Search

Suction-induced seepage flow can significantly reduce the soil resistance during the installation of suction buckets, thereby ensuring their intended penetration depths and the designed in-service capacities. However, the lack of analytical models describing seepage flow behavior in the literature poses a significant challenge, primarily due to the complexity of seepage boundary conditions and the anisotropy and spatial variation of soil permeability. This paper addresses this gap by presenting a novel analytical solution for analyzing suction-induced seepage flow around buckets, with a particular focus on the general multilayered soil profile featuring anisotropic permeability. The method of separation of variables is used initially to derive general solutions, and the final solutions are subsequently obtained by combining continuous conditions with the orthogonality of Bessel functions. The accuracy of the solutions is confirmed through comparisons with the results obtained from finite element analysis. Furthermore, this study discusses the seepage flow behavior in several typical scenarios, including permeability anisotropy, increased permeability within the bucket, and the presence of an overlying low-permeability layer. The analytical solutions presented in this paper provide a rapid and accurate method for the analysis of suction-induced seepage flow during suction-assisted installations across a wide range of complex soil permeability conditions. [ABSTRACT FROM AUTHOR]

Winkler modelling offers a flexible and computationally efficient framework for estimating suction caisson capacity. However, there is a limited understanding of the local soil resistance acting on caissons at capacity under combined six degrees-of-freedom (6DoF) loading, which is essential for accurately estimating caisson failure envelopes. Furthermore, existing simplified design models for caissons cannot assess capacity under non-planar lateral and moment loading, which is common in offshore wind applications. To address these limitations, this paper presents a comprehensive three-dimensional (3D) finite element analysis (FEA) study, which investigates the local soil resistance acting on the caisson at capacity in undrained clay under combined 6DoF loading. The paper introduces the concept of 'soil reaction failure envelopes' to characterise the interactions between soil reactions at capacity. Closed-form formulations are derived to approximate these soil reaction failure envelopes. An elastoplastic Winkler model is then developed, incorporating linear elastic perfectly plastic soil reactions based on these formulations. The results demonstrate that the Winkler model can provide efficient and reasonably accurate estimations of caisson capacity under combined 6DoF loading, even for irregular soil profiles that pose much uncertainty and challenges to existing macro-element models. [ABSTRACT FROM AUTHOR]

The tetrahedrons offer advantages in terms of its adaptability to complex geometries and high-efficiency of automated discretization. However, the performance is greatly limited by the weak accuracy suffered from first-order elements, as well as the significant computational burden required for quadratic cells. In this paper, a flexible mixed-order tetrahedron element is constructed on the basis of SBFEM theory, specifically, a formula for the interpolation of circumferential boundary is developed with the union of quadratic and first-order seamlessly, benefiting the combination of triangle area coordinates and the line drawing approach. Additionally, a flexural angle index of tetrahedral edges and regional customization are proposed as the modification method for determining order conversion. Subsequently, the accuracy of the proposed method in addressing various issues is investigated. The results show that the performance of tetrahedrons is satisfactorily enhanced through the utilization of 64 distinct order combination modes; and compared with its quadratic form, the calculation workload has been effectively decreased with no loss of accuracy. In summary, the analytical performance of tetrahedrons can be enhanced reasonably, which provides an effective approach for rapid and accurate analysis for critical structures. [ABSTRACT FROM AUTHOR]

The presence of discontinuities, such as fractures or geological faults, can significantly influence the fluid flow in a porous medium. In general, the discontinuities can act as preferential flow paths. However, depending on their aperture and filling material, they can act as barriers to fluid flow. To model these different possibilities, this paper presents an embedded approach in the context of the finite element method to model the presence of discontinuities inside a porous medium in transient analyses. The formulation is attractive since it does not require the mesh used to discretize the porous medium to conform to the discontinuities. The derivation of the formulation is based on the Strong Discontinuity Approach by enriching the pressure field of the finite element with a Heaviside function. The enriched part of the pressure field is discretized based on the pressure jumps evaluated at the nodes where the discontinuity intersects the finite element. The discontinuity internal pressure is taken as an independent field, allowing the modeling of high pressures inside the discontinuity. A strategy to condense the discontinuity internal pressure degrees of freedom is presented. Numerical examples are presented showing the flexibility of the formulation to capture the influence of discontinuities on the fluid flow in porous medium. The results obtained with the proposed formulation are compared with interface element models, showing a good agreement between the two approaches. • New fluid flow embedded formulation for conductive and impermeable fractures. • The formulation is successfully applied to steady-state and transient problems. • The formulation can be applied to problems with high pressures inside discontinuities. • The discontinuity internal pressure can be statically condensed. • The embedded formulation shows a good agreement against discrete fracture models. [ABSTRACT FROM AUTHOR]

The effect of pile installation is a critical issue in the analysis and design of pile foundations but it is commonly ignored due to various numerical difficulties. In this paper, the installation process of an open-ended pipe pile into a sand deposit is simulated by using the zipper technique combined with the Arbitrary Lagrangian-Eulerian (ALE) method in the framework of three-dimensional (3D) finite element modeling. The subsequent lateral load response of the pile is also simulated and compared with that without consideration of the pile installation. The state dependent behavior of sand in associated with the pile installation and the subsequent lateral load is described using an advanced constitutive model. The study shows that for a relatively loose sand deposit, the sand surrounding the pile exhibits contraction and the disturbance zone takes the form of a trapezoid, whereas for a dense sand deposit, the sand near the pile will dilate and the disturbance zone takes the form of an inversed trapezoid. Furthermore, the deformation mode of the surrounding sand under the lateral load differs to some extent from that without consideration of the installation effect. Particularly, the location of the rotation point for the laterally loaded pile tends to move downwards when the pile installation process is considered. [ABSTRACT FROM AUTHOR]

Considering the spatial variability of rock masses in tunnelling analysis is a challenge in geotechnical engineering. This paper focuses on predicting collapse loads and probabilities of design failure for dual circular tunnels constructed in anisotropic rock masses. This study employs the random adaptive finite element limit analysis method, which incorporates rotated anisotropic random fields, to model uncertainties in rock mass properties. The generalised Hoek–Brown constitutive model is employed to define the yield failure criteria of a rock mass. The adaptive finite element limit analysis is first validated against a previous study, demonstrating good agreement. Then, the probability of design failure for dual circular tunnels is comprehensively investigated. This study emphasises the importance of considering both geometric parameters and rotated anisotropic random fields in comprehensive probabilistic analyses. The results provide insights into the mean and coefficient of variation of the stability numbers, as well as the probability of design failure for different geometric configurations and rotated anisotropic random fields. In conclusion, the variation in failure probability for practical applications is presented, highlighting the significance of accounting for spatial variability, rotation angle and anisotropy in rock mass properties in tunnelling. [ABSTRACT FROM AUTHOR]

In this paper, a hydromechanical coupled XFEM approach is developed for simulating 3D nonplanar hydraulic fracturing, fracture–vug interactions and natural crack intersection problems. The extended finite element method associated with a high-order tip enrichment function is used for describing rock deformation, and the finite element method is chosen for discretizing fluid flow at the fracture surface. Rock deformation and fluid flow are coupled and solved by the Picard iteration method. The hybrid explicit–implicit representation method is adopted to represent 3D nonplanar fracture surfaces, and the displacement correlation method is chosen for extracting the mixed-mode stress intensity factor. A new mixed-mode failure criterion is introduced for determining 3D nonplanar fracture growth. Analytical solutions and experimental investigations are employed to verify the validity and effectiveness of our model. The simulations of fracture–vug interactions show that fracture surface growth on the side without vugs is constrained, while vugs can aggravate the tortuousness of the fracture surface on the side with vugs. In addition, four new intersection patterns (penetration, partial arrest, partial diversion, full arrest, and vertical propagation) are found in the 3D nonplanar fracture intersection simulations. The numerical examples highlight the considerable impacts of vertical growth and the mixed-mode effect on hydraulic fracturing. [ABSTRACT FROM AUTHOR]

Proper evaluation of seismic-induced excess pore water pressures in saturated sandy soils is still an open issue, which can be tackled with fully coupled to uncoupled approaches. The former are more accurate but computationally onerous, while the latter require seismic demand and pore pressure build-up to be computed in two successive steps, typically employing simple constitutive assumptions. Starting from the work by Seed et al. (1975) , this paper presents a novel uncoupled procedure to compute excess water pressures developing in a 1D soil column under partially drained conditions, when subjected to horizontal seismic excitations. Fundamental modifications are introduced to account for: non-uniform distribution of equivalent loading cycles; soil stiffness degradation; and modification of the frequency content of ground motion due to pore pressure build-up. The approach was implemented in Matlab via the Finite Difference Method and validated against both fully-coupled Finite Element analyses and one centrifuge test. An extensive parametric study was also performed for a two-layer soil column, by varying the thickness and hydraulic conductivity of the shallow layer, as well as the seismic input. The good agreement with both numerical and experimental data demonstrates that key features of liquefaction are well-captured by the proposed uncoupled approach. [ABSTRACT FROM AUTHOR]

Ground-borne vibrations are increasing at a rapid rate due to the rise in urban expansion and industrial activities. The current solution to mitigate the unwanted vibrations is limited to the use of single trenches that require unrealistic depths. This paper presents the possibilities of using dual open and infilled trenches to mitigate the vibrations generated due to continuous harmonic motions. Full-scale field tests and comprehensive numerical studies were performed to systematically design dual trenches. The field vibration tests were performed under a wide range of frequencies using the Lazan-type mechanical oscillator. Similarly, numerical studies have been performed using finite element analysis software, PLAXIS 2D. Expanded polystyrene (EPS) geofoams of different densities, bentonite, ceramsite, concrete, and sand-rubber mixture were used as the infill materials. The normalized depths of 0.40 and 0.50 were observed as the optimal values to reach an average amplitude reduction ratio (average ARR) of 0.25 for the dual open and EPS15-infilled trenches, respectively. The isolation efficiency of EPS15-infilled trenches was observed to be 178 % higher compared to the EPS48-infilled trenches. The performance difference between EPS15 and ceramsite-filled dual trenches was observed to be only 4 % in terms of average ARR , the former being superior. [ABSTRACT FROM AUTHOR]

In this paper, a novel numerical simulation approach based on the finite element method for dynamically modeling the excavation process of shield tunneling is proposed, with the shield-ground interactions well captured. This method is capable of mimicking the alternating modes of advancing and stopping of a shield boring machine during underground construction, with the important effects of the cutterhead rotation and slurry support pressure considered. Under the cutting action, the soil at the excavation face would experience irreversible deformation and damage, such that additional support needs to be provided by the cutterhead blades and slurry to maintain stability. The impacts of key construction parameters are examined, including cutterhead rotary speed, advance rate, and slurry support pressure, on shield tunneling operations and ground responses. The numerical model is rigorously validated against physical model experiments. This work provides useful insights into the mechanistic processes in the stratum during shield tunneling, including the spatiotemporal evolution of ground deformation patterns and stress redistributions. The results offer valuable guidance for optimizing shield tunneling operations and enhancing tunneling safety and efficiency. [ABSTRACT FROM AUTHOR]

A selective review is provided of the methods and solutions used to predict the response of various geomaterials in cavity expansion problems, both cylindrical and spherical cavities. As many authors have recognized, the solutions to these problems have numerous applications in geotechnics, and the more significant of these have been addressed in this paper. Some of the more important solutions already available in the literature are presented in addition to some novel results illustrating the effects of some unique features of soil behaviour, such as softening, rate-dependency, density dependent response and dilation. Some of the solutions are available in closed form, while others have required the use of numerical methods such as the finite element method. It is contended that the relatively simple problem of cavity expansion, be it either a cylindrical or a spherical cavity, is capable of revealing important aspects of the mechanical behaviour captured in both simplified and complex soil constitutive models. [ABSTRACT FROM AUTHOR]

The initiation, propagation, and coalescence of fractures in frozen rocks plays an important role in determining the deterioration and stability of the geotechnical engineering structure in cold regions. This study proposes a numerical method to consider the interaction of multiple fractures in frozen rock based on the volumetric expansion theory and extended finite element method (XFEM). The effective expansion coefficient is adopted in this paper to describe the volume change of ice-water mixture. To accurately determine the magnitude of frost-heaving pressure during the deformation and propagation of fractures, two iterative methods have been proposed. The correctness of the numerical method is verified by the analytical solution of frost-heaving pressure within a single fracture. In addition, the secant method shows the higher efficiency in solving the problems considering the fracture interaction. The evolution of frost-heaving pressure and cracking behavior under different geometric conditions were studied by the proposed method. The numerical results suggest that stress interference may promote the propagation of fractures and accelerate the deterioration of rock mass when the fractures are located in the favorable zone. After considering the multi-fracture interaction, the configuration of two fractures has a significant influence on the evolution of the frost-heaving pressure. [ABSTRACT FROM AUTHOR]

This paper investigates the role of basement depth on the response of framed buildings to tunnel construction in sandy soil using finite element modelling. Six frames are considered to explore the influences of tunnel cover depth, building width, eccentricity, and the number of storeys on the role of basement depth. The numerical models adopt the hypoplastic constitute model to simulate the behaviour of the sand. The results suggest that basement depth plays an important role in determining the settlements of the raft foundations and soil displacements due to tunnelling. Its effect on the structural shear distortion primarily depends on the ratio of tunnel depth to building width (C / B); an increase in basement depth decreases and increases building maximum shear distortion for C / B < 0.3 and for C / B > 0.35, respectively. The basement considerably increases the shear distortion of short eccentric structures by preventing tilt of the building, causing a divergence from existing empirical envelopes and modification factors for shear distortion. The applicability of the meta-model is extended to the embedded structures by linking the building tilt freedom coefficient with the basement depth parameter, achieving good agreement between the predicted results and calculated data. Limitations and practical implications of the research are briefly discussed. [ABSTRACT FROM AUTHOR]

Taking non-Darcian flow and multi-stage loading into consideration, a semi-analytical solution for one-dimensional consolidation of multi-layered soil under continuous drainage boundary based on a linearization method was derived in this paper. The correctness of the proposed solution was verified by comparing with the existing solutions and finite element method results. Accordingly, the influence of soil properties, load parameters, interface parameter and flow parameters on the consolidation characteristics of multi-layered soil was further analyzed. The results showed that the permeability coefficient and flow exponent of the first layer of soil has the most significant influence on the consolidation of multi-layered soil, while the volume compression coefficient of the bottom layer of soil has the greatest influence on the consolidation of multi-layered soil. Continuous drainage boundary, non-Darcian flow and multi-stage loading can all prolong the consolidation process of layered soil. However, the influence of continuous drainage boundary on soil consolidation is reduced when considering non-Darcian flow or multi-stage loading. [ABSTRACT FROM AUTHOR]

Shield-soil rotary friction is one of the reasons that cause asymmetrical settlements about the central axis of tunnel center line. This paper focuses on analytical analysis of the shield-soil rotary friction on tunnelling-induced ground mechanical reactions. According to the working principle of the shield machine, the way and process of the shield torque acting on the soil is proposed. Based on the calculation model of a spatial curved shield tunnel and the rewritten of the Mindlin solutions, this paper derives the analytical solutions of the effect of shield-soil rotary friction on the soil displacement field and the additional stress field, respectively. The derived theoretical solutions are verified and compared with the shield project of Beijing East Sixth Ring Road renovation project, and relevant parameters are analyzed in this paper. The numerical model analysis based on the finite element software and the field monitoring data verify the correctness of the method proposed. The theoretical study in this paper further improves the study of the construction load of shield machine. [ABSTRACT FROM AUTHOR]

This paper describes an advanced coupling method of finite element and discrete element called the Continuum-Discontinuum Element Method (CDEM). In this study, the Barton-Bandis model(BB model) for joint non-linear deformation is introduced into the CDEM to investigate the propagation of stress waves in jointed rock masses. The paper provides a detailed account of the development process of the BB model. Then, the developed model is utilized to simulate several representative cases of stress wave propagation in jointed rock masses, revealing the principles of stress wave propagation in jointed rock masses. The findings of this study demonstrate that the simulation results of the CDEM exhibit favorable consistency with experimental and theoretical results. This confirms the capability of the CDEM to accurately and effectively simulate stress wave propagation in jointed rock masses, thereby expanding the applicability of the CDEM. This research provides powerful support for further understanding and analysis of stress wave propagation problems in jointed rock masses. [ABSTRACT FROM AUTHOR]

This paper investigates the seismic performance of complex comprehensive interchange underground structures. As an example, the seismic performance of Nanjing underground bifurcated tunnels constructed in soft soil is analyzed. A three-dimensional (3D) numerical finite element analysis model is established considering soil-tunnel interaction to analyze the seismic response characteristics and failure mechanism of the bifurcated tunnels. The results show that the tunnel damage degree is closely associated with the deformation response, and that the inter-story drift ratio of the lower layer is significantly greater than that of the upper layer. The pushover analysis method is used to obtain the seismic performance curve of the tunnel, and inter-story drift ratio limits are defined. The IDA procedure is then used to conduct multiple non-linear dynamic time history analyses based on the 3D finite element model, and IDA curve clusters are drawn with peak ground acceleration (PGA) as the earthquake intensity measures and the peak inter-story drift ratio as the damage measures of tunnels. The corresponding IDA percentiles lines are calculated, and the seismic fragility curves of the bifurcated tunnels are established. The post-earthquake functional failure probability of the bifurcated tunnels is obtained under different seismic fortification performance level. [ABSTRACT FROM AUTHOR]

The meshless numerical manifold method (MNMM) inherits the advantages of handling continuous and discontinuous problems uniformly, improving interpolation precision, and avoiding linear dependence issues. This paper refines the MNMM method for slope stability analysis to overcome the dependence and sensitivity of the strength reduction method of the finite element method on the number of finite element meshes and the algorithm for solving the nonlinear equations when calculating slopes with soft and weak interlayers. First, the strength reduction method (SRM) was incorporated into MNMM to create the numerical model called MNMM-SRM. Based on the MNMM-SRM, a complementary Mohr-Coulomb (M−C) control equation compliant with Koiter's rule of multi-yielding surfaces was established. In the principal stress space, the subspace tracking method was used to track the eigenvalues and eigenvectors of the stress tensor, thereby addressing the corner problem of M−C multi-yield surfaces. Combining the k-means clustering algorithm with wavelet transformation and employing the slope's total nodal displacement field as an input variable, an intelligent and efficient critical slip surface (CSS) automatic extraction method was developed. Three typical cases were used to validate the accuracy of the numerical model. This numerical model has a wide range of potential applications in slope stability research. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the effectiveness of the cascadic multigrid method applied to improved Picard iteration method for nonlinear problems arising in deforming variably saturated porous media. The finite element method with 6-node triangular elements is applied to discretize the space and obtain nonlinear algebraic equations. Then the nonlinear iterative method is used for iterative solution. Since the classical nonlinear Picard iteration method (PI) can be slow to converge, two improved Picard iteration methods are proposed. One is the improved Picard method with iterations k on the coarse grid and number of multiple grids m (PI-MG(m , k)), and the other is the improved Picard method based on the cascadic multigrid method without parameter k (PI-NMG(m)). Three numerical examples are given to verify the effectiveness of the improved method. Results indicate that the convergence rate of PI is the slowest (10–25 nonlinear iterations per time step), followed by PI-MG(m , k) (3–5 nonlinear iterations), and PI-NMG(m) is the fastest (stable 2 nonlinear iterations). The computational efficiency of PI-NMG(m) is improved by about 90% relative to PI and by about 70% relative to AR-PI. This method can be applied to large-scale numerical calculation of seepage and deformation in unsaturated deforming porous media. [ABSTRACT FROM AUTHOR]

The aim of the paper is to simulate the response of a deep excavation supported by sheet pile walls and lime-cement columns. The application of the deep mixing technique using lime-cement products in deep excavations changes the initial state of the natural soil and creates substantial displacements associated with the installation effects. In this paper, the influence of lime-cement stabilisation was investigated using the finite element method for an instrumented braced excavation. The 2D finite element analyses were performed with advanced constitutive models for both natural clay and stabilised soil, exploiting the laboratory test made on both field mixed and laboratory mixed stabilised clay samples. The numerical results show that taking account of installation effects provides realistic predictions of deformation, excess pore water pressure evolution, as well as the structural forces in the struts. [ABSTRACT FROM AUTHOR]

This paper provides a numerical framework for seismic analyses for layered saturated ground under inclined plane P1-SV waves. A unified stiffness matrix method (SMM) formula for both u - w - p and u - p formulations is first derived to obtain the dynamic response of saturated fields. Then, the domain reduction method (DRM) is extended to two-phase media to reproduce the target wavefield within the numerical models. The accuracy of the proposed SMM-DRM framework is verified by comparisons with analytical solutions and other numerical methods. Its applicability in complex boundary value problems is also proven by solving a typical SSI problem. The numerical framework is especially advantageous in the analyses of complex subdomains under obliquely incident seismic waves. With the procedure given in the paper, the framework can be implemented into existing finite element models straightforwardly. [ABSTRACT FROM AUTHOR]

The swelling of clayey rocks originates at different scales of the material. Clay mineral swelling is governed by two different phenomena: crystalline and osmotic swellings. In this paper, we adapt a multiscale numerical model that considers both crystalline swelling and interlayer osmotic swelling (four water layers and more) to efficiently implement it in a finite element method code. To this end, we itemize the different interactions arising in the interlayer space with respect to the disjoining pressure, and in the interparticular space considering the capillary effects. The overall model is based on the upscaling of the constitutive law from the nanoscopic scale to the macroscopic scale by adding all the different interactions that appear while upscaling. Additionally, the general model adapted in this paper can be considered as a new definition of the effective stress governing the chemo-hydromechanical behavior of clayey rocks. The numerical model is then implemented in Code_Aster software. The validation of our model is conducted by reproducing constant-volume swelling test. Simulation results for different pore size distributions demonstrate fair agreement between the experimental results and the numerical modeling in comparison with linear elasticity that overestimate the final swelling pressure compared to the model developed herein. [ABSTRACT FROM AUTHOR]

Geosynthetic-reinforced embankments founded on piled beams have emerged as a new ground modification technique for supporting earth embankments over deep soft subsoil. This paper presents an analytical model for this technique that combines parts of two existing analytical design models. The soil arching behaviour that divides the vertical embankment load into a part that is transferred to the piled beams directly, and the residual load part that rests on the geosynthetic, is described by the 3D part of the Concentric Arches (CA) soil arching model of van Eekelen et al. (2013 and 2015), which was adopted in CUR226:2016. The paper also compares the difference between adopting the 2D or the 3D part of this CA model. The tensioned geosynthetic effect was described by the membrane action equation of Pham (2020b). This equation calculates the geosynthetic strain and includes load–deflection behaviour, adhesion, and friction along the geogrid/soil interface. Two field studies and fully coupled hydromechanical finite element analyses were used to verify the proposed analytical approach and its assumptions. The paper compares the effect of founding geosynthetic-reinforced embankments on piles or piled beams. Finally, a parametric study showed the impact of beam width, center-to-center pile spacing, and geogrid stiffness on load transfer efficiency. [ABSTRACT FROM AUTHOR]

The paper illustrates the development of metamodels of the response of steel piles driven in sand and subjected to pull-out. The metamodels are created for the prediction of the pile tensile capacity and secant stiffness. They were developed using the results of finite element analyses, which made use of finite element models of robustness assessed employing a selection of available data from large-scale model pile tests. Four hundred finite element analyses allowed for the calibration of very accurate metamodels, which were also demonstrated to closely track the outputs of the experimental results. Once calibrated, the metamodels can be used independently from the finite element models they stemmed from. The outcomes of the study show that metamodels of piles response can yield very accurate results within a wide and realistic range of soil-pile configuration, avoiding the laborious implementation and computational cost which underpins the use of finite element models. As the use of metamodels in this context is new, the paper relies on particularly simplified problem, but the procedure could be extended to accommodate modelling features of higher complexity. [ABSTRACT FROM AUTHOR]

Suction caissons are attractive solutions to support offshore structures. Their capacity, both pull-out and bearing, grows with their embedment depth. However, higher embedment depths increase risks of installation failure due to uncertainty of seabed condition, increased chance of piping and structural buckling. For the first time, this paper investigates installation of structurally enhanced caissons (SECs), in the form of flanges attached to the caisson shaft, through developing a numerical procedure based on finite element analysis. The SEC has the potential to offer additional (over 20%) pull-out and bearing capacity compared with standard caisson and can have substantial positive impacts on torsional capacity. Using the proposed numerical procedure, the impact of adding the flanges on the installation resistance was studied and compared against a standard caisson. A piping criterion was defined which allows tracking the soil region where piping develops and evolves as the installation proceeds. The impacts of flange base sizes and sand compaction on the required suction for installation were studied. The results of this paper can be used as guidance to predict the required suction to install flanged caissons and can facilitate the uptake of the proposed SEC. The proposed numerical framework is applicable to other SEC geometries. [ABSTRACT FROM AUTHOR]

The finite element (FE) method may suffer from numerical instability and mesh dependency when modelling the formation of shear bands using strain-softening constitutive models. Nonlocal methods have been shown to be capable of avoiding these numerical issues effectively. This paper proposes a novel generic algorithm for incorporating existing nonlocal methods into the FE formulation of elasto-plastic constitutive models with volumetric hardening laws. Using the example of the modified Cam Clay (MCC) model this paper shows that instabilities are inevitable if the nonlocal plastic volumetric strains are directly used to update the hardening parameter. The paper further proposes a robust regularisation algorithm to overcome this issue. This algorithm has been implemented into a bespoke FE code and its capability in significantly reducing mesh dependency while maintaining numerical stability is verified through a series of numerical analyses of biaxial compression tests for highly overconsolidated clays. The performance of various existing nonlocal methods is also critically assessed. [ABSTRACT FROM AUTHOR]

Rolling dynamic compaction (RDC) is a soil improvement technique, which involves towing heavy (6–15 t), non-circular (3-, 4-, and 5-sided) modules behind a tractor to achieve soil compaction. Both potential and kinetic energies are imparted to the underlying soil as the modules fall and impact the ground. This paper presents a combined, three-dimensional finite element method (FEM)-discrete element method (DEM) model to investigate the behaviour of the 1:13 scale, 3-sided roller. Numerical results are compared against results from a field study using the corresponding full-size, 3-sided roller in two aspects namely, ground settlements and induced peak pressures. It is demonstrated that the numerical results are in very good agreement with the field observations. This paper examines the influence of the twin modules of the 3-sided roller with respect to ground improvement and the results suggest that the soil beneath a single module is improved solely by the module above it. Therefore, the current practice of using the total weight of the 3-sided roller to predict the energy imparted to the ground and the depth of influence should be avoided. The validated numerical model is also used to predict the energy delivered to the soil and the depth of influence of the roller. The energy imparted to the ground is approximately 22.5 ± 3 kJ per impact with 95% confidence, and the depth of influence is approximately 1.5 m for each of the twin modules of the 13-t, 3-sided roller operating at 11 km/h on granular soils investigated in this study. [ABSTRACT FROM AUTHOR]

This paper studies the vertical performance of rock-socketed pile group embedded in layered saturated rock-soil mass. The three-node bar element is utilized to discretize the pile, and the global stiffness matrix equation of rock-socketed pile group is assembled by the finite element method. Based on the solution for the interaction between a rock-socketed single pile and rock-soil mass, the flexibility matrix equation of rock-soil mass for the pile group is derived by the boundary element method. Combination of the force balance and displacement compatibility conditions for the rigid pile cap leads to the solution of rock-socketed pile group embedded in saturated rock-soil mass. The correctness of the proposed method is examined by comparing the solutions predicted by the present paper with the solutions from existing literature and ABAQUS results. The relevant factors affecting the vertical performance of rock-socketed pile group, such as the socketed length, pile spacing, pile-rock mass modulus ratio, length-diameter ratio and the rock mass stratification, are further discussed [ABSTRACT FROM AUTHOR]

An automated computation method is proposed in this paper to address the problems of enormous computational difficulty and low efficiency in flexible protection systems. This method uses neural networks to demonstrate the complex nonlinear mapping relationships between the system's specifications and performance. Use the finite element numerical simulation model validated by a full-scale impact test on the 750 kJ passive flexible protection system for massive parametric analysis, and extract the critical computation results as the label space. Conducted mechanical tests on critical components, analyzed the mechanical characteristics of each component, and extracted training features to form a sample space. The label space and sample space formed a dataset containing 1828 sets of data and used 1700 sets of data to train a neural network while using the remaining 128 sets of data to test. The maximum predicted error was 8.33 %, and the maximum average error was 3.73 % from the test. The proposed method can complete the computation in just 6 s, with a computation speed of 520 times that of the fastest finite element method, significantly improving the computation efficiency of the flexible protection system and reducing the computational difficulty. [ABSTRACT FROM AUTHOR]

Research on the equivalent deformation parameters of grouted arch dam abutment rock masses has recently emerged as a key in the design, construction and stability assessment of arch dams. With the aim of synthetically considering scale effects and anisotropy of the rock mass equivalent deformation parameters after grouting, in this paper, a practical numerical calculation method is developed. First, the Latin hypercube sampling method is introduced to generate a network of fractures of the arch dam abutment rock mass. Subsequently, the finite element models of the rock masses with different sizes in various directions are constructed. On this basis, equivalent continuum theory and cohesive element model are applied for numerical calculation of grouting fractured rock masses. Then, the scale effect and anisotropy of the deformation modulus of rock mass under different grouting conditions are investigated. Finally, the Jinping super-high arch dam is taken as an example to validate the theoretical significance and application effect of the proposed method. The analysis results indicate that the process of fracture and fragmentation of grouted rock masses is characterized precisely, and the deformation of material units can be described as fully as possible to calculate more realistic equivalent deformation parameters of the fractured rock masses. [ABSTRACT FROM AUTHOR]

This paper adopted both the numerical and analytical methods to investigate the excavation stability against base heave failure. The finite element limit analysis method (OPTUM) was firstly employed to calculate the safety factor of the excavation stability against base heave failure, and the failure mechanism of the excavation was obtained. Based on the analysis and observation of the numerical results, a rigid block rotational failure mechanism was proposed, and the analytical formula of the safety factor of the excavation was developed through the upper bound method of limit analysis. In order to verify the rationality of the proposed failure mechanism, the analytical formula of the safety factor and the failure pattern of excavation were compared with the numerical results and the existing classical failure mechanism. Furthermore, the influences of soil and excavation conditions on the excavation stability were analyzed and discussed. Finally, a rigid block rotational failure mechanism under stratified stratum conditions was also proposed to consider effects of the complex soil conditions on the excavation stability. The results show that the proposed rigid block rotational failure mechanism provides a more critical safety factor calculation result for actual engineering examples and obtains a more continuous and smooth failure surface, which can serve as an alternative for the analytical method of excavation stability. [ABSTRACT FROM AUTHOR]

In the finite element (FE) modelling of transient coupled problems for soils, the associated equations need to be integrated numerically over a time interval during the solution process. A minimum time-step size has been observed to exist, below which spatial oscillations in the obtained solutions can occur. These oscillations might lead to an accumulation of the resultant errors, eventually leading to invalid final predictions. This paper presents an analytical approach for deriving the time-step constraints for FE modelling of the transient behaviour of unsaturated soils with a fully coupled hydro-mechanical (HM) formulation. The effects of both element type and nonlinear soil properties are accounted for in the derivation. The proposed time-step constraints were subsequently verified through a series of coupled HM FE analyses of unsaturated soils, showing an excellent agreement. The present work shows that, when dealing with unsaturated soils, the minimum time-step size depends on the suction range investigated. This dependency derives from the nonlinear variation of water content and permeability with suction, as demonstrated through a set of comparative studies with three different types of unsaturated clays. [ABSTRACT FROM AUTHOR]

Pre-existing (open) cracks at slope crests, especially tension cracks, are a significant factor in the transition from shallow to deep-seated landslides in unsaturated soil slopes induced by rainfall. This paper presents an analytical framework to assess the stability of unsaturated soil slopes for deep-seated rotational failure considering arbitrary crack depths and unsteady infiltration, and its effectiveness is verified by previous literature and finite element analysis. A closed-form formula is proposed for the maximum depth of cracks in unsaturated soils by the stability of the vertical crack boundary. A parametric study is performed to investigate the impact of some key parameters on the stability of unsaturated soil slopes with cracks. Dimensionless stability charts are developed, which can calculate the factor of safety for the slopes with cracksof any depth and can reflect that the potential slip surfaces through or without passing through the crack tip. In addition, given the existence of a critical crack depth and maximum crack depth, with a ratio ranging from 0.5 to 0.6 based on the stability charts, deep-seated rotational failure is more likely to occur than failure caused by a crack boundary. [ABSTRACT FROM AUTHOR]

The estimation of inversion parameters for seepage models is very important for ensuring the safety of earth/rockfill dams. In most existing studies, only hydraulic characteristics have been determined based on seepage pressure or discharge observation information, which may result in inversion results that do not accurately characterize the true properties of dam materials. In this paper, an advanced parameter inversion method considering the coupling effect of seepage and thermal transfer is proposed. A seepage–thermal transfer coupled finite element model is established, and hydraulic head and temperature data of monitoring points are obtained through the forward simulation method. The entropy weight (EW) method is used to preprocess the hydraulic head and temperature data, and a universal kriging (UK) surrogate model is established to replace the time-consuming finite element simulations. The multi-island genetic algorithm (MIGA) is applied to find the optimal solution, thereby obtaining the inversion results. The effectiveness and accuracy of the proposed method are verified through laboratory tests involving seepage and thermal transfer monitoring of a core rockfill dam. Joint inversion based on temperature and hydraulic head observation information can result in improvement in the accuracy of the inversion results. [ABSTRACT FROM AUTHOR]

Conventional finite element analyses generally suffer from mesh dependency when considering softening effects. Non-local strain regularisation techniques have been developed to address this issue, which are generally complex to implement. In view of this, this paper introduces an more efficient procedure for implementation of a non-local method in Abaqus for Coupled Eulerian-Lagrangian (CEL) large deformation finite element undrained analyses. Results from a series of biaxial compression simulations demonstrate that the non-local method with a strain-softening Tresca model in CEL avoids mesh dependency. Owing to the stationary Eulerian element and the built-in mapping algorithm in CEL, high computational efficiency is achieved, adding no more than 12% to the computational cost. Guidance is provided on selection of internal length scales, element sizes and the search radius to ensure efficient non-local calculations, and it is shown that a softening scaling rule can also be used to allow use of practical mesh densities for some boundary value problems. Simulations of a number of classical geotechnical problems demonstrate the type of boundary value problems where the non-local method can effectively mitigate the mesh dependency, whilst also highlighting that the method fails to control the strain localisation that develops at soil-structure interfaces due to geometrical issues. [ABSTRACT FROM AUTHOR]

This paper presents a novel mechanical model for seismic response analysis of vertical shafts. The model is based on elastic foundation beam theory and simplifies the shaft linings as parallel Euler Bernoulli beams. Their interaction is simulated using uniformly distributed springs. The governing differential equation for shaft vibration is derived for SH wave excitation. The seismic input motion is applied to the primary lining by converting the free field displacement into harmonic form. The closed-form solutions for seismic response of both primary and secondary linings are obtained via the transfer function method. The accuracy of analytical solution is validated by comparing with finite element analysis results. Additionally, the impact of foundation stiffness, secondary lining thickness, shaft outer diameter, and relative stiffness between linings on seismic response are investigated in the parametric analysis. The analytical solutions of the seismic response analysis of vertical shafts indicates that the relative stiffness between linings significantly affects the secondary lining's peak bending moment. Furthermore, higher stiffness of the elastic connection layer between the two linings can effectively reduce the peak displacement response of the secondary lining. [ABSTRACT FROM AUTHOR]

In-service pipelines in slope sections may experience a sudden increase in strain due to circular landslides. Obtaining the peak strain of pipelines (PSP) in engineering is often necessary to quickly evaluate the pipeline's safety status. Due to the lack of consideration of the influence of sliding surface shape, pipe laying location and diameter, the existing empirical model for peak strain prediction (EMPSP) does not perform satisfactorily, and the calculated error of PSP is far more than the acceptable range. A novel EMPSP for pipelines is proposed in this paper. First, a 3D nonuniform circular sliding finite element model (FEM) is established by the strength reduction method combined with the displacement function. Second, a detailed analysis is conducted on the impact of nondimensional parameters on the PSP. Finally, detailed discussions are presented to develop the coupling form between multiple parameters in the EMPSP, and a flowchart for pipeline design and evaluation is established. By comparing engineering case data, the accuracy of the novel EMPSP model has been improved by 59% or even higher compared to previous models. In conclusion, the novel EMPSP has a wide range of applications and can efficiently guide the evaluation of pipeline design based on strain. [ABSTRACT FROM AUTHOR]

The dynamic response and mechanical behaviors of rock masses are mainly governed by discontinuities. The field-enriched finite element method is proposed to study the mechanism of crack propagation in rock mass, and the multiaxial perfectly matched layer (M-PML) is introduced to absorb the reflected wave due to the existence of artificial boundary. The fundamental theory and numerical implementation of the proposed numerical method are described in detail. By comparing two numerical models, namely one with the absorbing boundary and the other without the absorbing boundary, the necessity of considering an absorbing boundary and the ability to verify the absorption effect of the absorbing boundary on the reflected waves are demonstrated. In addition, a numerical example of underground tunnel is established to investigate the influence of dynamic waves from the hole in underground space on the crack propagation in adjacent surrounding rocks of the tunnel. Finally, a numerical model of rock slope with cracks is considered, and the influence of the combination forms of rock bridge inclination angle and fissure spacing on the crack evolution patterns of rock slope with fissures under dynamic load is studied. The research in this paper demonstrates that the dynamic field-enriched finite element method with M-PML absorbing boundary can effectively simulate the dynamic behaviors of fractured rock masses under dynamic load. [ABSTRACT FROM AUTHOR]

This paper presents rigorous plasticity solutions to the classical active and passive earth pressure problems. The primary method adopted is a conventional equation based on the soil property and three stability factors (F c , F s, and F γ), that are analogous to Terzaghi's bearing capacity factors (N c , N s , and N γ) of strip footings. The proposed method is considered as a practical yet smart approach to the determination of earth pressures and is one of the main novelties in this study. To achieve this, the finite element limit analysis (FELA) of upper and lower bounds solutions, a powerful tool in studying the behaviour of soil stability, is employed to compute the three stability factors for a wide range of soil internal friction angles, wall roughness, and surcharge pressures. In addition, analytical solutions based on statistically admissible stress fields are adopted to validate the proposed FELA solutions. The validation satisfactorily demonstrated the accuracy and reliability of the proposed solutions. It follows that the numerical results are presented in the form of tables, figures, and several examples provided to demonstrate the practical use of the three factors in estimating active and passive earth pressures with various backfill soils, wall roughness, and surcharge pressure. The study should, therefore, be of value to practitioners. [ABSTRACT FROM AUTHOR]

Local instability of a compound slope is commonplace in practice. Extant analytical solutions only considered the single global failure pattern, which results in an inaccurate assessment of slope stability. This paper develops a unified analytical framework to account for the local and global instability of a compound slope. A failure pattern coefficient is proposed for the determination of instability behaviors. On this basis, the kinematically admissible three-dimensional (3D) failure mechanism is modified to describe the collapse of slopes. Under the framework of the upper-bound theorem of limit analysis, the external work rates and the internal dissipation rates can be calculated from the unified failure mechanism. The strength reduction technique is introduced into the work rate balance equation, and then the explicit solution of the safety factor is derived. The critical safety factor and slip surface are obtained through a hybrid optimization of the objective function. By way of example, the present solutions are compared with previous solutions and the results of the finite element method. Good agreements of the safety factor and slip surface show the good capability of this study to implement the stability analysis of compound slopes. A detailed parametric study is carried out to reveal the influence of slope geometry, soil strength, and external excitation on slope stability and failure pattern. The method presented in this paper provides a more rigorous solution for the stability assessment of compound slopes. [ABSTRACT FROM AUTHOR]

The tunnel segmental lining is a type of support structure that is very complex and widely used in tunnel excavation. Of particular importance is the behaviour of circular joints in contact with adjacent rings. The shear behaviour of the circular joint is studied in detail in this paper. Particularly, bolts, which are widely used to connect the adjacent segments, play a fundamental role in the mechanical behaviour of the circular joints and therefore of the tunnel segmental lining. A new FEM model has been developed to be able to analyse the shear deformation of bolts, when two adjacent segments show a relative transversal displacement. The model allows to consider also the interaction of the bolt with the walls of the hole. It was possible to obtain the trend of the shear stiffness of the circular joint as the relative transversal displacements varied. A successfully comparison of the calculation results with the laboratory measurements was obtained. Some suggestions are proposed in order to enhancing the practicality of the model. The proposed numerical model is a useful calculation tool capable of correctly evaluating the mechanical behaviour of the circular joints and therefore to correctly represent them during the design stage. [ABSTRACT FROM AUTHOR]

While the mechanics of cemented granular material have already been approached by means of constitutive modeling, the capacity of introducing the precise internal structure of multiphase media in numerical simulations offers an alternative perspective of investigation. In specific, means of X-ray computed tomography are able to quantify the internal irregular geometry of the composite material in the form of three-dimensional images. Image analysis can be applied in order to distinguish the topology of each material phase and advanced meshing techniques are able to form a twin meshed domain. The current paper deals with the quantitative description of the morphology of small cemented sand samples, the application of developed image analysis algorithms to treat imaging artefacts (mainly due to beam hardening), the equivalent mesh generation via the image adapted meshing technique and the numerical testing using the Finite Element Method. Four samples are imaged, meshed and numerically tested in uniaxial compression; the mesoscale finite element simulations are able to display the intergranular stress transmission chains. A statistical analysis of the load carried by the granular skeleton provides evidence of the influence of the cementation degree and the compaction of the aggregates on the uniformity of the stress distribution. [Display omitted] • Alleviation of image artifacts due to beam hardening. • Link between 3D images and finite element solvers. • Capture of the intergranular stress transmission mechanisms. • Statistical analyses over the stress distribution of the simulated particles. [ABSTRACT FROM AUTHOR]

Analytical solutions can quickly and simply evaluate stresses and displacements in tunnels and are widely adopted in the preliminary design phase of tunnels. Tunnels must be able to withstand static loading and seismic loading. This paper proposes new analytical solutions for the stresses and displacements of tunnels under static and seismic loading. The tunnel lining is treated as a thick-walled cylinder. Moreover, the contact stiffness coefficient k 0 and the stress release coefficient η 0 are introduced to consider the arbitrary contact conditions at the ground–lining interface and the amount of excavation unloading. The new analytical solutions are verified by comparison with finite element analysis results. The results demonstrate the accuracy and applicability of the proposed analytical solutions. In addition, parametric analyses are conducted to explore the effects of the stress release coefficient η 0 and stiffness coefficient k 0 at the ground–lining interface, as well as the incident angle α of shear waves. The analysis results indicate that the proposed analytical solutions offer satisfactory performance and can be applied as an effective tool for preliminary tunnel design. [ABSTRACT FROM AUTHOR]

Advanced constitutive models for soils are critical to achieve reliable results in geotechnical analyses, but their implementation in finite element programs should be accurate, efficient, and robust. This paper describes the algorithm used to integrate a complex elastoplastic constitutive model for clays, the MIT-E3, in the finite element framework, followed by extensive evaluations. The explicit substepping scheme with different order of accuracy is adopted in the integration due to its simplicity, and also because of complexities in the model formulation. Several important issues are highlighted in the integration to improve the model performance in the analysis, (i) rigorous update of the void ratio, (ii) efficient intersection with the bounding surface, (iii) consistent correction of the drifted stress to the bounding surface, and (iv) consistently linearized tangent operator in the explicit substepping scheme. The numerical integration is verified by reproducing the stress-strain behaviour in single element tests, and also by checking the error behaviour with the order of accuracy of the integration method. The accuracy and efficiency of different methods in the integration are evaluated in a rigorous and consistent manner, which has practical implications for choosing suitable methods and parameters in the analysis. Good convergence rate can be achieved using the proposed consistently linearized tangent operator. The substepping scheme with error control is shown to be stable in the challenging geotechnical problems, while the efficiency is affected by the strain increment size which is problem dependent. [ABSTRACT FROM AUTHOR]

The finite element method (FEM) is now widely used for stability analysis of earth slopes reinforced with stabilizing piles for the advantages of better simulation of soil–pile interactive behaviors and clearly capturing the complex failure mechanism of pile-reinforced slopes. However, the implementation of probabilistic simulation to model the influence of inherent random variables onto reinforced earth slopes is still challenging due to the extensive computational resources required for the repeated execution of the Finite Element Method (FEM) simulations. This paper proposes a framework for probabilistically analyzing the pile-reinforced earth slope based on a weighted uniform simulation (WUS) method implemented by secondary development of ABAQUS-via-Python codes. Using the proposed method, important information of probabilistic indices can be obtained with less computational cost, and the influence of different pile design parameters on the probabilistic FEM stability analysis of reinforced slopes is systematically studied. The reliability indices β and the most probable failure points (MPPs) for optimal designs of pile-reinforced earth slopes under different pile design parameter combinations (L , L x / L s , S , D) are obtained, which can provide useful reference information for conducting slope reinforcement practicing works. In addition, the influence of uncertainty and correlation of soil strength parameters on the reliability of the reinforced slope is also investigated. [ABSTRACT FROM AUTHOR]

A cyclic-softening macro element model that represents mono-bucket foundation supporting offshore wind turbines in clay is presented in this paper. The model is formulated based on multi-surface plasticity with kinematic and isotropic hardening rule. The softening behaviour of the foundation subjected to a cyclic load sequence is captured real-timely in the macro element model through the contraction of yield surfaces. The model parameters are calibrated by uniaxial quasi-static load–displacement curves, which are obtained by finite element analyses with the cyclic behaviour of soil simulated via the cyclic contour diagram approach. The performance of the macro element model in representing the softening of a bucket foundation during a cyclic load sequence is demonstrated by comparing with parallel finite element analyses. A reasonable agreement has been achieved. The procedure to apply the model is suggested, considering different working scenarios with various cyclic to average load ratios. The macro element model developed is capable of capturing the real-time displacement of foundation in a load sequence, with high computational efficiency and accuracy. [ABSTRACT FROM AUTHOR]

In this paper, a novel direct time-domain numerical method, called the FEM-SBFEM-SBPML, is proposed to study the wave propagation problems in soil-structure interaction (SSI) system with complex geometry and geological condition. In the bounded domain, the structure is modeled as beam element based on the finite element method (FEM), and the surrounding truncated soil is discretized using the scaled boundary finite element method (SBFEM) combined with an efficient quadtree mesh generation technique, respectively. In addition, a solid-modified beam coupling model considering the eccentric effect of the tangential traction at the outer surface of the structures is implemented. The unbounded domain is modeled by a recently proposed scaled boundary perfectly matched layer (SBPML) method, which is a novel high-accuracy absorbing layer method satisfying the radiation condition. As a result, the combined FEM-SBFEM-SBPML approach is capable of modeling SSI with complex geometries and soil properties automatically. Some benchmark tests are conducted to illustrate the accuracy and efficiency of the proposed scheme, and a vibration analysis of a soil-tunnel system is further presented to demonstrate the applicability of the proposed method in engineering. [ABSTRACT FROM AUTHOR]

This paper presents a stability study on the collapse mechanisms of a plane-strain tunnel face in c - ϕ soils using the upper bound finite element method with rigid translatory moving elements (UBFELA-RTME) and nonlinear programming technique. Practical considerations are given to the unlined length influence behind the tunnel face. An advanced mesh adaptive updating strategy is adopted, aiming to improve the computational efficiency, the accuracy of upper-bound solutions, as well as the produced collapse mechanisms. The unlined length influence on the face stability and collapse mechanism of the tunnel face are determined with various combinations of tunnel depth ratios, soil friction angles, and dilatancy angles. Using the UBFELA-RTME with the Davis's approach and a mesh adapting strategy, the non-associated plasticity flow rule can be well approximated. The developed technique was validated against different numerical methods, and it is concluded that the tunnel face stability can be improved by increasing soil friction and dilatancy angles, and yet weakens as the unlined length increases where a mesh-liked collapse zone gradually appears on the tunnel vault top. It gradually evolves to a global collapse failure till the ground surface. The findings contribute to a better understanding of the ground surface failure under the unlined support length influence in tunnel construction. [ABSTRACT FROM AUTHOR]

This paper presents the nodal integration-based particle finite element method (N-PFEM) for poro-elastoplastic analysis of saturated soils subject to large deformation, utilising the generalised Hellinger-Reissner variational principle to reformulate the governing equations for saturated soil dynamics into a min–max optimisation problem. With finite element discretisation and nodal integration over cells, the problem is transformed into a standard second-order cone programming problem, efficiently resolved using the advanced primal–dual interior point method. The N-PFEM method has several advantages, including the use of linear triangular elements without volumetric locking issues, the avoidance of regularisation techniques, and the elimination of tedious variable mapping after remeshing. The numerical model is validated for large deformation analysis of saturated soils with a series of benchmarks against available analytical and numerical solutions, with a case study of the deformation of an embankment considering stone column reinforcement also carried out. This N-PFEM framework offers an effective and efficient simulation approach for the evolutionary behaviour of saturated soils with large deformation in complex geotechnical configurations of practical relevance. [ABSTRACT FROM AUTHOR]

If no regularisation method is used during finite element modelling of strain-softening (brittle) materials, results become mesh dependent: manifesting as very thin shear bands whose thickness and orientation depends on the mesh discretisation. The objectives of this paper were to determine if mesh independent results were achieved, and to track the evolving width of the shear band when considering naturally occurring properties of soft clays, including a rate dependent stress-strain-strength relationship. The constitutive model included a destructuration process and strain-rate dependency, and the analyses allowed for local pore water flow. A bearing capacity problem was loaded to failure. Analyses were conducted with different mesh discretisation, loading rates and permeabilities. The results demonstrated mesh independent failure loads, and the strain-softening occurred in zones with thickness independent of mesh size. Local pore water flow delayed the initiation of strain softening and resulted in higher failure loads. The softening zones grew in thickness to over one meter, reinforcing that the finite element method is suitable for the determination of the bearing capacity of strain-softening sensitive clays. In conclusion, the rate dependent constitutive model is a promising method for regularising strain localisation in soft brittle clays under quasi-static loading conditions. [ABSTRACT FROM AUTHOR]