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Develop a local radial point interpolation method (LRPIM) to analyze the dissipation process of excess pore water pressure in porous media and verify its numerical capability.

Terzaghi's consolidation theory is used to describe the dissipation process. A local residual form is formulated over only a sub‐domain. This form is spatially discretized by radial point interpolation method (RPIM) with basis of multiquadrics (MQ) and thin‐plate spline (TPS), and temporally discretized by finite difference method. One‐dimensional (1D) and two‐dimensional consolidation problems are numerically analyzed.

The LRPIM is suitable, efficient and accurate to simulate this dissipation process. The shape parameters, q=1.03, R=0.1 for MQ and η=4.001 for TPS, are still valid.

The asymmetric system matrix in LRPIM spends more resources in storage and CPU time.

Local residual form requires no background mesh, thus being a truly meshless method. This provides a fast and practical algorithm for engineering computation.

This paper provides a simple, accurate and fast numerical algorithm for the dissipation process of excess pore water pressure, largely simplifies data preparation, shows that the shape parameters from solid mechanics are also suitable for the dissipation process.

The purpose of this paper is to present a semi-analytical solution to one-dimensional (1D) consolidation induced by a constant inner point sink in viscoelastic saturated soils.

Based on the Kelvin–Voigt constitutive law and 1D consolidation equation of saturated soils subject to an inner sink, the analytical solutions of the effective stress, the pore pressure and the surface settlement in Laplace domain were derived by using Laplace transform. Then, the semi-analytical solutions of the pore pressure and the surface settlement in physical domain were obtained by implementing Laplace numerical inversion via Crump method.

As for the case of linear elasticity, it is shown that the simplified form of the presented solution in this study is the same as the available analytical solution in the literature. This to some degree depicts that the proposed solution in this paper is reliable. Finally, parameter studies were conducted to investigate the effects of the relevant parameters on the consolidation settlement of saturated soils. The presented solution and method are of great benefit to provide deep insights into the 1D consolidation behavior of viscoelastic saturated soils.

The presented solution and method are of great benefit to provide deep insights into the 1D consolidation behavior of viscoelastic saturated soils. Consolidation behavior of viscoelastic saturated soils could be reasonably predicted by using the proposed solution with considering variations of both flux and depth because of inner point sink.

This paper aims to present a new discrete method to predict average excess pore pressure and degree of consolidation for soft ground using prefabricated vertical drains under time-dependent surcharge and/or vacuum loading and multi-soil layers.

The drain is discretized into a number of mesh points at which the average excess pore pressure is estimated. The conventional Laplace technique is used to solve the analytical equations. The proposed method is validated with previous findings reported in the literature. Moreover, field measurements are used to verify the accuracy of the proposed method with a case history of ground improvement by prefabricated vertical drains using the vacuum consolidation technique.

In comparison to past studies, this new discrete method is simpler to be implemented in a spreadsheet calculation to achieve a rational solution with less computational time for similar consolidation problems. Moreover, the current approach also incorporates a solution for multi-soil layers, which can hardly be derived by analytical solutions.

According to authors’ knowledge, this is the first-time discrete method by Laplace transform technique is applied for the vertical drain.

Large deformation problems are frequently encountered in various fields of geotechnical engineering. The particle finite element method (PFEM) has been proven to be a promising method to solve large deformation problems. This study aims to develop a computational framework for modelling the hydro-mechanical coupled porous media at large deformation based on the PFEM.

The PFEM is extended by adopting the linear and quadratic triangular elements for pore water pressure and displacements. A six-node triangular element is used for modelling two-dimensional problems instead of the low-order three-node triangular element. Thus, the numerical instability induced by volumetric locking is avoided. The Modified Cam Clay (MCC) model is used to describe the elasto-plastic soil behaviour.

The proposed approach is used for analysing several consolidation problems. The numerical results have demonstrated that large deformation consolidation problems with the proposed approach can be accomplished without numerical difficulties and loss of accuracy. The coupled PFEM provides a stable and robust numerical tool in solving large deformation consolidation problems. It is demonstrated that the proposed approach is intrinsically stable.

The PFEM is extended to consider large deformation-coupled hydro-mechanical problem. PFEM is enhanced by using a six-node quadratic triangular element for displacement and this is coupled with a four-node quadrilateral element for modelling excess pore pressure.

It is well known that the prefabricated vertical drain (PVD) installation process generates a significant soil disturbance around PVD. This disturbed zone significantly affects the rate of settlement and excess pore pressure dissipation. However, the characteristics of these zones were still uncertain and difficult to quantify; there remains large discrepancy among researchers. This study aims to develop a simple analytical solution for radial consolidation analysis of PVD-installed deposit considering mandrel-induced disturbance.

The proposed solution takes into account the nonlinear distributions of both horizontal hydraulic conductivity and compressibility toward the drain. The proposed solution was applied to analyze field behavior of test embankment in New South Wales, Australia.

Both effects significantly increased the time required to achieve a certain degree of consolidation. The effect of hydraulic conductivity on the consolidation rate was more significant than the effect of compressibility variation. And, the increased compressibility in the soil-disturbed zone due to mandrel installation significantly increased vertical strain of the PVD-improved soil deposit. The predicted results using the proposed analytical solution were in good agreement with the field measurements.

A geotechnical engineer could use the proposed analytical solution to predict consolidation behavior of drainage-installed ground.

Consolidation behavior of PVD-installed ground could be reasonably predicted by using the proposed solution with considering variations of both hydraulic conductivity and compressibility due to PVD installation.

Liquefaction of soils is defined as significant reduction in shear strength and stiffness due to increase in pore water pressure. This phenomenon can occur in static (monotonic) or dynamic loading patterns. However, in each pattern, the inherent variability of the soil parameters indicates that this problem is of a probabilistic nature rather than being deterministic. The purpose of this paper is to present a method, based on random finite element method, for reliability assessment of static liquefaction of saturated loose sand under monotonic loading.

The random finite element analysis is used for reliability assessment of static liquefaction of saturated loose sand under monotonic loading. The soil behavior is modeled by an elasto-plastic effective stress constitutive model. Independent soil parameters including saturated unit weight, peak friction angle and initial plastic shear modulus are selected as stochastic parameters which are modeled using a truncated normal probability density function (pdf).

The probability of liquefaction is assessed by pdf of modified pore pressure ratio at each depth. For this purpose pore pressure ratio is modified for monotonic loading of soil. It is shown that the saturated unit weight is the most effective parameter, within the selected stochastic parameters, influencing the static soil liquefaction.

This research focuses on the reliability analysis of static liquefaction potential of sandy soils. Three independent soil parameters including saturated unit weight, peak friction angle and initial plastic shear modulus are considered as stochastic input parameters. A computer model, coded in MATLAB, is developed for the random finite element analysis. For modeling of the soil behavior, a specific elasto-plastic effective stress constitutive model (UBCSAND) was used.

It is well-known that consolidation rate of prefabricated vertical drain (PVD)-installed ground is closely related to the discharge capacity of PVD, which decreases with an increase in effective stress. This paper aims to present consolidation behaviors of PVD-improved ground considering a varied discharge capacity of PVD.

A simple equivalent vertical hydraulic conductivity (k′_ve method) was proposed in plane strain numerical analysis, in which the effect of decreased discharge capacity with depth was considered. Numerical analysis was applied to analyze field behaviors of test embankment of soft mucky deposit.

Finite element method results indicated that consolidation behaviors of PVD-improved soil with a nonlinear distribution of discharge capacity with depth were in a good agreement with the observed field behaviors, compared with those with a constant discharge capacity and a linear distribution of discharge capacity. At a given time and depth, the consolidation rate in the case of discharge capacity with a nonlinear distribution is lower than that of a linear or constant distribution.

A geotechnical engineer could use the proposed method to predict consolidation behaviors of drainage-installed ground.

Consolidation behaviors of PVD-installed ground could be reasonably predicted by using the proposed method with considering effect of discharge capacity reduction.

The purpose of the article is to extend the node-based smoothed point interpolation method (NS-PIM) for soil consolidation analysis based on the Biot’s theory.

The shape functions for displacements and pore pressures are constructed using the PIM separately, leading to the Kronecker delta property and easy implementation of essential boundary conditions. Then, a benchmark problem of 2D consolidation under ramp load is solved to investigate the validity of this application. Meanwhile, convergence features of different solutions are studied. Furthermore, the incompressible and impermeable condition under instant load is investigated. The results calculated by the NS-PIM solution with different orders of shape functions are compared. Finally a 2D consolidation problem in construction period is solved. An error estimation method is applied to check the mesh quality.

The results of the NS-PIM solution show good agreement with those certified results. Useful convergence features are found when comparing the results of the NS-PIM and the FEM solutions. A simple method is introduced to estimate the errors of the model with rough grids. The convergence features and error estimation method can be applied to check the mesh quality and get accurate results. More stable results can be obtained using the NS-PIM solution with lower order of pore pressure shape functions under the incompressible and impermeable condition.

It cannot be denied that the calculation of NS-PIM solution takes more time than that of the FEM solution, and more work needs to be carried out to optimize the NS-PIM solution. Also, in further study, the feasibility of more complicated and practical engineering problems can still be probed in the NS-PIM solution.

This paper introduced a method for the consolidation analysis on the situation of construction loads (“ramp load”) using the NS-PIM which is quite indispensable in many foundation problems. Also, more stable results can be obtained using the NS-PIM solution with lower order of pore pressure shape functions than that with same order of shape functions.

This study first focuses on the situation of construction loads (“ramp load”) in the NS-PIM consolidation analysis which is quite indispensable in many foundation problems. An error estimation method is introduced to evaluate the mesh quality and get accurate values based on the convergence features of the FEM and NS-PIM solutions. Then, the incompressible and impermeable condition under instant load is investigated, and the analysis show that the NS-PIM with lower order of pore pressure shape functions can get stable results in such conditions.

The consolidation behavior of prefabricated vertical drain (PVD)-installed soft deposits mainly depends on the PVD performance. The purpose of this study is to propose a numerical solution for the consolidation of PVD-installed soft soil using the large-strain theory, in which the reduction of discharge capacity of PVD according to depth and time is simultaneously considered.

The proposed solution also takes into account the general constitute relationship of soft soil. Subsequently, the proposed solution is applied to analyze and compare with the monitoring data of two cases, one is the experimental test and another is the test embankment in Saga airport.

The results show that the reduction of PVD discharge capacity according to depth and time increased the duration required to achieve a certain degree of consolidation. The consolidation rate is more sensitive to the reduction of PVD discharge capacity according to time than that according to the depth. The effects of the reduction of PVD discharge capacity according to depth are more evident when PVD discharge capacity decreases. The predicted results using the proposed numerical solution were validated well with the monitoring data for both cases in verification.

In this study, the variation of PVD discharge capacity is only considered in one-dimensional consolidation. However, it is challenging to implement a general expression for discharge capacity variation according to time in the two-dimensional numerical solution (two-dimensional plane strain model). This is the motivation for further study.

A geotechnical engineer could use the proposed numerical solution to predict the consolidation behavior of the drainage-improved soft deposit considering the PVD discharge capacity variation.

The large-strain consolidation of PVD-installed soft deposits could be predicted well by using the proposed numerical solution considering the PVD discharge capacity variations according to depth and time.

Prediction of excess pore water pressure and estimation of soil parameters are the two key interests for consolidation problems, which can be mathematically quantified by a set of partial differential equations (PDEs). Generally, there are challenges in solving these two issues using traditional numerical algorithms, while the conventional data-driven methods require massive data sets for training and exhibit negative generalization potential. This paper aims to employ the physics-informed neural networks (PINNs) for solving both the forward and inverse problems.

A typical consolidation problem with continuous drainage boundary conditions is firstly considered. The PINNs, analytical, and finite difference method (FDM) solutions are compared for the forward problem, and the estimation of the interface parameters involved in the problem is discussed for the inverse problem. Furthermore, the authors also explore the effects of hyperparameters and noisy data on the performance of forward and inverse problems, respectively. Finally, the PINNs method is applied to the more complex consolidation problems.

The overall results indicate the excellent performance of the PINNs method in solving consolidation problems with various drainage conditions. The PINNs can provide new ideas with a broad application prospect to solve PDEs in the field of geotechnical engineering, and also exhibit a certain degree of noise resistance for estimating the soil parameters.

This study presents the potential application of PINNs for the consolidation of soils. Such a machine learning algorithm helps to obtain remarkably accurate solutions and reliable parameter estimations with fewer and average-quality data, which is beneficial in engineering practice.