Towards parameter limits of displacement boundary value problems for Mohr-Coulomb models

In this paper, a meshfree method called adaptive CTM–RPIM is developed to model geotechnical problems with large deformation. The developed adaptive CTM–RPIM is a combination of the Cartesian transformation method (CTM), the radial point interpolation method (RPIM) and the alpha shape method. To reduce the requirement for meshes, the CTM is adopted to transform domain integrals into line integrals, and the RPIM is applied to construct interpolation functions. The alpha shape method, which is capable of capturing severe boundary evolution due to large deformations, is then introduced into the CTM–RPIM to form the adaptive CTM–RPIM. The accuracy of CTM–RPIM is first verified by considering a cantilever beam under small deformation, where the influence of key parameters on the simulation results is explored. Afterward, the ability of the adaptive CTM–RPIM to handle large deformation problems is demonstrated by simulating cantilever beams with large deformations for which analytical solutions are available. Finally, the ability of the proposed method to model the geotechnical large deformations is illustrated from both quasi-static and dynamic aspects, where a slope failure problem and a footing bearing capacity problem are modeled to evaluate the stability of geotechnical structures; and a 2-D soil collapse experiment using small aluminum bars is simulated to show the method capability in describing the soil flows. These benchmark examples demonstrate that the adaptive CTM–RPIM is a numerical method with broad application prospects for modeling large deformation problems in geotechnical engineering.

This work has, as its main objective, the development of an efficient and large scale optimizer, that allows the practical application of Numerical Limit Analysis (NLA) with Finite Element Method (FEM) to solve real problems in Geotechnical Engineering. For that purpose, an optimizer was developed for GEOLIMA (GEOtechnical LIMit Analysis) program (Carrin, 2004), based on Interior Points algorithm, computationally more efficient than the existing commercial optimizers. Due to the fact that soils have random properties, the possibility to apply Reliability Analysis with Limit Analysis using the FORM method was also investigated. Initially, Limit Analysis theory was presented together with its numerical formulation using the FEM. In sequence, the use of commercial optimizers was investigated in order to solve the resulting mathematical problem. Subsequently, the theorical foundations of the developed optimizer, based on the Interior Points algorithm were described. A summary of Reliability Analysis was also presented together with a description of computational procedures using FORM and two examples were developed.

Three dimensional image of stress space geotechnical constitutive model

T. Wichtmann, T. Triantafyllidis: Behaviour of granular soils under environmentally induced cyclic loads. - D. Muir Wood: Constitutive modelling. - C. di Prisco: Creep versus transient loading effects in geotechnical problems. - M. Pastor et al.: Mathematical models for transient, dynamic and cyclic problems in geotechnical engineering. - M. Pastor: Discretization techniques for transient, dynamics and cyclic problems in geotechnical engineering: first order hyperbolic partial diffential equations. - M. Pastor et l.: Discretization techniques for transient, dynamic and cyclic problems in geotechnical engineering: second order equation. - C. di Prisco: Cyclic mechanical response of rigid bodies interacting with sand strata. - D. Muir Wood: Macroelement modelling. - M. F. Randolph: Offshore design approaches and model tests for sub-failure cyclic loading of foundations. - M.F. Randolph: Cyclic interface shearing in sand and cemented solis and application to axial response of piles. - M. F. Randolph: Evaluation of the remoulded shear strength of offshore clays and application to pipline-soil and riser-soil interaction.

SummaryTo solve large deformation geotechnical problems, a novel strain‐smoothed particle finite element method (SPFEM) is proposed that incorporates a simple and effective edge‐based strain smoothing method within the framework of original PFEM. Compared with the original PFEM, the proposed novel SPFEM can solve the volumetric locking problem like previously developed node‐based smoothed PFEM when lower‐order triangular element is used. Compared with the node‐based smoothed PFEM known as “overly soft” or underestimation property, the proposed SPFEM offers super‐convergent and very accurate solutions due to the implementation of edge‐based strain smoothing method. To guarantee the computational stability, the proposed SPFEM uses an explicit time integration scheme and adopts an adaptive updating time step. Performance of the proposed SPFEM for geotechnical problems is first examined by four benchmark numerical examples: (a) bar vibrations, (b) large settlement of strip footing, (c) collapse of aluminium bars column, and (d) failure of a homogeneous soil slope. Finally, the progressive failure of slope of sensitive clay is simulated using the proposed SPFEM to show its outstanding performance in solving large deformation geotechnical problems. All results demonstrate that the novel SPFEM is a powerful and easily extensible numerical method for analysing large deformation problems in geotechnical engineering.

Numerical modeling using finite element method (FEM) is well-recognized as a powerful method for both engineers and researchers to solve boundary value problems. In the modeling of geotechnical problems, the analyses are often limited to simple static problems with either steady-state effective or total stress approach while the transient response (development and dissipation of excess pore water pressure, uex) is seldom considered. Besides, infinitesimal small soil deformation is usually assumed. The simulation is further complicated when the soil-structure interaction problems involve significant soil displacements; like a pile subject to negative skin friction (NSF) and a cone/pile penetration. However, conventional FEM analysis prematurely terminates due primarily to excessive mesh distortion. One could see that simulating a transient problem with large deformation and distortion remains a great challenge. In this study, advanced FE simulations are performed to give new insights into the problems of (1) a pile subject to NSF; and (2) a cone penetration. The transient response of the NSF problem is modeled with the fluid-coupled consolidation technique and geometric nonlinearity. The fluid-coupled cone penetration problem is modeled with a newly developed adaptive approach.
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\nThe NSF and cone penetration simulations involve complex soil-structure interface modeling. Two types of modified interface responses are developed and verified which consider fluid coupling. The developed algorithm is applied to back analyze a case history of a pile subject to NSF induced by surcharge loading. Promising results were shown. Development of dragload and neutral plane (NP) with time is studied. NP locates at 75% of the pile embedded length (D) in long-term. Next, a parametric study is performed to investigate the influences of pile geometries, ground compressibility and loading conditions towards the pile responses. The long-term NP locates at around 0.55D to 0.65D in the studied engineering scenarios. The maximum downdrag can be up to 10% of the pile diameter. NP shifts upward when the head load increases. A simple design chart is proposed which helps engineers to estimate the long-term axial load distribution. An illustrative example is given to demonstrate the application and performance of the chart.
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\nThe study is extended to investigate the cone penetration problem. An advanced adaptive method is developed and implemented into the FE package ABAQUS to resolve the problems of numerical instability, excessive mesh distortion and premature termination. The proposed method is verified by modeling a ground consolidation problem. Next, total stress back analysis of cone penetration is conducted with the proposed method. The development of cone factor predicted by the proposed method gives a better match with the laboratory result when comparing with the built-in ALE method. Next, the development and dissipation of uex during cone advancing with the proposed method and fluid-coupled technique is investigated. uex develops dramatically around the cone tip. The soil permeability is back calculated from the dissipation test and agrees well with the input value. It is believed that the construction effects of a press-in pile and the subsequence NSF on that pile can be modeled by utilizing the finding of this study.

In this paper, a meshless local maximum-entropy finite element method (LME-FEM) is proposed to solve 1D Poisson equation and steady state convection---diffusion problems at various Peclet numbers in both 1D and 2D. By using local maximum-entropy (LME) approximation scheme to construct the element shape functions in the formulation of finite element method (FEM), additional nodes can be introduced within element without any mesh refinement to increase the accuracy of numerical approximation of unknown function, which procedure is similar to conventional p-refinement but without increasing the element connectivity to avoid the high conditioning matrix. The resulted LME-FEM preserves several significant characteristics of conventional FEM such as Kronecker-delta property on element vertices, partition of unity of shape function and exact reproduction of constant and linear functions. Furthermore, according to the essential properties of LME approximation scheme, nodes can be introduced in an arbitrary way and the $$C^0$$ C 0 continuity of the shape function along element edge is kept at the same time. No transition element is needed to connect elements of different orders. The property of arbitrary local refinement makes LME-FEM be a numerical method that can adaptively solve the numerical solutions of various problems where troublesome local mesh refinement is in general necessary to obtain reasonable solutions. Several numerical examples with dramatically varying solutions are presented to test the capability of the current method. The numerical results show that LME-FEM can obtain much better and stable solutions than conventional FEM with linear element.

Abstract:Seepage is an important issue in geotechnical engineering projects such as dams, levees, canals, reservoirs, etcetera, and has made researchers and specialists to pay special attention to this problem. Lots of destructions in buildings, towers, dams, tunnels, slopes, and etcetera have been reported in history which, have been caused by liquefaction, ground water movement or other related seepage problems. In this article, seepage in soil-water systems and their related problems are studied using Element Free Galerkin Method (EFGM). For time dependent problems, implied finite difference method is used. A program is also written for both stable and time dependent cases. With estimation of a function and comparing the results with the exact function, the quantity of the errors is calculated and the accuracy of the method is evaluated. Based on this method, various geotechnical engineering problems are solved and analyzed. The results showed that not only is the EFGM more exact and accurate in comparison with other conventional methods but the time and costs for network production is omitted. With variations in boundaries, the application of EFGM is easier than that of Finite Element Method (FEM). Also, the ability of solving seepage problems without any limitation is a preference of EFGM in comparison with other approximate methods.

The integration of numerical modeling and physical measurements through inverse analysis in geotechnical engineering

The study introduces the formulation of the radial basis function-based finite element method (RBF-FEM) for bending, free vibration, and buckling analysis of Mindlin-Reissner laminated composite plates by first-order shear deformation theory. The method utilizes the radial basis functions to construct the shape functions from the finite nodes. Compared with the conventional finite element method (FEM), the present RBF-FEM obtains the shape functions with simplicity, especially when the number of element nodes is increasing. The proposed RBF-FEM eight-node element (RBF-FEM-8) is utilized. By applying the Gauss point reduction technique, the method could solve the thick and thin laminated composite plates with high accuracy, quick convergence, reducing mesh size in discretization, and could remove the shear locking phenomenon. Several numerical example studies of the thick and thin Mindlin-Reissner plates with the difference in geometries (including line and curve boundary edges), oriented layers, edge boundary conditions, Young’s modulus ratio, length-to-thickness ratio, are carried out. The results are then compared with other numerical methods and analytical solutions.

Prediction of freezing and thawing times for multi-dimensional shapes by numerical methods

The transient thermal behavior of a two-dimensionalcirculating porous bed is analyt- ically investigated. A one-energy equationmodel, representing both the gas and solid phases via a unified temperature, is employed to describe the thermal behaviorof the circulatingbed. The latter isessentiallya tubeand shellheatexchanger com- monly used in technologically important applica- tions. The model equation is transformed into a simpler set of partial differential equations using an analytical procedure. The analytical solution, based on the method of separation of variables and the principle of superposition, is formulated for the calculation of the temperature distribution in the radial and axial directions of the bed. The temperature distribution can be determined under different process parameters and conditions. Con- vergence criteria of the solution are derived for typicalprocess conditions. Thedeveloped closed- form solutionofthetransientone-equationenergy model provides a simple and convenient means for estimating the thermal behavior of the circu- lating bed.

This study derives the differential equations of free vertical bending and torsional vibrations for two- and three-pylon suspension bridges using d'Alembert's principle. The respective algorithms for natural vibration frequency and vibration mode are established through the separation of variables. In the case of the three-pylon suspension bridge, the effect of the along-bridge bending vibration of the middle pylon on the vertical bending vibration of the entire bridge is considered. The impact of torsional vibration of the middle pylon about the vertical axis on the torsional vibration of the entire bridge is also analyzed in detail. The feasibility of the proposed method is verified by two engineering examples. A comparative analysis of the results obtained via the proposed and more intricate finite element methods confirmed the former feasibility. Finally, the middle pylon stiffness effect on the vibration frequency of the three-pylon suspension bridge is discussed. It is found that the vibration frequencies of the first- and third-order vertical bending and torsional modes both increase with the middle pylon stiffness. However, the increase amplitudes of third-order bending and torsional modes are relatively small with the middle pylon stiffness increase. Moreover, the second-order bending and torsional frequencies do not change with the middle pylon stiffness.

Proof of unconditional stability for a single-field discontinuous Galerkin finite element formulation for linear elasto-dynamics

A hybridization of the finite element method (FEM) [Jin, 1993] and the spectral domain method of moments (MoM) [Zavosh and Aberle, 1994; Aberle and Zavosh 1994] is utilized in the analysis of cavity-backed patch antennas mounted on an infinite ground plane. The spectral domain MoM models the fields in the external region of the cavity through the use of the half-space Green's function whereas the FEM models the fields inside the cavity using linear edge-based tetrahedral elements. The two regions are coupled through the continuity of the fields in the aperture. The MoM formulation can be completely decoupled from the FEM formulation with the use of the physical equivalence principle after a surface magnetic current is introduced just above and below the aperture plane. The use of edge-based tetrahedral elements inside the cavity volume results in a triangular discretization of both the aperture and patch surfaces. The spectral domain implementation of the Rao, Wilton and Glisson [1982] basis functions with triangular support is one of the most appropriate choices in our case, if indeed arbitrary shaped apertures and/or patches are to be considered in the analysis.