterministic correlations (DC) that need to be modeled to close the equation system.The primary purpose of this study is to provide insight into the DC characteristics and the influence of DC on the time-averaged flow field of the APES.In Part 1 of this two-part paper,firstly a 3D viscous unsteady and time-averaging flow CFD solver is developed to investigate the APES technique.Then steady and unsteady simulations are conducted in a transonic compressor stage.The results from both simulations are compared to highlight the significance of the unsteady interactions.Furthermore,the distribution characteristics of DC are studied and the DC at the rotor/stator interface are compared with their spatial correlations (SC).Lastly,steady and time-averaging (employing APES with DC) simulations for the downstream stator alone are conducted employing DC derived from the unsteady results.The results from steady and time-averaging simulations are compared with the time-averaged unsteady results.The comparisons demonstrate that the simulation employing APES with DC can reproduce the time-averaged field and the 3D viscous time-averaging flow solver is validated.     

Influence of grading on the undrained behavior of granular materials

This paper aims at investigating the influence of grading on the undrained behavior of granular materials. Series of undrained triaxial tests were carried out with two different materials, glass balls and Hostun sand. For each material, samples with different gradings and similar relative densities were prepared. Experimental results show that the undrained shear strength decreases when the coefficient of uniformity C_u=d₆₀/d₁₀$C_{\mathrm{u}}=d_{60}/d_{10}$ increases from 1.1 to 20. The conditions of instability for the selected granular materials were also analyzed, based on the sign of the second-order work during undrained triaxial loading. The results demonstrate a significant influence of the grading: increasing the coefficient of uniformity heightens the potential of static liquefaction and the materials become more unstable. Furthermore, numerical tests using the three-dimensional discrete element method (DEM) were conducted on assemblies of spheres. The DEM inter-particle parameters were derived from the experimental test results on glass balls. The DEM simulations showed similar behaviors compared to experimental results and confirmed the influence of the grain size distribution on the stress–strain relationship and instability phenomena.     

Effect of Particle Morphology,Compaction, and Confinement on the High Strain Rate Behavior of Sand

The effect of grain shape, size distribution, intergranular friction, confinement, and initial compaction state on the high strain rate compressive mechanical response of sand is quantified using Long Split Hopkinson Pressure Bar (LSHPB) experiments, generating up to 1.1 ms long load pulses. This allowed the dynamic characterisation of different types of sand until full compaction (lowest initial void ratio) at different strain rates. The effect of the grain morphology and size on the dynamic compressive mechanical response of sand is assessed by conducting experiments on three types of sand: Ottawa Sand with quasi-spherical grains, Euroquartz Siligran with subangular grains and Q-Rok with polyhedral grain shape are considered in this study. The adoption of rigid (Ti64) and deformable (Latex) sand containers allowed for quasi-uniaxial strain and quasi-uniaxial stress conditions to be achieved respectively. Additionally, the effect of intergranular friction was studied, for the first time in literature, by employing polymer coated Euroquartz sand. Appropriate procedures for the preparation of samples at different representative initial consolidation states are utilized to achieve realistic range of naturally occurring formations of granular assembly from loose to dense state. The results identify material and confining sample state parameters which have significant effect on the mechanical response of sand at high strain rates and their interdependency for future integration into rate dependent constitutive models.     

Wing/body kinematics measurement and force and moment analyses of the takeoff flight of fruitflies

In the paper, we present a detailed analysis of the takeoff mechanics of fruitflies which perform voluntary takeoff flights. Wing and body kinematics of the insects during takeoff were measured using high-speed video techniques.Based on the measured data, inertia force acting on the insect was computed and aerodynamic force and moment of the wings were calculated by the method of computational fluid dynamics. Subtracting the aerodynamic force and the weight from the inertia force gave the leg force. The following has been shown. In its voluntary takeoff, a fruitfly jumps during the first wingbeat and becomes airborne at the end of the first wingbeat. When it is in the air, the fly has a relatively large "initial" pitch-up rotational velocity(more than5 000°/s) resulting from the jumping, but in about 5 wingbeats, the pitch-up rotation is stopped and the fly goes into a quasi-hovering flight. The fly mainly uses the force of jumping legs to lift itself into the air(the force from the flapping wings during the jumping is only about 5%–10% of the leg force). The main role played by the flapping wings in the takeoff is to produce a pitch-down moment to nullify the large "initial" pitch-up rotational velocity(otherwise, the fly would have kept pitching-up and quickly fallen down).     

Modeling liquefaction of water saturated granular material under undrained cyclic shearing

The tendency of particles in a water-saturated granular mass to re-arrange into a denser state during cyclic shearing under pressure results in an increase in pore water pressure. The increase in the pore water pressure causes a reduction in the inner particle contact forces, and in turn easier re-arrangement of the particles. Eventually, the material loses its shear strength, partially or almost completely. In this paper, a general three-dimensional continuum mechanics model is presented for the deformation of granular materials. A physically based model is also presented for characterization of liquefaction of the water saturated granular material under undrained cyclic shearing. The model incorporates the fabric of the granular mass, which develops as the frictional granular mass is deformed in shear. It includes the coupling between shearing and excess pore water pressure. The model parameters are estimated, based on the results of cyclic shearing experiments on large hollow cylindrical samples of silica sand. Basically, the calculation results utilizing this model can embody liquefaction phenomena of the water saturated granular material under undrained cyclic shearing.     

Hybrid algorithm for modeling of fluid-structure interaction in incompressible, viscous flows

The objective of this paper is to present and to validate a new hybrid coupling (HC) algorithm for modeling of fluid-structure interaction (FSI) in incompressible, viscous flows. The HC algorithm is able to avoid numerical instability issues associated with artificial added mass effects, which are often encountered by standard loosely coupled (LC) and tightly coupled (TC) algorithms, when modeling the FSI response of flexible structures in incompressible flow. The artificial added mass effect is caused by the lag in exchange of interfacial displacements and forces between the fluid and solid solvers in partitioned algorithms. The artificial added mass effect is much more prominent for light/flexible structures moving in water, because the fluid forces are in the same order of magnitude as the solid forces, and because the speed at which numerical errors propagate in an incompressible fluid. The new HC algorithm avoids numerical instability issues associated with artificial added mass effects by embedding Theodorsen’s analytical approximation of the hydroelastic forces in the solution process to obtain better initial estimates of the displacements. Details of the new HC algorithm are presented. Numerical validation studies are shown for the forced pitching response of a steel and a plastic hydrofoil. The results show that the HC algorithm is able to converge faster, and is able to avoid numerical instability issues, compared to standard LC and TC algorithms, when modeling the transient FSI response of a plastic hydrofoil. Although the HC algorithm is only demonstrated for a NACA0009 hydrofoil subject to pure pitching motion, the method can be easily extended to model general 3-D FSI response and stability of complex, flexible structures in turbulent, incompressible, multiphase flows.     

A note on the definition of fractional derivatives applied in rheology

It is known that there exist obivious differences between the two most commonly used definitions of fractional derivatives—Riemann–Liouville (R–L) definition and Caputo definition. The multiple definitions of fractional derivatives in fractional calculus have hindered the application of fractional calculus in rheology. In this paper, we clarify that the R–L definition and Caputo definition are both rheologically imperfect with the help of mechanical analogues of the fractional element model (Scott–Blair model). We also clarify that to make them perfect rheologically, the lower terminals of both definitions should be put to ∞. We further prove that the R–L definition with lower terminal a →∞ and the Caputo definition with lower terminal a →∞ are equivalent in the differentiation of functions that are smooth enough and functions that have finite number of singular points. Thus we can define the fractional derivatives in rheology as the R–L derivatives with lower terminal a →∞ (or, equivalently, the Caputo derivatives with lower terminal a →∞) not only for steady-state processes, but also for transient processes. Based on the above definition, the problems of composition rules of fractional operators and the initial conditions for fractional differential equations are discussed, respectively. As an example we study a fractional oscillator with Scott–Blair model and give an exact solution of this equation under given initial conditions.     

Pore pressure generation in a saturated sand layer subjected to a cyclic horizontal acceleration at its base

A compaction theory for saturated sand, of differential type, is applied to shear wave propagation through a layer induced by cyclic horizontal acceleration of its base. The compaction relation incorporates dependence on the pore fluid pressure, and in turn the pore pressure is related to the compaction through the elastic compression relations. An assumption of undrained flow, which will yield the maximum pore pressures, allows straightforward numerical solution of the simplified dynamic equations. A variety of results are computed for comparison with alternative predictions.