Two-dimensional Plane Strain Analysis Research Articles

Numerical assessment of equivalent hydraulic conductivity and electro-osmotic conductivity for electro-osmotic consolidation under two-dimensional plane-strain analysis

Numerical assessment of equivalent hydraulic conductivity and electro-osmotic conductivity for electro-osmotic consolidation under two-dimensional plane-strain analysis

Stability of slope corners: a displacement-based FEM study

The stability of slopes is typically evaluated by two-dimensional plane strain analysis. However, many slopes exhibit three-dimensional (3D) geometries, including slope corners. Several researchers have studied the stability of slope corners but found that the factor of safety (FS) was close to the FS for the plane strain case. The results of a new series of 3D finite element method (FEM) simulating slope corners, including slope angle, plan view angle, radius of curvature, and slope height are presented. They confirm that the FS does not vary much for corners compared to the plane strain case. However, 220 cases using an elastic-perfectly plastic soil model together with the FEM shear strength reduction method show that the displacement field is very different at the corners compared to plane strain with differences reaching over 100%. The displacement ratio between corners and plane strain is presented as a function of the plan view angle of the corner. Often failure is defined at a chosen large displacement, as in the ultimate load of foundation elements. If this concept is carried over to slope stability, it would indicate that the FS of corners should be very different from the plane strain case. A possible explanation is discussed.

Load-Settlement Characteristics of Stone Column Reinforced Soft Marine Clay Deposit: Combined Field and Numerical Studies

Foundations supporting infrastructure built on soft and compressible marine soil are unlikely to sustain due to possibility of undrained shear failure or excessive settlement of the supporting soil. This necessitates the importance of implementing an adequate ground improvement strategy. Among different techniques, soft soil reinforcing by the installation of stone columns is one of the most successful methods in terms of long-term stability of foundations. To investigate the load-settlement characteristics of such reinforced soil, a group of closely spaced stone columns was constructed at a location along the eastern coast of Australia. The site geology revealed thick layers of soft, compressible marine clay deposit. These stone columns were loaded by constructing earthen embankment and the resulting load-settlement characteristics were measured by an array of sensors. A two-dimensional plane strain analysis was performed using finite element modeling simulations. Comparison of numerical results with the field data demonstrated accuracy of the numerical model. Additional studies were carried out to investigate the efficiency of the model. This paper integrates the new findings from the full-scale field study and advanced numerical simulations while drawing pertinent conclusions.

Seismic response analysis of a hydraulic fill dam

The seismic response of a highly heterogeneous hydraulic fill dam was evaluated by studying the natural frequencies of the first and second modes of vibration and analyzing the crest accelerations of different two-dimensional or 2D sections of the dam when subjected to two different earthquake excitations. The existing methods for determination of the natural frequency of earthen embankment structures can only be used to analyze the structural response at small strain levels. However, during seismic events, the natural frequency of an earthen dam is significantly affected by the nonlinear material behavior exhibited by the geomaterials at high strain levels. Hence, a novel method was devised to evaluate the strain-dependent natural frequency for plane strain 2D dam sections, using a synthesized multi-sine base excitation. The degradation of first and second natural frequencies of transverse vibration for all the 2D sections followed a linear trend when plotted against the respective crest’s root mean square strain on a logarithmic scale. The slope of the degradation curve was found to depend on the constituent material properties prevalent in the individual sections. The observed variations in natural frequencies and crest accelerations of the 2D dam sections were also used to assess the suitability of using two-dimensional plane strain analyses for studying the response of a long earthen dam having variability in material properties. Results indicate that there is a considerable chance of erroneous estimation of the seismic response of such highly heterogeneous earthen dams that are conventionally analyzed using plane strain models. A 2D analysis was found to merely capture the seismic response of the individual sections of the dam as independent entities while ignoring the stiffening or weakening effect of the adjacent neighboring segments that may have different material properties.

Assessing the impact of vertical heat exchangers on the response of a retaining wall

Shallow geothermal energy systems, e.g. borehole heat exchangers or thermo-active structures, provide sustainable space heating and cooling by exchanging heat with the ground. When installed within densely built urban environments, the thermo-hydro-mechanical (THM) interactions occurring due to changes in ground temperature, such as soil deformation and development of excess pore water pressures, may affect the mechanical behaviour of adjacent underground structures. This paper investigates the effects of vertical heat exchangers installed near a deep basement by performing fully coupled THM finite element analyses using the Imperial College Finite Element Program. Different heat exchanger configurations are considered and their influence on the response of the basement wall is assessed in two-dimensional plane strain analyses, where different methods of modelling the heat sources in this type of analysis are employed to evaluate their effect on the temperature field and the non-isothermal soil response.

Sound insulation properties in low-density, mechanically strong and ductile nanoporous polyurea aerogels

Aerogels are quasi-stable, nanoporous, low-density, three-dimensional assemblies of nanoparticles. In this paper, an extremely high sound transmission loss for a family of ductile polyurea aerogels (e.g., over 30dB within 1 to 4kHz at bulk density 0.25g/cm3 and 5mm thickness) is reported. The fundamental mechanisms behind the aerogel acoustic attenuations are investigated. Sharing striking similarities with acoustic metamaterials, initially, aerogels are studied via a one-dimensional multi degree-of-freedom mass-spring system. Different effects such as spring constant disparity are investigated in regards to the structural vibration wave transmission loss. Results are given for different configurations consistent with the aerogel nano/microstructures. A significant wave attenuation is observed by considering a random spring distribution. In the next step towards modeling such a complex hierarchical and random structural material, the continuum Biot's dynamic theory of poroelasticity is implemented to analyze the experimental sound transmission loss results. In this framework, a two-dimensional plane strain analysis is considered for the interaction of a steady state time-harmonic plane acoustic wave with an infinite aerogel layer immersed in and saturated with air. The effects of bulk density and thickness on the aerogel sound transmission loss are elucidated. By comparing the theoretical results with the experimental observations, this study develops a qualitative/quantitative basis for the dynamics of the aerogel nanoparticle network as well as the air flow and solid vibroacoustic interactions. This basis provides a better understanding on the overall acoustic properties of the aerogels that might also be helpful in the design of the future hierarchical materials.

A simplified plane strain analysis of lateral wall deflection for excavations with cross walls

Previous studies have shown that installation of cross walls in deep excavations can reduce lateral wall deflection to a very small amount. To predict the lateral wall deflection for excavations with cross walls, it is necessary to perform a three-dimensional numerical analysis because the deflection behavior of the diaphragm wall with cross walls is by nature three dimensional. However for the analysis and design of excavations, two-dimensional plane strain analysis is mostly used in practice . For this reason, based on the deflection behavior of continuous beams and the superimposition principle, an equivalent beam model suitable for two-dimensional plane strain analysis was derived to predict lateral wall deflection for excavations with cross walls. Three excavation cases were employed to verify the proposed model. Case studies confirm the proposed equivalent beam model for excavations with cross walls installed from near the ground surface down to at least more than half the embedded depth of the diaphragm wall. For the case with a limited cross-wall depth, the proposed model yields a conservative predicted lateral wall deflection.

Effect Of Poisson’s Ratio Of Core Clay On Dynamic Settlement Of The Earth Dams

Construction earth dam is developed to access supply resources. This paper tried to evaluate numerical analysis of the dynamic settlement during the earthquake in different conditions of the Poisson's ratio from core clay. Models were carried out with NAGAN record. ANSYS software is used regard to Finite-element method. Literature indicated that the maximum displacement during the earthquake is conducted at the crest. Interaction between dam and foundation is cased it. Lateral strain is administered the zero so models were considered in plan strain method. This paper considered end of construction with fill up reservoir when the core clay is saturated. Effect of Poisson's ratio on maximum settlement is evaluated. It was regarded the range between 0.2-0.45 for saturate and un saturate respectively. Results indicated that increase of the Poisson's ratio for saturate condition was caused to reduction of the maximum settlement at the crest and middle of core. It is mentioned the end of construction was at the critical state. Due to design of the earth dam regard an increase of construction, control dynamic settlement is required because there are good samples was damaged during the earthquake. Therefore, it is concerned to evaluate and best researches about influence of the dynamic load settlement in the earth dam during an earthquake. Literature review indicated that since the beginning of 1920s and up to 1960s 'Pseudo-static method' of analysis was well-known. However, this method was very simple, and it could not account on the nature of the slope-forming material or the foundation material. Based on deformation characteristics, NEWMARK (8) was proposed 'Sliding block method'. Among other methods, 'Shear beam model' analysis was quite popular. This method was introduced by MONONOBE (7). GAZETAS (3) proposed an improved 'Inhomogeneous shear beam model' which can take care of the fact that the shear modulus in earth or rock-fill dams is not constant but increases with 2/3 power of depth from the crest. CLOUGH and CHOPRA (2) were introduced the finite-element method for two-dimensional plane-strain analysis to estimate the dynamic response of an embankment assuming that it consists of linearly elastic, homogeneous, isotropic materials. Later, several other researchers developed the finite element and finite difference method for non-linear, inelastic, non homogeneous, anisotropic behavior of materials under seismic conditions. ZEGHAL and ABDEL- GHAFFAR (13) were proposed a local-global finite element method of analysis for determination of the non- linear seismic behavior of earth dams. Ming and Li (6) conducted a fully coupled finite-element analysis of failure of Lower San Fernando dam and examined the possible reason of the dam failure. Quick development of computer programs had a useful information of earthquake engineering research. For example, several computer programs like (4, 5, 9and12) were used worldwide for the intensive seismic analysis of the earthen dam. SEID- KARBASI and BYRNE (11) and PIAO et al(10) were represented the dynamic analysis of the earth dams using the finite difference method based computer code FLAC. ZHU et al (1) have presented a two-dimensional analysis of embankment using finite element based program PLAXIS. Shortly, the maximum displacement during the earthquake is induced at the crest. Interaction between dam, and foundation is caused it. This paper considered the effect of Poisson's ratio on maximum settlement at the end of construction regard to two conditions. The first is represented the un saturated dam and second is conducted to saturated dam when it is coupled the reservoir. Briefly, this paper was evaluated the effect of Poission's ratio in clay core on dynamic settlement of the earth dam. II.

Long term behaviour of a retaining wall resting on clayey soil

The magnitude and distribution of lateral earth pressure acting on a retaining wall due to dry cohesionless backfilling material and existence of saturated consolidated clay in the foundation are studied by a series of two-dimensional plane-strain analyses. For the particular wall geometry and soil condition, effects of wall height and elapsed time of consolidation are investigated and discussed. The analysis was carried out using the finite element computer program, CRISP, with some modifications to cope with the objective of the analysis. The behaviour of the concrete retaining wall is represented by a linear elastic model. The backfilling material was assumed to be elasto-plastic with Mohr-Coulomb failure criterion, while the clay foundation is assumed to follow Cam-clay model. The thin layer interface element is used to represent the interface between the wall and the surrounding soil. The results showed that the wall tilted towards the backfilling material during consolidation. Also, it was found that the permeability and Poisson's ratio of the foundation soil are the most important material parameters that influence the behaviour of the retaining wall.

Crack Mouth Opening Displacement-Based η Factors for SE(B) Specimens

Abstract Three-dimensional finite element analysis of SE(B) fracture toughness specimens with crack sizes ranging from a/W=0.1–0.6 were performed to develop ηCMOD values for estimating Jpl in fracture toughness tests. The analyses included specimens with smooth sides and 20 % sidegrooves. The results for ηCMOD were 4–9 % lower than previously published results based on two-dimensional plane strain analysis. A simple linear expression for ηCMOD(a/W) was proposed for introduction into ASTM E1820 for calculating Jpl in SE(B) specimens with 0.05≤a/W≤0.7.

Simulation of 3D effect of excavation face advancement using a neural network trained by numerical models

By the use of convergence-confinement method, three-dimensional problem of tunnel excavation is simulated by an equivalent two-dimensional plane strain analysis. In this method, the evaluation of the convergence occurred before the time support starts interacting with ground is the critical point. The aim of this paper is to assess this convergence for deep tunnels excavated in elastoplastic continuum and anisotropic stress conditions with the aid of a neural network approach. Numerical 3D FE models supply data sets required for the training process of the network. About 170 circular tunnels between 100 and 1000 meters deep, excavated in fair to good rock masses (according to RMR classification), are analyzed. The trained network will be capable to evaluate the convergence values for different distances to the excavation face with regard to rock specifications and stress conditions and is used for a sensitivity analysis of the parameters involved. (A) This paper was presented at Safety in the underground space - Proceedings of the ITA-AITES 2006 World Tunnel Congress and the 32nd ITA General Assembly, Seoul, Korea, 22-27 April 2006. For the covering abstract see ITRD E129148. Reprinted with permission from Elsevier.

Investigation into three-dimensional effects of finite contact width on fretting fatigue

Three-dimensional effects due to finite contact width on the contact characteristics and fretting fatigue behavior were investigated. Two contact configurations were considered: cylinder-on-flat and flat with rounded edge-on flat. Three-dimensional finite element methodology was developed based on the submodeling technique. Stress components and relative displacement converged well with ease in both contact configurations; however, the flat pad configuration provided a slightly better and faster convergence. The contact region affected by the free edge boundary was dependent on the contact geometry, i.e. it was slightly more in the cylindrical pad than the flat pad, however the affected region was less than 7% of the total contact surface in the case of cylindrical-on-flat configuration. The contact pressure and stick region decreased at the free edge, which were in agreement with their experimental counterparts, hence a localized gross slip condition can develop near the free edge even though stick–slip condition prevails over most of the contact area. Analysis using a critical plane based multi-axial fatigue parameter showed that there is a very small effect due to free edge boundary on fretting fatigue crack initiation, which was confined near the edge. Two-dimensional plane strain analysis provided the contact characteristics and fretting fatigue behavior that were in agreement with their counterparts from three-dimensional analysis over most of the contact area. Therefore, two-dimensional plane strain methodology can be used for the analysis of fretting fatigue tests involving finite width.

C-Specimen Fracture Toughness Testing: Effect of Side Grooves and η Factor

Elastic-plastic crack front fields in arc-shaped tension specimens (C-specimens) were analyzed by a three-dimensional finite element method. The effect of side grooves on the ductile fracture behavior was investigated by studying the J-integral distribution, plane-strain constraint parameter, and development of plastic zones and comparing to experimental data. The applicability of the η factor (derived for use with compact tension specimens) for the calculation of J-integral values for the C-specimen was also investigated. The results show that side grooves promote and establish near plane strain conditions at the crack front in sub-size specimens. It was also found that a two-dimensional plane-strain analysis in conjunction with the standard American Society for Testing and Materials (ASTM) tests was sufficient to determine the fracture toughness values from side-grooved C-specimen. The results indicate the η factor for compact tension specimen as specified in the ASTM standards appears to produce reliable results for the calculation of J of C-specimens.

Nodal Constraint, Shear Deformation and Continuity Effects Related to the Modeling of Debonding of Laminates, Using Plate Elements

The effects of several critical assumptions and parameters on the computation of strain energy release rates for delamination and debond configurations modeled with plate elements have been quantified. The method of calculation is based on the virtual crack closure technique (VCCT), and models of the upper and lower surface of the delamination or debond that use two-dimensional (2D) plate elements rather than three-dimensional (3D) solid elements. The major advantages of the plate element modeling technique are a smaller model size and simpler configurational modeling. Specific issues that are discussed include: constraint of translational degrees of freedom, rotational degrees of freedom or both in the neighborhood of the debond front, shear deformation assumptions; and continuity of material properties and section stiffness in the vicinity of the debond front. Where appropriate, the plate element analyses are compared with corresponding two-dimensional plane strain analyses.

Performance of Embankment Stabilized with Vertical Drains on Soft Clay

The authors have carried out several two-dimensional plane strain analyses of the Muar test embankment in which the rate of settlement was overpredicted unless clogging of the vertical drains was assumed to have occurred. The modeling of drain clogging in the finite-element analysis is an interesting development, and the discussers would welcome clarification of the modeling method and how this differs from the use of a zone of reduced permeability adjacent to the drain. However, while accepting that clogging could have been a significant factor. the discussers suggest two further causes for the authors' overprediction of the rate of consolidation. namely, incorrect modeling of the vertical drains in the plane strain analysis and the use of a constant permeability during consolidation. The discussers have developed a matching procedure by which vertical drains installed in a regular grid can be modeled in a plane strain finite-element analysis (Hird et al. 1992) that has been validated for several case histories (e.g .. Russell 1992a). The method equates Hansbo's (1981) axisymmetric analytical solution for the consolidation of the soil surrounding a single vertical drain, termed a unit cell. with a similar solution for a plane strain unit cell. The method takes into account. if necessary. both well resistance and smear and can be summarized by two equations

On the use of infinite elements in the analysis of two-dimensional layered elastic systems via discretized integral equations

A boundary integral equation approach is presented for the two-dimensional plane strain analysis of horizontally layered elastic systems resting on a rough and rigid base. The validity of Somigliana identity for unbounded layers is discussed and an Infinite Boundary Element is proposed in order to take into account the lateral unboundedness of the physical problem in the discretized equations. This element is implemented in a computer code based on a successive stiffness solution procedure. A series of numerical tests concerning single- and multi-layered problems is illustrated, and the performance of the proposed solution method is compared with that of more traditional boundary element and finite element techniques.