ABSTRACT This study systematically investigates the small‐strain stiffness of sand‐rubber mixtures, focusing on combined particle disparity—both larger sand with smaller rubber and smaller sand with larger rubber—using the discrete element method. The effectiveness of various state variables in capturing stiffness behavior across different rubber contents and size disparities (SDs) is evaluated. Conventional state variables developed for natural sands, such as void ratio and mechanical void ratio were found to be less effective in describing the small‐strain stiffness characteristics of sand‐rubber mixtures due to distinct properties of rubber. This study then demonstrates that the stiffness contribution of rubber materials could be negligible, emphasizing that particle property disparity is more significant than SD between sand and rubber materials. Therefore, an adapted state variable, considering only active sand particles, shows improved performance for capturing the correlation between small‐strain stiffness with increasing rubber contents, suggesting its potential utility over conventional variables. Additionally, a refined void ratio, including inactive sand particles but excluding rubber, offers a practical alternative for capturing small‐strain stiffness in experimental and engineering practices, aligning with previous experimental observations. These findings underscore the need for developing more effective state variables that accurately reflect the interactions within heterogeneous materials like sand‐rubber mixtures.
This study proposes a generalised framework for developing a hybrid machine learning (ML) model that combines support vector regression (SVR) with hyperparameter optimisation to predict thermal conductivity ( k) with uncertainty. The framework contains four phases: data pre-processing, determining the best-performing hybrid model, selecting the optimal input combination, and uncertainty implementation. A database containing 2197 data points is first compiled to train the ML model. Three hyperparameter optimisation algorithms are adopted to tune hyperparameters, and their performance is evaluated by model evaluation metrics. Results show that SVR with Bayesian optimisation (SVR-BO) is the best-performing model since it produces more accurate predictions for k than models that employ grid and random searches. Given the sample insufficiency issue encountered in practice, the SVR-BO models with 144 input combinations are analysed. The compassion among models under various input combinations indicates that incorporating temperature as an additional input can provide moderate improvement in the accuracy and generalisability of the hybrid model. Based on the comparison, a five-input model is selected as the best candidate to implement the uncertainty evaluation for k. Results demonstrate that the predicted k possesses higher reliability for denser datasets and shows promising potential for applications in k with uncertainty assessments.
Abstract The use of horizontal drains assisted by vacuum loading is an effective method for speeding up the consolidation of dredged soil slurry. However, few studies developed models for the large strain consolidation of clayey slurry with prefabricated horizontal drains (PHDs) under self-weight and vacuum loading considering the effects of nonlinear compression and creep. This study introduces a PHD-assisted finite strain consolidation model considering nonlinear compression and limited creep by incorporating an improved elasto-viscoplastic constitutive equation. Firstly, the governing equations for the consolidation of very soft soil with PHDs were derived and solved by the finite-difference method. Subsequently, the proposed consolidation model was verified by comparing the calculations with the finite element solutions, a laboratory model test, and a field trial performed in Hong Kong. Good agreement with the numerical solutions and measured results indicates that the proposed model can capture the consolidation features with PHD combining staged filling and time-dependent vacuum loading. Then, the proposed model was used to estimate a self-weight consolidation test and field test in Japan to show the performance of the proposed model. Finally, parametric studies were conducted to explore the influence of nonlinear compression and creep on the consolidation of soft soil with PHDs.
SUMMARY Difficulties are involved in discrete element method (DEM) modelling of the flexible boundary, that is, the membranes covering the soil sample, which can be commonly found in contemporary laboratory soil tests. In this paper, a novel method is proposed wherein the finite difference method (FDM) and DEM are coupled to simulate the rubber membrane and soil body, respectively. Numerical plane strain and triaxial tests, served by the flexible membrane, are implemented and analysed later. The effect of the membrane modulus on the measurement accuracy is considered, with analytical formulae derived to judge the significance of this effect. Based on an analysis of stress‐strain responses and the grain rotation field, the mechanical performances produced by the flexible and rigid lateral boundaries are compared for the plane strain test. The results show that (1) the effect of the membrane on the test result becomes more significant at larger strain level because the membrane applies additional lateral confining pressure to the soil body; (2) the tested models reproduce typical stress and volumetric paths for specimens with shear bands; (3) for the plane strain test, the rigid lateral boundary derives a much higher peak strength and larger bulk dilatation, but a similar residual strength, compared with the flexible boundary. The latter produces a more uniform (or ‘diffuse') rotation field and more mobilised local kinematics than does the former. All simulations show that the proposed FDM‐DEM coupling method is able to simulate laboratory tests with a flexible boundary membrane.
Abstract The node‐based smoothed particle finite element method (NS‐PFEM) offers high computational efficiency but is numerically unstable due to possible spurious low‐energy mode in direct nodal integration (NI). Moreover, the NS‐PFEM has not been applied to hydromechanical coupled analysis. This study proposes an implicit stabilised T3 element‐based NS‐PFEM (stabilised node‐based smoothed particle finite element method [SNS‐PFEM]) for solving fully hydromechanical coupled geotechnical problems that (1) adopts the stable NI based on multiple stress points over the smooth domain to resolve the NI instability of NS‐PFEM, (2) implements the polynomial pressure projection (PPP) technique in the NI framework to cure possible spurious pore pressure oscillation in the undrained or incompressible limit and (3) expresses the NI for assembling coefficient matrices and calculating internal force in SNS‐PFEM with PPP as closed analytical expressions, guaranteeing computational accuracy and efficiency. Four classical benchmark tests (1D Terzaghi's consolidation, Mandel's problem, 2D strip footing consolidation and foundation on a vertical cut) are simulated and compared with analytical solutions or results from other numerical methods to validate the correctness and efficiency of the proposed approach. Finally, penetration of strip footing into soft soil is investigated, showing the outstanding performance the proposed approach can offer for large deformation problems. All results demonstrate that the proposed SNS‐PFEM with PPP is capable of tracking hydromechanical coupled geotechnical problems under small and large deformation with different drainage capacities.
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