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The Material Point Method is a versatile technique, however, it may be unable to provide a valid solution if there is a snap-through or snap-back response in the equilibrium path. One approach of overcoming this issue is the use of path following techniques and one example is the arc-length method. This technique is well established in finite element analysis but not in any Material Point Method formulation. This paper details the modifications made to the standard arc-length scheme for use within the Material Point Method. A numerical example is presented to demonstrate the implementation of the Material Point-Based Arc-length scheme in tracking a snap-through response.

Cone Penetration Tests (CPTs) can be used to determine in-situ soil properties and represent a practical choice for site investigation offshore, especially for linear infrastructure, such as offshore wind export cables. Information gained from CPTs is key for predicting soil-structure interaction behaviour, for example when predicting the tow forces involved in seabed ploughing, as the CPT provides an analogue to the process. The numerical modelling of CPTs is challenging due to the significant distortion in the soil displaced by the penetrating cone. This means that solving this sort of problem using finite elements, although not impossible, is numerically tiresome in terms of remeshing and mapping of state variables. Therefore, in this paper we adopt the Material Point Method (MPM) to develop a CPT prediction tool in layered soils. This MPM is combined with a novel non-matching mesh frictional boundary to represent the penetrometer. The developed tool will be used to understand the response of layered soils commonly found offshore as a step towards predicting the interaction of ploughs and anchors with the seabed.

There is considerable interest in the Material Point Method (MPM) in the computational geotechnics community since it can model problems involving large deformations, e.g. landslides, collapses etc. without being too far from the standard finite element method, which can struggle with large deformation problems. The open-source code AMPLE developed at Durham University in recent years is a compact set of MATLAB functions that “address the severe learning curve for researchers wishing to understand, and start using, the MPM”. It is well known that MATLAB can be very slow hence limiting its utility for major studies of large problems, so here we introduce an MPM code with the same aims as AMPLE but written in the relatively new language Julia, specifically for fast runtimes. We highlight areas where MATLAB code constructs are inefficient if just transferred to Julia and show that to unlock large speed gains with Julia, one needs to code in a different way and we demonstrate this on a geotechnical problem. While this paper is concerned with the MPM, the advice regarding coding using Julia is transferable to other computational geotechnics methods and tools.

Implicit boundary methods, which enrich the interpolation structure with implicit weight functions, are straightforward methods for the enforcement of Dirichlet boundary conditions. In this article, we follow the implicit boundary method that uses approximate step functions (the step boundary method) developed by Kumar et al. and provide modifications that have several advantages. Roller boundary conditions have wide practical applications in engineering, however, the step boundary method for roller boundary conditions with inclinations has yet to be fully formulated through to the final linear system of equations. Thus we provide a complete derivation that leads to simplified sti↵ness matrices compared to the original approach, which can be implemented directly in fictitious domain finite element analysis. The approach is then extended, we believe for the first time, to the nonlinear cases of frictional boundary conditions and elasto-plastic material behaviour. The proposed formulation and procedures are validated on a number of example problems that test di↵erent aspects of the method.

Offshore pipeline ploughs have previously been modelled at 1g with small 1:50 scale models designed to derive the parameters required for prediction of ploughing in terms of tow force requirements and potential advance rates. This was scaled up to prototype with the validity of the scaling verified through ‘modelling of models’ and with comparison to typical prototype tow forces but without direct validation. To allow further validation, a long centrifuge box and actuation system was developed for use on a medium-sized beam centrifuge. Previous approaches to 1g ploughing were also improved through the use of micro-electro-mechanical systems accelerometers and new low-cost surface scanning techniques. A wide range of ploughing velocities were explored through increasing actuation speeds and the use of pore fluids of different viscosities. The study has shown that although there may be initial concerns over low effective stress scaling issues at 1g, in shallow problems with small-scale models, the large deformation nature of the ploughing problem can be replicated with appropriate scaling. This allows the use of 1g modelling for more efficient parametric studies for this application and has given further confidence to performance parameters for prototype modelling derived from 1g and centrifuge studies.

COM; International audience

Computational modelling of fracture has been attempted in the past with a range of numerical approaches including finite element, extended finite element and meshless methods. The cracking particle method (CPM) of Rabczuk is a pragmatic alternative to explicit modelling of crack surfaces in which a crack is represented by a set of cracking particles that can be easily updated when the crack propagates. The change of cracking angle is recorded in discrete segments of broken lines, which makes this methodology suitable to model discontinuous cracks. In this paper, a new CPM is presented that improves on two counts: firstly, crack path curvature modelling is improved by the use of bilinear segments centred at each particle and secondly, efficiency for larger problems is improved via an adaptive process of both refinement and recovery. The system stiffness is calculated and stored in local matrices, so only a small influenced domain should be recalculated for each step while the remainder can be read directly from storage, which greatly reduces the computational expense. The methodology is applied to several 2D crack problems, and good agreement to analytical solutions and previous work is obtained.

Multiple crack simulation is of great importance in failure analysis since fracture in brittle materials in practice usually comprises multiple cracks. Traditional numerical methods like the extended finite element and the element free Galerkin methods meet dilemmas when solving this kind of problem, as the computational expense increases with the number of level set functions used for crack descriptions. The cracking particle method (CPM) developed by Rabczuk, by which crack patterns are simplified and discretized through a set of cracking segments, has shown to be a promising alternative. The branched crack problem, as a representative of multiple crack problems, is studied here to demonstrate the advantages of the CPM. Cracking particles can be split multiply due to the use of bilinear cracking lines and then the discontinuity at the intersection is fulfilled easily. An adaptivity strategy is adopted to control the size of cracking segments and the number of degrees of freedom. Stress intensity factors at the crack tips are calculated and show good agreement with previous results.

The Material Point Method (MPM) is a method that allows solid mechanics problems with large deformation and non-linearity to be modelled using particles at which state variables are stored and tracked. Calculations are then carried out on a regular background grid to which state variables are mapped from the particles. There have been a selection of extensions to the MPM, for example, a problem in the original method that arises when a material point crosses the boundary between one background grid cell and another is addressed by the Generalised Interpolation Material Point (GIMP) method [2]. An area yet to be studied in as much depth in MPM is that conventional analysis techniques constructed in terms of stress and strain are unable to resolve structural instabilities such as necking or shear banding. This is due to the fact that they do not contain any measure of the length of the microstructure of the material analysed such as molecule size of grain structure. Gradient elasticity theories provide extensions of the classical equations of elasticity with additional higher-order terms [3]. This use of length scales makes it possible to model finite thickness shear bands that is not possible with traditional methods. Much work has been done on including the effect of microstructure on a linear elastic solid and has previously been combined with the Finite Element Method and with the Particle In Cell Method. In this work the MPM will be developed to include gradient effects.

The Material Point Method (MPM) is a numerical boundary value problem (BVP) solver developed from particle- in-cell (PIC) methods that discretises the continuum into a set of material points. Information at these material points is mapped to a background Eulerian grid which is used to solve the governing equations. Once solved information is updated at the material points and these points are convected through the grid. The background grid is then reset, allowing the method to easily handle problems involving large deformations without mesh distortion. However, imposition of essential boundary conditions in the (MPM) is challenging when the physical domain does not conform to the background grid. In this research, an implicit boundary method (IBM), based on the work of Kumar et al. [1], is proposed to ensure that essential boundary conditions are satisfied in elastostatic MPM problems.

Scientific investigations into the structural properties of rammed earth (RE) are gaining momentum and a number of parameters (e.g. suction, particle size distribution and water content), influential on material strength and other properties, have been identified and investigated. Cement stabilisation is undergoing continued investigation, while fibrous stabilisation, also known as fibre reinforcement, is beginning to gain attention. Recent experiments have shown that the addition of fibres such as straw or wool to RE or other earthen materials can improve its flexural strength. Less attention, however, has been paid to the fracture behaviour of RE, and to its shearing behaviour. This paper presents a preliminary investigation into the shearing behaviour of stabilised and unstabilised RE reinforced with waste natural fibres. The Direct Shear Test (DST) is used to obtain peak shear stresses and displacements, from which strength parameters (φ’) and cohesion (c’) are obtained. This paper also presents some scanning electron microscope (SEM) images of these materials. The results show that wool fibres decrease the density and peak shear strength of RE. The effect of water, wool and cement content on φ’ and c’ are also discussed.

There is considerable interest in development of solid mechanics modelling which can cope with both material and geometric nonlinearity, particularly in areas such as computational geotechnics, for applications such as slope failure and foundation installation. One such technique is the Material Point Method (MPM), which appears to provide an efficient way to model these problems. The MPM models a problem domain using particles at which state variables are kept and tracked. The particles have no restriction on movement, unlike in the Finite Element Method (FEM) where element distortion limits the level of mesh deformation. In the MPM, calculations are carried out on a regular background grid to which state variables are mapped from the particles. It is clear, however, that the MPM is actually closely related to existing techniques, such as ALE and in this paper we review the MPM for solid mechanics and demonstrate these links.

In this paper, a new method for coupling the finite element method (FEM) and the element-free Galerkin method (EFGM) is proposed for linear elastic and geometrically nonlinear problems using local maximum entropy shape functions in the EFG zone of the problem domain. These shape functions possess a weak Kronecker delta property at the boundaries which provides a natural way to couple the EFG and the FE regions as compared to the use of moving least square basis functions. In this new approach, there is no need for interface/transition elements between the EFG and the FE regions or any other special treatment for shape function continuity across the FE-EFG interface. One- and two-dimensional linear elastic and twodimensional geometrically nonlinear benchmark numerical examples are solved by the new approach to demonstrate the implementation and performance of the current approach.

Three dimensional analyses including geometric and material non--linearity require robust, efficient constitutive models able to simulate engineering materials. However, many existing constitutive models have not gained widespread use due to their computational burden and lack of guidance on choosing appropriate material constants. Here we offer a simple cone-type elasto-plastic formulation with a new deviatoric yielding criterion based on a modified Reuleaux triangle. The perfect plasticity model may be thought of as a hybrid between Drucker-Prager (D-P) and Mohr-Coulomb (M-C) that provides control over the internal friction angle independent of the shape of the deviatoric section. This surface allows an analytical backward Euler stress integration on the curved surface and exact integration in the regions where singularities appear. The attraction of the proposed algorithm is the improved fit to deviatoric yielding and the one--step integration scheme, plus a fully defined consistent tangent. The constitutive model is implemented within a lean 3D geometrically non-linear finite-element program. By using an updated Lagrangian logarithmic strain--Kirchhoff stress implementation, existing infinitesimal constitutive models can be incorporated without modification.

Conservation and repair of historic rammed earth sites should only be undertaken if there is a good understanding of the consequences of any intervention technique. Until recently there has been little interest in the characterisation of historic rammed earth construction, yet it is only with this understanding that successful conservation strategies can be adopted. A survey of around 60 historic rammed earth sites in Spain constructed between 967AD and 1837AD has recently been undertaken. While all the sites are built primarily in rammed earth, the construction techniques and state of repair vary greatly. The high density of historic rammed earth structures in the Iberian peninsula is likely due to the Muslim presence there from the 8th century onwards. Initial expansion, a period of civil war and eventual defeat by Christians led to the construction of a large number of fortifications, many constructed in rammed earth. A famous example is the Alhambra at Granada, but there are hundreds of smaller sites throughout Spain. By the end of the 15th century Christians had replaced Muslims through most of Spain, but rammed earth continued to be used in both vernacular and monumental architecture. Examples of historic construction techniques are presented and common features of historic rammed earth construction are identified. A classification is outlined and a clear development of the rammed earth technique is observed.

Iterative solvers are of increasing interest in geomechanics with the move towards 3D finite element modelling. Potentially, these methods can lead to reduced computational complexity as, unlike direct methods, they do not require the full system matrix to be assembled. In general, however, iterative solvers have not been widely adopted in geomechanics due to problems with convergence. This paper reviews the background to iterative methods for elastic and elasto-plastic material models. In some cases, existing numerical methods can be taken from research in the mathematics community. For other systems, further work is needed. The paper provides demonstrations of the capabilities of some strategies.

Oedometer tests were carried out on a silt used in flood embankment construction in Indonesia. Three test series were carried out under dry-of-optimum, wet-of optimum and prepared wet and then dried, initial conditions. Where collapse was observed, the collapse potential for the specimen was evaluated and severity of collapse determined. This material has been sampled from embankments in East Java, Indonesia where there is a recurrent history of geotechnical failures. These preliminary results show the importance of good compaction control at the site and help to explain some failures observed at the site.

The work is part of a wider research program in progress since many years at the Dipartimento di Ingegneria Idraulica, Geotecnica e Ambientale (DIGA) of the Università degli Studi di Napoli Federico II, focusing on the analysis of the effects of the partially saturated state on the seismic response of soil deposits. This study is particularly relevant for the relatively high seismic area of the city of Naples (Italy), where unsaturated soils are often encountered. The paper summarises a parametric study based on the experimental results obtained during a comprehensive laboratory program carried out using a RCTS device working in suction controlled conditions. A set of 1D linear analyses were carried out and interpreted in terms of transfer function, in order to highlight the role played by the unsaturated condition on the amplification function. Finally a rationale synthesis of the results is attempted in order to quantify the effect of the unsaturated state on subsoils characterized by different PI values. Results clearly show relevant effects of unsaturated state of soil deposits on the local seismic response in terms of both amplification ratio and natural frequency. The unsaturated state could be meaningful in the local response especially that of deposits of limited thickness.