The reliability of a geotechnical simulation depends strongly on the selection of material parameters and in recent years Bayesian Inference (BI) has become a popular coherent framework for this task. It has generally been used to reduce the uncertainties based on measurements, but it is challenging due to material non-linearity and paucity of measurement data. Applications to geotechnics of BI to date have struggled with the high dimensionality of the modelled problems (e.g. in 3D FEA) and many studies report considerable computational time needed to achieve the accuracy one might hope to get via an expert assessment. In this paper we introduce a Finite Element–BI (FE–BI) system for geotechnics using a two stage process where the material parameters and the simulation results themselves (the “states”) are updated one after the other. The method is demonstrated on three examples with increasing complexity: parameter determination for undrained compression triaxial tests with the modified Cam clay model; parameter determination from FE simulation of cyclic triaxial tests with the Small Strain Overlay (SSO) model, and 3D FE simulations of a braced excavation. Results show that the FE-BI system can effectively infer both the parameters and states, reducing uncertainty in parameter and state distributions, giving good agreement with the reference solutions provided. The technique proposed in this paper provides a rigorous and efficient approach to obtain material parameters with greater certainty, and could have wide application in geotechnical engineering practice.

The reliability of a geotechnical simulation depends strongly on the selection of material parameters and in recent years Bayesian Inference (BI) has become a popular coherent framework for this task. It has generally been used to reduce the uncertainties based on measurements, but it is challenging due to material non-linearity and paucity of measurement data. Applications to geotechnics of BI to date have struggled with the high dimensionality of the modelled problems (e.g. in 3D FEA) and many studies report considerable computational time needed to achieve the accuracy one might hope to get via an expert assessment. In this paper we introduce a Finite Element-BI (FE-BI) system for geotechnics using a two stage process where the material parameters and the simulation results themselves (the “states”) are updated one after the other. The method is demonstrated on three examples with increasing complexity: parameter determination for undrained compression triaxial tests with the modified Cam Clay model; parameter determination from FE simulation of cyclic triaxial tests with the Small Strain Overlay (SSO) model, and 3D FE simulations of a braced excavation. Results show that the FE-BI system can effectively infer both the parameters and states, reducing uncertainty in parameter and state distributions , giving good agreement with the reference solutions provided. The technique proposed in this paper provides a rigorous and efficient approach to obtain material parameters with greater certainty, and could have wide application in geotechnical engineering practice.

The Material Point Method (MPM) is widely used to analyse coupled (solid-water) problems under large deformations/displacements. However, if not addressed carefully, MPM u-p formulations for poromechanics can be affected by two major sources of instability. Firstly, inf-sup condition violation can arise when the spaces for the displacement and pressure fields are not chosen correctly, resulting in an unstable pressure field when the equations are monolithically solved. Secondly, the intrinsic nature of particle-based discretisation makes the MPM an unfitted mesh-based method, which can affect the system's condition number and solvability, particularly when background mesh elements are poorly populated. This work proposes a solution to both problems. The inf-sup condition is avoided using two overlapping meshes, a coarser one for the pressure and a finer one for the displacement. This approach does not require stabilisation of the primary equations since it is stable by design and is particularly valuable for low-order shape functions. As for the system's poor condition number, a face ghost penalisation method is added to both the primary equations, which constitutes a novelty in the context of MPM mixed formulations. This study frequently makes use of the theories of functional analysis or the unfitted Finite Element Method (FEM). Although these theories may not directly apply to the MPM, they provide a robust and logical basis for the research. These rationales are further supported by four numerical examples, which encompass both elastic and elasto-plastic cases and drained and undrained conditions.

Rammed earth is a sustainable construction method with a lower carbon footprint and embodied energy compared to traditional materials like steel and concrete. However, its lower mechanical properties when compared to these forms of construction make it vulnerable to seismic forces. This paper reviews the published literature on enhancing rammed earth's mechanical properties through both chemical stabilisation and fibre reinforcement, with a focus on reusing waste materials. The effectiveness of these techniques are highlighted by comparing experimental results with minimum specifications taken from relevant guidelines and standards for building rammed earth structures in seismic zones. These findings demonstrate that chemical stabilisation and fibre reinforcement can improve rammed earth's mechanical properties, ensuring it meets these minimum specifications thus making it a viable form of construction in areas with seismic activity.

The thickness of shear bands, which form along slip surfaces during certain modes of geotechnical failure, depends directly on the size of the soil particles. Classical continuum models, however, are invariant to length scale, so the strain localisation zone cannot converge to a finite size when employing numerical techniques such as the finite element method. Instead, the present approach adopts the micropolar (Cosserat) continuum, a weakly non-local higher-order theory which incorporates a characteristic length and allows independent rotations of the material micro-structure as well as transmission of couple stresses. As a result, strain can localise naturally in micropolar continua to form realistic finitesized shear bands. By extending an elastic finite-strain micropolar implementation of the material point method (a numerical method well-suited to modelling large deformation problems) with an elasto-plastic constitutive model suitable for geomaterials, this novel combined approach will provide a powerful tool to analyse numerically challenging localisation problems in geotechnics.

Randomly distributed fibres can be a potential reinforcement material to improve the shear strength of soils. However, gaps remain in experimental research and predictive modelling of the shear strength of fibre reinforced high plasticity clays. In light of this, a series of consolidated undrained triaxial tests were carried out to investigate the shear strength behaviour of London Clay reinforced with 0.3% to 0.9% polypropylene fibre by dry weight of soil. The effects of fibre length and confining pressure were also considered. The results indicated that fibres significantly improve the shear strength of soil. The shear strength improvement increases with the fibre length, but decreases with increasing confining pressure at test scale. The addition of fibres also leads to the increase in the pore water pressure of soil. Using these and other experimental results, a predictive model was developed based on the concept of equivalent confining stress. The model is able to describe the deviator stress-strain and pore water pressure-strain relationship of fibre reinforced clay and can be used efficiently to predict the shear strength of fibre reinforced clay subjected to different confining pressures.

Poromechanics is a well-established field of continuum mechanics which seeks to model materials with multiple phases, usually a stiff solid phase and fluid phases of liquids or gases. Applications are widespread particularly in geomechanics where Terzaghi’s effective stress is widely used to solve engineering soil mechanics problems. This approach assumes that the solid phase is incompressible, an assumption that leads to many advantages and simplifications without major loss of fidelity to the real world. Under the assumption of finite (as opposed to infinitesimal) strains, the poromechanics of two- or bi-phase materials gains complexity and while the compressible solid phase case has received attention from researchers, the incompressible case has received less. For the finite strain - incompressible solid phase case there is a fundamental issue with standard material models, in that for some loadings solid skeleton mass conservation is violated and negative Eulerian porosities are predicted. While, to the authors’ best knowledge, acknowledgement of this essential problem has been disregarded in the literature, an elegant solution is presented here, where the constraint on Eulerian porosity can be incorporated into the free energy function for a material. The formulation is explained in detail, soundly grounded in the laws of thermodynamics and validated on a number of illustrative examples.

Accurate and robust modelling of large deformation three dimensional contact interaction is an important area of engineering, but it is also challenging from a computational mechanics perspective. This is particularly the case when there is significant interpenetration and evolution of the contact surfaces, such as the case of a relatively rigid body interacting with a highly deformable body. The numerical challenges come from several non-linear sources: large deformation mechanics, history dependent material behaviour and slip/stick frictional contact. In this paper the Material Point Method (MPM) is adopted to represent the deformable material, combined with a discretised rigid body which provides an accurate representation of the contact surface. The three dimensional interaction between the bodies is detected though the use of domains associated with each material point. This provides a general and consistent representation of the extent of the deformable body without introducing boundary representation in the material point method. The dynamic governing equations allows the trajectory of the rigid body to evolve based on the interaction with the deformable body and the governing equations are solved within an efficient implicit framework. The performance of the method is demonstrated on a number of benchmark problems with analytical solutions. The method is also applied to the specific case of soil-structure interaction, using geotechnical centrifuge experimental data that confirms the veracity of the proposed approach.

Poro-mechanics is a branch of mechanics considering the hydro-mechanical behaviour of a porous solid medium whose pores are saturated by a fluid. The presence of both these constituents significantly influences the overall macro-response of the material. Regardless of the application, Terzaghi’s effective stress decomposition is a well-established hypothesis regarding how the total stress tensor is decomposed into a part directly related to strain (effective stress) and a part borne by the fluid phase (interstitial pressure). The assumption of an incompressible solid medium physically justifies Terzaghi’s effective decomposition. However, under the further assumption of finite strain mechanics, a more restrictive constraint on the volume change arises, which the vast majority of formulations neglect. This work details how disregarding this constraint on the volume change can lead to the violation of solid mass balance, which can be counted among the fundamental principles of continuum mechanics. Furthermore, to address this issue practically, an ad hoc stress-strain relationship is designed to respect Terzaghi stress decomposition and solid mass balance in the context of finite-strain hyper-elasticity.

The popularity of the rammed earth building technique has increased over recent decades due to its low ecological impact. Despite the presence of numerous vernacular rammed earth houses across eastern Croatia, research on their properties and behaviour is still in its early stages and appropriate standards to assess vulnerability do not exist. Despite local interest in repairing deterioration that has occurred in some of these houses, without proper knowledge, an important part of Croatian cultural heritage will be lost. To investigate the problem, in this study, laboratory tests of rammed earth material from a rammed earth house in eastern Croatia were carried out. The strength of the material was determined at different moisture contents (4–12

The ability to model rigid body interaction with highly deformable solids is a very useful tool in geoengineering, including the modelling of drag anchors on seabeds and seabed ploughing [7, 1]. However, these simulations entail several numerical challenges, such as modelling frictional contact, and incorporating inertia forces for analyses whose simulated time is considerable. Here the implicit Generalised Interpolation Material Point Method (GIMPM) is adopted to model the highly deformable solid, whilst a rigid body is used to model the significantly stiffer engineering object, such as an anchor. The whole system is integrated in time with the Newmark method with interaction between the two bodies occurring through a normal penalty contact and a penalty enforced Coulomb stick-slip friction law.

Modelling the mechanical behaviour of structural systems where the system size approaches that of the material microstructure (such as in MEMS) presents challenges to the standard continuum assumption and classical models can fail to predict important phenomena. Of the various non-conventional continuum frameworks developed to tackle this issue, the micropolar (Cosserat) continuum is widely acknowledged as a suitable and rigorous alternative for its ability to naturally predict size effects by introducing characteristic length scales. This work proposes an implementation of geometrically non-linear micropolar theory using an implicit Material Point method, for the purpose of simulating nanoscale large-deformation problems involving Hookean materials. The framework employs an analytically-derived consistent tangent, and is verified with a novel benchmark problem derived using the Method of Manufactured Solutions. Due to similarities between the methods, many aspects of the formulation could be used to construct an Updated Lagrangian Finite Element Method.

Summary The material point method is a versatile technique which can be used to solve various types of solid mechanics problems, especially those involving large deformations. However, the capability of the material point method to track a load‐displacement response can deteriorate once a limit point, such as snap‐through or snap‐back, in the response is encountered. One way of overcoming this is to use path following techniques, such as an arc‐length method. This technique is well established in finite element analysis but not within any material point method formulation. This paper provides for the first time an arc‐length controlled implicit, quasi‐static material point method. The modifications to the standard arc‐length scheme to allow for the stable execution of an arc‐length solver within the material point method are detailed. The capability of the material point‐based arc‐length method is demonstrated through a number of problems, which include linear elastic, non‐linear elastic, linear elastic‐perfectly plastic and linear elastic‐plastic softening material behaviour under large deformations. The techniques presented in this paper are essential for arc‐length techniques to be applied effectively to the material point method and the combination of these techniques makes the method suitable for new problems that cannot be solved with existing implicit material point approaches.

Modelling the interaction between rigid and deformable bodies holds significant relevance in geotechnical engineering, particularly in scenarios involving stiff engineering objects interacting with highly deformable material such as soil. These processes are challenging due to the combined nonlinear mechanisms including large deformation, elasto-plasticity, and contact with friction. For highly deformable material, the Material Point Method is a natural choice over the Finite Element Method due to its ability to handle large deformations without remeshing by carrying material information at points. This paper uses the Implicit General Interpolation Material Point Method (GIMPM) to demonstrate a new approach for modelling this type of interaction, and exploits the GIMPM's inherent definition of the boundary of a deformable domain to formulate a consistent contact formulation, negating the need for boundary reconstruction. The formulation is demonstrated through validations and comparisons to alternative methods for simulating contact. The combination of the contact formulation with an implicit framework is shown to be an efficient method for modelling geotechnical problems. The proposed method exhibits optimal convergence for contact problems, accurately captures stick-slip Coulomb friction, and ensures consistent stress fields at the contact surface of a rigid body.

The kinematic behaviour of drag embedment anchors has become a recent research focus due to the increase in offshore renewable energy devices. This is due to their potential use as an anchoring system for future floating wind applications, in addition to the need to understand their penetration behaviour as a part of the Cable Burial Risk Assessment. Studies on the behaviour of anchors typically consist of field scale or model centrifuge tests, where such facilities are not readily available to all and can result in significant cost. In addition to this, measuring the load–penetration behaviour of an anchor has proven to be a significant challenge, as any contact-based methods are likely to influence the penetration behaviour of the anchor. In this paper, a novel wireless method of recording the inclination of the anchor and calculating the penetration depth is presented. A comparison of the penetration behaviour of a Class F (AC-14) anchor has been made in sand using centrifuge and 1g model scale testing. The results indicate that the 1g testing can match the behaviour of the anchor testing in the centrifuge in terms of both the position of the anchor and its orientation during the dragging event.

The phase field method is becoming the de facto choice for the numerical analysis of complex problems that involve multiple initiating, propagating, interacting, branching and merging fractures. However, within the context of finite element modelling, the method requires a fine mesh in regions where fractures will propagate, in order to capture sharp variations in the phase field representing the fractured/damaged regions. This means that the method can become computationally expensive when the fracture propagation paths are not known a priori. This paper presents a 2D hp-adaptive discontinuous Galerkin finite element method for phase field fracture that includes a posteriori error estimators for both the elasticity and phase field equations, which drive mesh adaptivity for static and propagating fractures. This combination means that it is possible to be reliably and efficiently solve phase field fracture problems with arbitrary initial meshes, irrespective of the initial geometry or loading conditions. This ability is demonstrated on several example problems, which are solved using a light-BFGS (Broyden–Fletcher–Goldfarb–Shanno) quasi-Newton algorithm. The examples highlight the importance of driving mesh adaptivity using both the elasticity and phase field errors for physically meaningful, yet computationally tractable, results. They also reveal the importance of including p-refinement, which is typically not included in existing phase field literature. The above features provide a powerful and general tool for modelling fracture propagation with controlled errors and degree-of-freedom optimised meshes.

The Material Point Method (MPM) is well suited to modelling dynamic solid mechanics problems undergoing large deformations with non-linear, history dependent material behaviour. However, the vast majority of existing material point method implementations do not inherit conservation properties (momenta and energy) from their continuum formulations. This paper provides, for the first time, a dynamic updated Lagrangian material point method for elasto-plastic materials undergoing large deformation that guarantees momenta and energy conservation. Sources of energy dissipation during point-to-grid and grid-to-point mappings for FLuid Implicit Particle (FLIP) and Particle In Cell (PIC) approaches are clarified and a novel time-stepping approach is proposed based on an efficient approximation of the Courant-Friedrich-Lewy (CFL) condition. The formulation provided in this paper offers a platform for understanding the energy conservation nature of future/existing features of material point methods, such as contact approaches.

Desiccation cracking in clay soils is a combined mechanical and hydraulic problem and such soils can be improved by various methods including reinforcement with fibres. The relationships between tensile strength, cracking resistance and water-retention properties of fibre-reinforced fine-grained soils lack coverage in the literature to date. In this study, these three properties are evaluated and connected by way of a series of tensile strength and desiccation cracking tests on fibre-reinforced London clay. The results confirm that increased fibre addition delays the occurrence of peak stress and changes failure behaviour from brittle to ductile. The tensile strength increment gets higher as water content decreases, and reaches a maximum value of 460 kPa when the water content is 12%. The crack intensity factor reduces from 7.20% to 0.89% when 12 mm long fibre is used at a ratio of 0.9%. Fibre reinforcement also changes the crack development pattern by reducing the size of large cracks and increasing the proportion of small individual cracks. However, the presence of fibres was not observed to change the water-retention properties of the soil, indicating that the tensile improvement comes from the pull-out resistance of the fibres rather than suction changes.

Raw (unfired) earth represents a sustainable and efficient alternative to traditional construction materials but its dissemination into building practice has been hindered by a relatively high vulnerability to water erosion. Enzyme induced carbonate precipitation (EICP) can improve the durability of earth materials without using traditional chemical binders such as cement and lime. EICP utilises the urease enzyme to catalyse the hydrolysis of urea, which produces carbonate ions that react with the calcium ions dissolved in the pore water, thus resulting in the precipitation of calcium carbonate. The calcium carbonate fills the soil voids and binds particles together, which reduces water permeability and increases material strength. The urease enzyme is a hexameric protein that is found in the tissues of many common plants. This work proposes a low-cost and simple stabilisation technology that makes use of crude urease enzyme extracted from soybeans. This technology is applied to the stabilisation of compacted earth, whose properties are then assessed via unconfined compression, moisture buffering and durability tests. The findings suggest a noticeable improvement of material strength and durability, though further investigation is necessary to increase the competitiveness of EICP stabilisation against standard techniques using cement and lime.

Screw piles potentially offer quieter installation and enhanced axial tensile capacity over straight-shafted driven piles. As such, they have been suggested as a possible foundation solution for offshore jacket-supported wind turbines in deeper water. To investigate the feasibility of their use in this setting, centrifuge testing of six model screw piles of different designs was conducted to measure the installation requirements and ultimate axial capacity of the piles in very dense and medium-dense sand. The screw piles were designed to sustain loads generated by an extreme design scenario using published axial capacity and torque prediction formulae. Single- and double-helix designs, including an optimised design, intended to minimise installation requirements, with reduced geometry were installed and tested in-flight. Piles in the medium-dense sand, for example, had significant installation requirements of up to 18·4 MNm (torque) and 28·8 MN (vertical force), which were accurately predicted using correlations with cone resistance data (cone penetration test). Existing axial capacity design methods did not perform well for these large-scale screw piles, overestimating compressive and tensile capacities. Revised analytical methods for installation and axial capacity estimates are proposed here based on the centrifuge test results.