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The local flow field and seepage induced drag obtained from Pore Network Models (PNM) is compared to Immersed Boundary Method (IBM) simulations, for a range of linear graded and bimodal samples. PNM were generated using a weighted Delaunay Tessellation (DT), along with the Modified Delaunay Tessellation (MDT) which considers the merging of tetrahedral Delaunay cells. The local pressure field was very accurately captured in all linear graded and bimodal samples. Local flux (flow rate) exhibited more scatter, but the PNM based on the MDT clearly provided a better correlation with the IBM. There was close similarity in the network shortest paths obtained from PNM and IBM, indicating that the PNM captures dominant flow channels. Further, by overlaying the PNM on a streamline profile, it was demonstrated that local pressure drops coincided with the pore constrictions. A rigorous validation was undertaken for the drag force calculated from the PNM by comparing with analytical solutions for ordered array of spheres. This method was subsequently applied to all linear graded and bimodal samples, and the calculated force was compared with the IBM data. Linear graded samples were able to calculate the force with reasonable accuracy, while the bimodal sample exhibited slightly more scatter., Comment: 37 pages, 28 figures. Article published in Computers and Geotechnics (see https://doi.org/10.1016/j.compgeo.2019.02.007)

In a FE analysis of transient heat transfer, a lower limit of the time-step size exists below which numerical oscillations of temperatures may occur. Although time-step constraints for simulating 1D heat diffusion have been well established in the literature, the conclusions cannot be directly applied to 2D cases. In this paper, both analytical and computational studies are carried out to obtain the time-step constraints for 2D linear and quadratic elements. It is noted that in the simulation of 2D heat diffusion employing quadratic elements is not always beneficial. Recommendations are provided on selecting the numerical scheme to minimise numerical oscillations.

Experimental data have demonstrated that a strong relationship exists between the state parameter and the peak strength and dilatancy characteristics of sands. This paper proposes a way of reproducing this behaviour using a modified Mohr-Coulomb failure criterion, which retains its simplicity while improving substantially its modelling capabilities. The formulated constitutive model is calibrated for Nevada sand following a well-defined procedure and used in the prediction of four centrifuge tests investigating the behaviour of axially loaded footings. It is shown that the proposed model reproduces well both the element tests and the more complex footing problems, demonstrating its usefulness for engineering practice. Moreover, a simplified version which does not require the definition of the Critical State Line is proposed for situations when this aspect of soil behaviour cannot be determined with confidence. It is shown that such simplification results in only slightly less accurate predictions than the full version of the model, while simulating aspects of soil response that cannot be reproduced using constant values for strength and dilatancy parameters.

This paper presents a novel approach for hydromechanical modelling of fractured rocks by linking a finite-discrete element solid model with a control volume-finite element fluid model based on an immersed-body approach. The adaptive meshing capability permits flow within/near fractures to be accurately captured by locally-refined mesh. The model is validated against analytical solutions for single-phase flow through a smooth/rough fracture and reported numerical solutions for multi-phase flow through intersecting fractures. Examples of modelling single- and multi-phase flows through fracture networks under in situ stresses are further presented, illustrating the important geomechanical effects on the hydrological behaviour of fractured porous media., Computers and Geotechnics, 103, ISSN:0266-352X, ISSN:1873-7633

A new Petrov-Galerkin finite element method for two-dimensional (2D) highly advective flows in porous media, which removes numerical oscillations and retains its precision compared to the conventional Galerkin finite element method, is presented. A new continuous weighting function for quadratic elements is proposed. Moreover, a numerical scheme is developed to ensure the weighting factors are accurately determined for 2D non-uniform flows and 2D distorted elements. Finally, a series of numerical examples are performed to demonstrate the capability of the approach. Comparison against existing methods in the simulation of a benchmark problem further verifies the robustness of the proposed method.

Cone penetration testing (CPT) is a preferred method for characterizing soil profiles for evaluating seismic liquefaction triggering potential. However, CPT has limitations in characterizing highly stratified profiles because the measured tip resistance ( q c ) of the cone penetrometer is influenced by the properties of the soils above and below the tip. This results in measured q c values that appear “blurred” at sediment layer boundaries, inhibiting our ability to characterize thinly layered strata that are potentially liquefiable. Removing this “blur” has been previously posed as a continuous optimization problem, but in some cases this methodology has been less efficacious than desired. Thus, we propose a new approach to determine the corrected q c values (i.e. values that would be measured in a stratum absent of thin-layer effects) from measured values. This new numerical optimization algorithm searches for soil profiles with a finite number of layers which can automatically be added or removed as needed. This algorithm is provided as open-source MATLAB software. It yields corrected q c values when applied to computer-simulated and calibration chamber CPT data. We compare two versions of the new algorithm that numerically optimize different functions, one of which uses a logarithm to refine fine-scale details, but which requires longer calculation times to yield improved corrected q c profiles.

This paper outlines a framework for using molecular dynamics to simulate the compression of kaolinite saturated at alkaline pH (=8) in a low (1 mM) concentration solution. The particles are modelled as flat (3D) ellipsoids and their interactions are described by a modified form of the Gay-Berne potential, calibrated against DLVO theory. The LAMMPS software was used to generate monodisperse and slightly polydisperse samples, and to simulate isotropic compression to 100 kPa. The influences of sample size and strain rate on the void ratio and the arrangement of particles within the samples were investigated via parametric studies. It is useful to consider the extent to which the system temperature (a measure of the average kinetic energy) is controlled when assessing whether the applied strain rate is appropriate. It is found that the number of particles that can be considered a representative element volume is orders of magnitude larger than the number simulated in earlier studies and that larger number of particles are required in polydisperse samples than in the monodisperse case. A comparison between the results obtained and those of published experimental studies show that the methodology proposed can deliver sensible results for the material considered.

The numerical dissipation characteristics of the Newmark and generalised-α time-integration schemes are investigated for P-wave propagation in a fully saturated level-ground sand deposit, where higher frequencies than those for S-waves are of concern. The study focuses on resonance, which has been shown to be of utmost importance for triggering liquefaction due to P-waves alone. The generalised-α scheme performs well, provided that the time-step has been carefully selected. Conversely, the dissipative Newmark method can excessively damp the response, changing radically the computed results. This implies that a computationally prohibiting small time-step would be required for Newmark to provide an accurate solution.

Concurrent growth of multiple fractures in brittle rock is a complex process due to mechanical interaction effects. Fractures can amplify or shield stress on other fracture tips, and stress field perturbations change continuously during fracture growth. A three-dimensional, finite-element based, quasi-static growth algorithm is validated for mixed mode fracture growth in linear elastic media, and is used to investigate concurrent fracture growth in arrays and networks. Growth is governed by fracture tip stress intensity factors, which quantify the energy contributing to fracture extension, and are validated against analytical solutions for fractures under compression and tension, demonstrating that growth is accurate even in coarsely meshed domains. Isolated fracture geometries are compared to wing cracks grown in experiments on brittle media. A novel formulation of a Paris-type extension criterion is introduced to handle concurrent fracture growth. Fracture and volume-based growth rate exponents are shown to modify fracture interaction patterns. A geomechanical discrete fracture network is generated and examined during its growth, whose properties are the direct result of the imposed anisotropic stress field and mutual fracture interaction. Two-dimensional cut-plane views of the network demonstrate how fractures would appear in outcrops, and show the variability in fracture traces arising during interaction and growth.

The accurate reproduction of the hysteretic behaviour exhibited by soils under cyclic loading is a crucial aspect of dynamic finite element analyses and is typically described using the concept of damping ratio. In this paper, a general algorithm is presented for assessing the damping ratio simulated by any constitutive model based on the registered behaviour in three-dimensional stress–strain space. A cyclic nonlinear elastic model capable of accurately reproducing a wide range of features of soil behaviour, including the variation of damping ratio with deformation level, is chosen to illustrate the capabilities of the proposed algorithm. The constitutive model is described and subsequently employed in two sets of finite element analyses, one involving the dynamic response of a sand deposit subjected to different types of motion and another focussing on the simulation of a footing subjected to cyclic vertical loading. The application of the presented algorithm provides insight into the processes through which energy is dissipated through hysteresis.

Fundamental numerical studies of seepage induced geotechnical instabilities and filtration processes depends on accurate prediction of the forces imparted on the soil grains by the permeating fluid. Hitherto coupled Discrete Element Method (DEM) simulations documented in geomechanics have most often simulated the fluid flow using computational fluid dynamics (CFD) models employing fluid cells that contain a number of particles. Empirical drag models are used to predict the fluid-particle interaction forces using the flow Reynolds number and fluid cell porosity. Experimental verification of the forces predicted by these models at the particle-scale is non-trivial. This contribution uses a high resolution immersed boundary method to model the fluid flow within individual voids in polydisperse samples of spheres to accurately determine the fluid-particle interaction forces. The existing drag models are shown to poorly capture the forces on individual particles in the samples for flow with low Reynolds number values. An alternative approach is proposed in which a radical Voronoi tesselation is applied to estimate a local solids volume fraction for each particle; this local solids fraction can be adopted in combination with existing expressions to estimate the drag force. This tessellation-based approach gives a more accurate prediction of the fluid particle interaction forces.