Modeling of shear localization during confined granular flow in silos within non-local hypoplasticity

The paper deals with multiple shear zones in the interior of cohesionless granular bodies during plane strain quasi-static granular flow with controlled outlet velocity in experimental silos. The finite element calculations were carried out with a hypoplastic constitutive model enhanced by a characteristic length of micro-structure by means of a non-local theory to obtain mesh-independent results. The constitutive model can reproduce the essential features of granular materials during shear localization. FE analyses were performed with the help of an Arbitrary Lagrangian-Eulerian formulation using an explicit time integration approach for experimental silos containing initially dense dry cohesionless sand. Silo walls were assumed to be very rough or smooth. Emphasis was given to the propagation of multiple shear zones in the interior of flowing sand. The numerical results were compared with corresponding experimental tests.     

Vibratory pile driving in water-saturated sand: Back-analysis of model tests using a hydro-mechanically coupled CEL method

The development of a hydro-mechanically coupled Coupled-Eulerian–Lagrangian (CEL) method and its application to the back-analysis of vibratory pile driving model tests in water-saturated sand is presented. The predicted pile penetration using this approach is in good agreement with the results of the model tests as well as with fully Lagrangian simulations. In terms of pore water pressure, however, the results of the CEL simulation show a slightly worse accordance with the model tests compared to the Lagrangian simulation. Some shortcomings of the hydro-mechanically coupled CEL method in case of frictional contact problems and pore fluids with high bulk modulus are discussed. Lastly, the CEL method is applied to the simulation of vibratory driving of open-profile piles under partially drained conditions to study installation-induced changes in the soil state. It is concluded that the proposed method is capable of realistically reproducing the most important mechanisms in the soil during the driving process despite its addressed shortcomings.     

Seismo-hypoplasticity with a granular temperature

Skeletons of hard grains reveal rate-dependence, creep and relaxation almost as soils with soft particles. This non-linear viscosity is explained with a granular temperature T _g instead of T. The framework of hypoplasticity is used and briefly outlined, first without viscosity and then with it. Biaxial test results with monotonous deformations can be matched with a suitable T _g. This is deformation-controlled and thus rate-independent. Cumulative changes of shape and state due to irregular cycles can be modelled with a suitably increased T _g. Applications are indicated, and the physical background is discussed.     

Silo-quake—measurements, a numerical approach and a way for its suppression

Silo-quake can be observed in granular bodies during silo emptying in the form of dynamic effects as pulsations or shocks. Measurements were carried out in full-scale aluminium silos containing potato powder and polymer granulates, and in a model perspex silo containing different fills to investigate this phenomenon. Theoretically, dynamic effects in silos were analysed with a finite element method developed in the frame of a polar (Cosserat) continuum using an elastoplastic and a hypoplastic approach. The onset of a dynamic silo flow with controlled and free outlet velocity in a plane strain model silo was simulated. A reliable, practical method to significantly reduce dynamic effects and to suppress resonance effects in mass flow during silo emptying was proposed. It was verified with experiments and FE-calculations.     

Effect of inherent anisotropy on acceleration wave speeds in hypoplasticity

Generally, soils possess an inherent fabric with transverse isotropy on the bedding plane. As a consequence, the deformation-stress characteristics show a dependence on the loading direction. Anisotropy is characterized by a vector normal to the bedding plane. In this paper we investigate the speeds of acceleration waves in an inherently anisotropic hypoplastic material. For the incrementally nonlinear hypoplastic constitutive equation the wave speed spectrum is continuous in contrast to discrete spectra in incrementally linear constitutive models. The so-called flutter instability arises when the equation for the wave speeds has complex solutions. In the principal stress space, a surface of first occurrence of flutter instability can be identified by analogy with the failure surface defined by a vanishing stress rate. We analyse the influence of the anisotropy on these surfaces and the change in their shape and symmetries depending on the bedding angle.     

Bedding effects in bulk solids in silos: experiments and a polar hypoplastic approach

This paper is concerned with bedding effects in granular bulk solids in silos. Finite element (FE)-analyses were performed for a cylindrical thin-walled steel model silo with imperfections containing dry sand. Numerical calculations were carried out for an axisymmetric case with a polar hypoplastic constitutive relation which can capture the salient properties of granular materials. In the FE-calculations, different types of wall displacements along the silo height were taken into account to model roughly the formation of buckles due to initial imperfections of the silo wall. The effects of the initial void ratio and mean grain diameter of bulk solids, initial stress state, wall roughness, and size and form of buckles were studied. The numerical results clearly show that the modelling of a bedding effect of bulk solids in silos by means of springs is too simple and can lead to strongly unrealistic predictions of the bedding modulus.     

FE-investigation of shear localization in granular bodies under high shear rate

Shear localization in granular materials under high shear rate is analysed with the finite element method and a micro-polar hypoplastic constitutive model enhanced by viscous terms. We consider plane strain shearing of an infinitely long and narrow granular strip of initially dense sand between two very rough walls under conditions of free dilatancy. The constitutive model can reproduce the essential features of granular materials during shear localization. The calculations are performed under quasi-static and dynamic conditions with different shear rates. In dynamic regime, the viscosity terms are formulated based on a modified Newtonian fluid and according to the formula by Stadler and Buggisch (Proceedings of the conference on Reliable flow of particulate solids, EFCE Pub. Series, vol 49. Chr. Michelsen Institute, Bergen, 1985). Emphasis is given to the influence of inertial and viscous forces on the shear zone thickness and mobilized wall friction angle.     

Numerical modelling of quaking in tall silos

Quaking in tall mass flow silos is a significant problem faced by industry, and can be treated as a simple one-dimensional system. In this paper, quaking in tall silos is examined using a dynamic version of Janssen's equation, based on a one-dimensional version of a hypoplastic constitutive model. This model is used to examine the motion of rarefaction waves such as those present at the beginning of each quake cycle, and the numerical solutions for this system show many features in common to experimental findings from previous studies. In particular, the model shows the same exponential growth of the amplitude of quakes with the height of the silo, as that observed experimentally. Through this model the role of wall friction in the quaking process can be understood.     

FE-studies on Shear Localization in an Anistropic Micro-polar Hypoplastic Granular Material

The effect of transverse isotropy on shear localization in cohesionless granular materials is numerically investigated upon monotonous plane strain deformation paths using a hypoplastic constitutive model enhanced by micro-polar terms. In this model, a so-called density function is reformulated and made anisotropic. Dense sand specimens under constant lateral pressure are numerically tested for uniform and stochastic distributions of the initial void ratio and for two different mean grain diameters.