Numerical stability for modelling of dynamic two‐phase interaction

Dynamic two‐phase interaction of soil can be modelled by a displacement‐based, two‐phase formulation. The finite element method together with a semi‐implicit Euler–Cromer time‐stepping scheme renders a discrete equation that can be solved by recursion. By experience, it is found that the CFL stability condition for undrained wave propagation is not sufficient for the considered two‐phase formulation to be numerically stable at low values of permeability. Because the stability analysis of the two‐phase formulation is onerous, an analysis is performed on a simplified two‐phase formulation that is derived by assuming an incompressible pore fluid. The deformation of saturated porous media is now captured in a single, second‐order partial differential equation, where the energy dissipation associated with the flow of the fluid relative to the soil skeleton is represented by a damping term. The paper focuses on the different options to discretize the damping term and its effect on the stability criterion. Based on the eigenvalue analyses of a single element, it is observed that in addition to the CFL stability condition, the influence of the permeability must be included. This paper introduces a permeability‐dependent stability criterion. The findings are illustrated and validated with an example for the dynamic response of a sand deposit. Copyright © 2015 John Wiley & Sons, Ltd.     

Modelling of sand behaviour under earthquake excitation

In this paper, liquefaction potential of loose sand deposit subjected to an earthquake loading is evaluated. The analysis is performed by using a finite element technique incorporating the equations of dynamics of saturated porous elastoplastic media. The soil response is modelled by an anisotropic hardening rule, similar to that as proposed by Poorooshasb and Pietruszczak.¹ The concept is based on the theory of bounding surface plasticity incorporating a non-associated flow rule and the idea of reflected plastic potential. The present paper provides a modified formulation to that discussed in Reference 1. Modifications are aimed at simplifying the concept for numerical implementations.     

An updated reference configuration formulation for large-deformation problems

This paper examines difficulties encountered when using the Green-Nagdi rate and presents an updated configuration formulation for problems dealing with large deformations. It is shown that a natural link can be established between the updated reference configuration and linearized updated Lagrangian formulations, if Truesdell's objective stress rate is used. Owing to this connection, any limitations associated with the described formulation would be expected to also apply to an updated Lagrangian formulation and vice versa. It is pointed out that, if second-order effects are induced, the Truesdell rate appears in the rate equation for equilibrium even when strains are infinitesimal. By examining a simple-shear problem, where hypoelastic material behaviour with ‘Hooke's law’ is assumed, it is shown that the spherical state of stress is coupled with the shear stress when using the Truesdell or Green-Nagdi stress rate. It is suggested that objective stress rates, introduced in large-deformation formulations, may contribute to erroneous predictions if a constitutive law is developed independent of the adopted stress rate.     

Investigation of a hybrid polygonal finite element formulation for confined and unconfined seepage

This study presents a formulation for field problems using hybrid polygonal finite elements, taking steady state seepage through a porous material as the focus. We make comparisons with a conventional finite element formulation based on a single primary variable, focussing on the advantages of the hybrid formulation in terms of flux field accuracy and extension to convex polygonal shaped elements. For the unconfined case, we adopt a head dependent hydraulic conductivity that does not require remeshing. The performance of the hybrid polygonal element formulation is demonstrated through a series of numerical examples. The results show a sensitivity of the location of the free surface in unconfined seepage to mesh configuration for hybrid quadrilateral meshes with various aspect ratios, but not for hybrid polygonal meshes with various orientations and irregularity. Examination of the free surface location results for several conforming shape function options shows an insensitivity to choice of interpolation function, provided that it conforms with the assumptions in the formulation. Copyright © 2016 John Wiley & Sons, Ltd.     

Two‐phase dynamic analysis by material point method

This paper extends the material point method to analyze coupled dynamic, two‐phase boundary‐valued problems via a velocity formulation, in which solid and fluid phase velocities are the variables. Key components of the proposed approach are the adoption of Verruijt's sequence of update steps when integrating over time and the enhancement of volumetric strains. The connection between fractional step method and the time‐stepping algorithm presented in this paper is addressed. Enhancement of volumetric strains allows lower order variations in pressure and mitigates spurious pressure fields and locking that plague low‐order finite‐element implementations. A stress averaging technique to smoothen stress variations is proposed, and the local damping procedure adopted by FLAC is extended to handle two‐phase problems. Special Kelvin‐Voigt boundaries are developed to suppress reflections at artificial boundaries. Idealized examples are presented to demonstrate the capability of the proposed framework to accurately capture the physics of wave propagation, consolidation and wave attack on a sea dike. Copyright © 2012 John Wiley & Sons, Ltd.     

Landslide prediction from machine learning

Predicting where and when landslides are likely to occur in a specific region of interest remains a key challenge in natural hazards research and mitigation. While the basic mechanics of slope‐failure initiation and runout can be cast into physical and numerical models, a scarcity of sufficiently detailed and real‐time measurements of soil, rock‐mass and groundwater conditions prohibits accurate landslide forecasting. Researchers are therefore increasingly exploring multivariate data analysis techniques from the fields of data mining or machine learning in order to approximate future occurrences of landslides from past distribution patterns. This work has elucidated patterns of spatial susceptibility, but temporal forecasts have remained largely empirical. Most machine learning techniques achieve overall success rates of 75–95 percent. Whilst this may seem very promising, issues remain with data input quality, potential overfitting and commensurate inadequate choice of prediction models, inadvertent inclusion of redundant or noise variables, and technical limits to predicting only certain types and sizes of landslides. Simpler models provide only slightly inferior predictions to more complex models, and should guide the way for a more widespread application of data mining in regional landslide prediction. This approach should especially be communicated to planners and decision makers. Future research may want to develop: (1) further best‐practice guidelines for model selection; (2) predictions of occurrence and runout of large slope failures at the regional scale; and (3) temporal forecasts of landslides.     

Deformation of strain softening materials: Part I: Objectivity of finite element solutions based on conventional strain softening formulations

This paper is a continuation of the research initiated by the first author and Z. Mroz [1] during the 1980–1981 period. It is intended as a prelude to a series of articles which extend the concepts and ideas introduced at that time.In the present article, finite element analysis for conventional strain-softening concepts is provided. Sensitivity of the solution to the details of discretization (the type and number of elements) and to the strain-softening rate is discussed. The solutions obtained in this study, though unique in a mathematical sense, prove to be very sensitive to both factors. In order to avoid this sensitivity, the introduction of the geometrical strain-softening effect into the constitutive relation is recommended (after ref. [1]). An extended and generalized version of such a concept will be presented separately.