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Bentonite is a material considered to be used as a component of a barrier in deep geological repositories for nuclear waste. Its behaviour is affected by temperature, humidity and chemical composition of water saturating its pores. Reproduction of bentonite behaviour in such thermo-hydro-mechanical (THM) conditions involves extensive use of empirical and physical coupled relationships. This paper investigates parameters, which influence the bentonite behaviour in THM experiments relevant to the conditions in the repositories. For the study, a numerical investigation is performed based on test simulation computed with the finite element code Thebes (Abed and Sołowski 2017). A numerical simulation by Abed and Sołowski (2017) of a non-isothermal infiltration experiment (Villar and Gomez-Espina 2009) has been taken as a basis for the investigation. The results of this simulation were compared with a series of 7 other simulations that are set up by inactivating the selected thermally coupled variables, one at a time. Presented results identify the key parameters the simulation is sensitive to and provide insights on the relevance of the underlying coupled processes.

The paper focuses on confined silo flow of cohesionless sand. The problem considered is a quasi-static flow in a plane strain model silo with parallel walls simulated with the material point method (MPM). The simulation used a non-local hypoplastic constitutive model. Initially, the paper validated the implemented numerical approach with basic element tests and a plane strain compression test. The subsequent MPM calculations for a model silo were performed with different initial void ratios of sand and silo wall roughness. The flow simulations took also into account the different both location and width of the outlet. The emphasis was on the evolution of both shear zones (wall and internal curvilinear shear zones) and their impact on wall stresses/forces during flow. The numerical findings enhance the understanding of shear localization in granular materials during confined controlled flow in silos and its immense effect on the magnitude and distribution of wall pressures.

Wood is a naturally occurring material widely used for construction. Due to its natural origin, wood properties vary and its behaviour is complex. This paper shows an implementation of a multi-surface elasto-plastic constitutive material model for wood into a custom explicit material point method code. The constitutive model chosen is one proposed by Schmidt & Kaliske with minor modifications to ensure better internal consistency. The model parameters are chosen based on literature data for spruce. The paper presents two Convected Particle Domain Interpolation Material Point Method simulations of experiments, both performed with the previously established model parameters. The first simulation replicates a compression test of a spruce specimen perpendicular to grain direction, carried out at the Department of Civil Engineering, Aalto University. The second simulation replicates an experiment from literature, in which a spruce specimen with knots is tensioned until failure. The numerical simulations successfully replicate the experimental outcomes qualitatively in terms of the deformation and load-displacement curves. Simulations of the three knotted specimens under tension, with introduced slight variation in wood grain direction, replicate different failure patterns with a similar failure load, resembling the behaviour of natural wooden structural elements. Additionally, one of the obtained failure patterns replicates that of the experiment well.

Funding Information: The first author acknowledges the financial support provided by the Erasmus+ programme for her stay at Aalto University. Publisher Copyright: © 2021 The Authors The chemical composition of pore fluid and matric suction rule the mechanical behaviour of soils. In case of clays, their fabric changes in line with those variables. Since both the increase in matric suction and salinity cause a transition from an open to a close microstructure of low and medium activity clayey materials, a unique framework could tackle problems where salinity and saturation changes are expected. This paper presents a simple elasto-plastic model capable of reproducing the behaviour of unsaturated clayey soils in saline environments. Changes in the pore fluid composition are addressed through the use of osmotic suction as a variable. The proposed model extends the Barcelona Basic Model for partially saturated soils to consider the effect of osmotic suction. The model, implemented in the Thebes code, is calibrated for Boom Clay. The reproduced tests include mechanical loading at different matric and osmotic suctions in oedometric conditions, as well as more complex chemo-mechanical stress paths. Despite the simplicity of the formulation, the agreement between the experimental results and the simulations is encouraging. It seems that the modelling approach addresses the most important features of partially saturated soils with saline pore fluid which are slightly or moderately expansive.

Applying the Convected Particle Domain Interpolation (CPDI) to the Material Point Method has many advantages over the original Material Point Method, including significantly improved accuracy. However, in the large deformation regime, the CPDI still may not retain the expected convergence rate. The paper proposes an enhanced CPDI formulation based on least square reconstruction technique. The Convected Particle Least Square Interpolation (CPLS) Material Point Method assumes the velocity field inside the material point domain as non‐constant. This velocity field in the material point domain is mapped to the background grid nodes with a Moving Least Squares reconstruction. In this paper, we apply the Improved Moving Least Squares method to avoid the instability of the conventional Moving Least Squares method due to a singular matrix. The proposed algorithm can improve convergence rate, as illustrated by numerical examples using the Method of Manufactured Solutions.

This paper introduces Granular algorithm enhancing Material Point Method (MPM) that allows for simulation of granular flows in the quasi-static state, the moderate flow state and the disconnected flow state. The paper first shows the shortcomings of MPM algorithms in modelling the different states of granular flows. Next, it proposes Granular MPM, an enhancement that explicitly introduces the different states of granular flow into MPM and defines the rules for the transition between those states. Subsequently, the paper gives the algorithm and implementation for Granular MPM. The provided algorithm can enhance the common versions of MPM, including original MPM, Generalised Interpolation Material Point and Convected Particle Domain Interpolation. Finally, the paper evaluates Granular MPM and compares it with other available formulation based on: (i) an examination of the behaviour of granular points on a slope, (ii) a simulation of a granular flow over two disconnected inclined surfaces, (iii) a simulation of a silo filling and (iv) a simulation of Toyoura sand flow experiment. The results of Granular MPM simulations are significantly more realistic when compared to the results obtained by other available MPM formulations. The results also indicate that Granular MPM allows for more accurate replication of steady state flows and reduces the grid dependency of MPM when modelling the disconnected flow state, as the initial contact is independent from the grid size. (C) 2021 The Author(s). Published by Elsevier Ltd.

In this paper a water retention model is developed based on soil mineralogy and microscopic features of material behaviour. The model estimates the water content at a given total suction as the sum of the bentonite minerals’ interlayer water and water in the interparticle pores. The paper proposes simple formulae to estimate the interlayer water content and interlayer void ratio based on mineralogical properties. Additionally, the model uses mercury intrusion porosimetry (MIP) measurements to approximate the water content in the larger pores. The validation of the proposed procedure relies on published data for MX-80 and GMZ bentonites and yields promising results. Even though the discussion and the validation are restricted to bentonite here, the procedure is generic in nature and can be modified easily for other geomaterials. The paper also offers insights into the links between a soil's microstructure and its macroscopic behaviour. The contribution provides a new tool for quick indirect estimation of the water retention behaviour of porous materials with known mineral composition and available microstructural data – for example, based on the MIP tests. Such a tool is of great practical interest in design – for example, nuclear waste repositories, where a large material pool may be considered initially.

The paper gives an overview of Material Point Method and shows its evolution over the last 25 years. The Material Point Method developments followed a logical order. The article aims at identifying this order and show not only the current state of the art, but explain the drivers behind the developments and identify what is currently still missing. The paper explores modern implementations of both explicit and implicit Material Point Method. It concentrates mainly on uses of the method in engineering, but also gives a short overview of Material Point Method application in computer graphics and animation. Furthermore, the article gives overview of errors in the material point method algorithms, as well as identify gaps in knowledge, filling which would hopefully lead to a much more efficient and accurate Material Point Method. The paper also briefly discusses algorithms related to contact and boundaries, coupling the Material Point Method with other numerical methods and modeling of fractures. It also gives an overview of modeling of multi-phase continua with Material Point Method. The paper closes with numerical examples, aiming at showing the capabilities of Material Point Method in advanced simulations. Those include landslide modeling, multiphysics simulation of shaped charge explosion and simulations of granular material flow out of a silo undergoing changes from continuous to discontinuous and back to continuous behavior. The paper uniquely illustrates many of the developments not only with figures but also with videos, giving the whole extend of simulation instead of just a timestamped image.

This paper introduces a novel explicit algorithm to solve the finite element equation linking the nodal displacements of the elements with the external forces applied via means of non-linear global stiffness matrix. The proposed method solves the equation using Runge-Kutta scheme with automatic error control. The method allows any Runge-Kutta scheme, with the paper demonstrating the algorithm efficiency for Runge-Kutta schemes of second to fifth order of accuracy. The paper discusses the theoretical background, the implementation steps and validates the proposed algorithm. The numerical tests show that the proposed method is robust and stable. In comparison to the iterative implicit methods (e.g. Newton-Raphson method), the new algorithm overcomes the problem of occasional divergence. Furthermore, considering the computation time, the fifth-order accurate scheme proves to be competitive with the iterative method. It seems that the proposed algorithm could be a powerful alternative to the standard solution procedures for the cases with strong nonlinearity, where the typical algorithms may diverge.

The article shows Generalized Interpolation Material Point Method numerical simulation of the Sainte Monique landslide. The simulation uses a strain-rate dependent Tresca constitutive model, extended with strain softening behaviour for structured clays. First, the paper replicates fall cone tests to validate the constitutive model and to select the material parameters. Afterwards, the paper shows the Sainte Monique landslide simulation which additionally considers shear band thickness to reduce the mesh-dependence. The results suggest that the strain-rate affects the prediction of the run-out distances and leads to the landslide acceleration-deceleration cycles (reported in, e.g. Corominas et al., 2005; Wang et al., 2010).

This paper presents two numerical applications of a newly developed fully coupled thermo-hydro-mechanical-chemical finite-element code (Thebes code). The paper starts with an introduction of the adopted theoretical framework and its implementation, followed by a description of the performed simulations. The first application involves the modelling of a large-scale mock-up test performed by the Centro de Investigaciones Energeticas Medioambientales y Tecnologicas (Madrid, Spain), which also serves as a validation benchmark. In the second application, the paper shows the solution to the Elder problem, which verifies the code’s capability to capture the density-driven salt transport triggered by hydro-chemical coupling. The results of both simulations are in good agreement with the published data and the experimental measurements, serving as a further validation of the theoretical assumptions and verification of the correctness of the code implementation.

This paper presents the simulations replicating two well-documented benchmarks on coupled gas-liquid flow in unsaturated soil. The results serve as validation and verification of the formulation of the gas flow in unsaturated geomaterials in the newly developed THMC coupled FEM code Thebes. The paper first discusses the basis of the compositional method and the role of the dry air mass balance equation in the theoretical framework. The fundamental constitutive assumptions related to gas flow, as adopted in the Thebes code, are also discussed in details. Afterwards, the paper discusses simulation of a two-phase infiltration test in unsaturated sand, as well as a one dimensional drainage test. The numerical results of these two examples show that the code is able to capture the main features associated with the gas flow in unsaturated soil. The possible future improvements, both related to the theoretical framework and the numerical implementation, are discussed at the closure of the paper.

Freezing and thawing of soils are of the utmost importance in the design of infrastructure in seasonally cold regions. Cycles of freezing-thawing can severely affect the performance of thinly paved low-volume roads, causing frost heave during the winter and thaw weakening in the spring. Thus, a designer must have an understanding of freezing effects on infrastructure and adequate design tools to deal with them. Freezing of soils entails several coupled processes, necessitating advanced analysis tools such as numerical modelling. This paper applies the Frozen and Unfrozen Soil material model for the finite element program Plaxis 2D into a case study of freezing and thawing induced deformation of a low-volume road on dry-crust clay subgrade in Vesilahti, Finland supported by a literature review and a laboratory study. The Vesilahti test site monitoring results of frost heave, temperature and groundwater level were used in this study to simulate the frost heave of a pavement with shallow structural layers. In addition, soil sampling and laboratory tests were performed to determine the Vesilahti dry-crust clay material properties at the Aalto University. These were combined to simulate the frost heave and thaw settlement measured on the site and to study the feasibility of the material model in replicating actual measured frost action. The road deformation at the measurement times was replicated qualitatively well and the model performed mostly according to expectations. However, the multitude of parameters, complexity of the coupled phenomena modelled and the black box nature of the model implementation in Plaxis make the evaluation of calculation errors tough and time-consuming. Further research on the model could include the implementation of various user-friendly improvements in Plaxis, development of cryogenic suction-and temperature-controlled laboratory testing for the model parameter determination and better utilization of the model’s predictive capabilities by studying continuous frost heave measurements.

This paper describes a thermo-hydro-mechanical framework suitable for modelling the behaviour of unsaturated soils. In particular, this paper focuses on bentonite clay subjected to a thermo-hydromechanical load, as in the case of nuclear waste engineering barriers. The paper gives a theoretical derivation of the full set of coupled balance equations governing the material behaviour as well as an extended physical interpretation. Finally, a finite element discretisation of the equations and number of simulations verifying their implementation into a custom finite element code is provided. Some aspects of the formulation are also validated against experimental data.

The deviatoric stress-deviatoric strain relationship in soils is highly nonlinear, especially in the small strain range. However, the constitutive models which aim to replicate the small strain nonlinearity are often complex and rarely used in geotechnical engineering practice. The goal of this study is to offer a simple way for updating the existing constitutive models, widely used in geotechnical practice, to take into account the small strain shear modulus changes. The study uses an existing small strain relationship to derive a yield surface. When the yield surface is introduced to an existing soil model, it enhances the model with the nonlinear deviatoric stress-deviatoric strain relationship in the small strain range. The paper also gives an example of such a model enhancement by combining the new yield surface with the Modified Cam Clay constitutive model. The validation simulations of the undrained triaxial tests on London Clay and Ham River sand with the upgraded constitutive models replicate the experiments clearly better than the base models, without any changes to existing model parameters and the core source code associated with the base model.

Streamlined drift correction is introduced into Runge-Kutta algorithms.Optimal streamlined algorithm for drift correction in stress integration identified.Simpler implementation than standard drift correction algorithm.Stress integration accuracy same as with standard drift correction algorithm. The paper proposes an efficient method of drift correction in explicit stress integration schemes. The new method does not require significant changes to existing implementations and may, in fact, be regarded as a streamlining modification to standard drift correction schemes which may be used in tandem.

Soil-water characteristic curve (SWCC) is an important characteristic of unsaturated soil. This paper investigates the total suction of the MX-80 bentonite, under different saturation and different concentrations of sodium chloride solutions. To create the soil-water characteristic curves for different amounts of NaCl, but same dry densities, the study used chilled-mirror dew-point WP4 potentiometer. The experimental results show that the concentration of salt in pore water has significant influence on the bentonite. With the increase of the NaCl concentration, the samples total suction increased gradually and the matric suction decreased. When the soil saturation was greater than 50%, the pore solution’s addition led to the rapid increase of the soil’s total suction. The low concentration of salt has relatively little effect on the matric suction of the MX-80 bentonite; while when the ion concentration is high, the solutions’ matric suction has a very significant impact on the soil matric suction.

Seven teams took part in a benchmarldng exercise on selection of parameter values for the Barcelona Basic Model (BBM) from experimental data on an unsaturated soil. All teams were provided with experimental results from 9 tests performed on a compacted soil in order to determine values for the ten BBM soil constants and an initial value for the hardening parameter. The coordinating team then performed simulations (at stress point level) with the 7 different sets of parameter values, in order to explore the implications of the differences in parameter values and hence to investigate the robustness of existing BBM parameter value selection procedures. The major challenge was found to be selection of values for the constants lambda(0), r, beta, N(0) and p(c) and an initial value for the hardening parameter (p) over bar (0)(0), with the various teams proposing significantly different values for some of these key parameters. A key lesson emerging from the exercise is the importance of choosing a method for selecting values for the parameters beta and p(c) which places the main emphasis on attempting to optimise the match to the experimental spacing of normal compression lines at different values of suction. (C) 2015 Elsevier B.V. All rights reserved.

Summary The first part of the paper presents a material point method solution for the bearing capacity of a deep foundation in purely cohesive soil, which is a widely known engineering problem. The results computed with the generalised interpolation material point method are compared to the results obtained previously with an advanced limit analysis code. The second part of the paper shows material point method simulations of collapsing piles of granular material and compares the results with experimental observations from the literature. The problems considered are problematic to solve using the displacement finite element method as they generally include very large deformations. Copyright © 2014 John Wiley & Sons, Ltd.

The material point method is a novel numerical technique which is especially well-suited to solving problems involving large or extreme deformations. This paper shows the results of the modelling of flow of granular material in inclined channels. During the calculations the granular material is approximated by a Mohr-Coulomb constitutive model. The computed flow is subsequently compared to experimental results published in the literature.

The presence of the sensitive clays in Scandinavia and Canada creates quick clay landslide hazards. The ability to predict the likelihood of such landslides occurrence, as well as their outreach would reduce the damage to the infrastructures and loss of life. Recently, a simple experimental technique named a quickness test (Thakur V, Degago S, Geotech Lett 2:87–95, 2012) has been employed to investigate the susceptibility of the clay to create large retrogression landslides. In this paper, we applied Generalized Interpolation Material Point Method (a numerical method suitable for large displacement dynamic problems) to replicate the quickness test experiment. The primary goal of the presented simulations is to further validate the modelling technique and the constitutive model used. In particular, the computations suggest the importance of the strain rates for the prediction of the run-out distance of the remoulded sensitive clays.

As a first step towards modelling the coupled Thermo-Hydro-Mechanical-Chemical (THMC) behaviour of bentonite, the Barcelona Basic Model (BBM) has been implemented into Numerrin finite element code. This model has been fully coupled with the single phase flow equation for unsaturated soils which models liquid water transport. Suction obtained from solving the flow equation is used as an input for the BBM model and the volumetric deformations from the mechanical analysis are used to update the pore water pressure field. As an alternative, BBM is used alongside the Kröhn’s model which assumes that bentonite re-saturation is mainly driven by water vapour diffusion. The paper simulates one dimensional infiltration test on MX-80 bentonite with both implemented models for water transport and compares the results with those from a laboratory experiments based on X-ray tomography.The numerical results of the simulations are similar despite taking into account different physical phenomena.

The paper compares the accuracy and stability of implicit and explicit stress integration schemes applied to the Barcelona Basic Model. In addition, the effect of the integration scheme on the convergence of Newton–Raphson algorithm is studied. By running a Newton–Raphson algorithm for a single stress point, the number of iterations required to reach convergence gives some insight on the convergence of the finite element solution at the global level. The explicit algorithms tested incorporate substepping with error control and are based on Runge–Kutta methods of different orders or on the Richardson extrapolation method. The implicit return-mapping algorithms follow the procedures of Simo and Hughes [1] and Hofmann [2].

SUMMARY This article presents an equivalent stress approach that can be used in many elastoplastic constitutive models for unsaturated soils. The use of the equivalent stress leads to a modified yield locus that is independent of the suction. In addition, the equivalent stress becomes the major stress variable, with suction required only as an additional variable in calculations. The model on the basis of equivalent stress predicts exactly the same soil behaviour, with the sole difference being the use of equivalent stress instead of original stress variables. This article also presents the equivalent stress formulations of several constitutive models for unsaturated soils, including the Barcelona Basic Model. The predictions from these models remain unchanged, with the only difference being in their implementation. Finally, the equivalent stress approach and the net stress approach are compared for the Barcelona Basic Model. Copyright © 2011 John Wiley & Sons, Ltd.

The numerical integration of the stress–strain relationship is an important part of many finite element code used in geotechnical engineering. The integration of elasto-plastic models for unsaturated soils poses additional challenges associated to the presence of suction as an extra constitutive variable with respect to traditional saturated soil models. In this contribution, a range of explicit stress integration schemes are derived with specific reference to the Barcelona Basic Model (BBM), which is one of the best known elasto-plastic constitutive models for unsaturated soils. These schemes, however, do not address possible non-convexity of the loading collapse (LC) curve and neglect yielding on the suction increase (SI) line. The paper describes eight Runge–Kutta methods of various orders with adaptive substepping as well as a novel integration scheme based on Richardson extrapolation. The algorithms presented also incorporate two alternative error control methods to ensure accuracy of the numerical integration. Extensive validation and comparison of different schemes are presented in a companion paper. Although the algorithms presented were coded for the Barcelona Basic Model, they can be easily adapted to other unsaturated elasto-plastic models formulated in terms of two independent stress variables such as net stress and suction.

The water retention behaviour of partially saturated MX-80 bentonite with pure water is relatively well investigated. However, in practical cases, the water contains a number of chemical compounds which affects the bentonite behaviour. In particular, bentonite is used in buffer applications of geological repositories for spent nuclear fuel, where the concentration of total dissolved solids in groundwater is expected to increase significantly with time. This paper investigates water retention behaviour of MX-80 type bentonite partially saturated with deionised water as well as 1M NaCl solution. In the experiments the specific volume of bentonite has been kept approximately constant.

This paper introduces an equivalent stress for elastoplastic modeling of unsaturated soils. This equivalent stress unifies various models for unsaturated soils with regard to the stress variables used and allows for a simple separation of the saturated and unsaturated phases of behavior. Moreover, the equivalent stress computed for a given model for unsaturated soil can be used in an existing model for saturated soil so it will gain the ability to model the former. The unsaturated plastic volumetric behavior of the new model is inherited mostly from the parent model for unsaturated soil. The behavior upon shearing depends on both models: the shape of the yield locus is inherited from the original model and the increase of the elastic zone (and possible shift of the elastic zone) from unsaturation depends on the model for the unsaturated soil from which the equivalent stress was taken.

The Barcelona Basic Model (Alonso et al. 1990) yield locus has been proven to be non-convex for certain set of parameters (see Wheeler at al. 2002). This paper shows that as this model is formulated in the semi-logarithmic space, the elastic stress path corresponding to a given strain increment is not a straight line. Therefore, the simple assumption that the stress increment is elastic when the stress state is elastic at the beginning and the end of the stress path is no longer correct. The paper examines some strain increments leading to elasto-plastic stress paths which may be easily mistaken for being fully elastic. Some of the stress paths described in the paper can only occur when certain sets of parameters of the Barcelona Basic Model are selected, but others are not dependent on the model parameter set. In the latter case the described mechanism may be relevant to great many other constitutive models which assume a constant shear modulus G and are formulated in the semi-logarithmic space.