Two-dimensional Finite Element Program Research Articles

Numerical Study on the Effects of Helix Diameter and Spacing on the Helical Pile Axial Bearing Capacity in Cohesionless Soils

The methods employed to calculate the axial bearing capacity of a helical pile depends on the shear failure model around the pile, which is also influenced by the spacing and diameter of the helical plates. However, studies on the transition of the failure mode and the load transfer mechanism with the change of helical plate spacing and diameter in cohesionless soil subjected to axial compressive load have been limited. Thus, this paper investigated the effects of helix diameter and spacing on the axial compressive load-bearing capacity, shear failure model, and load transfer mechanism of helical piles with two helical plates embedded in the homogeneous medium and dense sands, as well as in the stratified medium to very dense sand. Axial loading tests on helical piles with various helix diameters and spacings were simulated using a two-dimensional finite element program with axisymmetric modeling to obtain the load-settlement curve, which was later used to estimate the ultimate bearing capacity of the helical piles. The ultimate bearing capacity of the helical piles was also computed using the conventional methods, i.e., the individual bearing and cylindrical shear methods, and then compared to the numerical-based axial bearing capacity. The stress-strain behaviors of pile and soil were modeled using the Linear Elastic and Mohr-Coulomb material models, respectively. The results show that the numerical-based ultimate bearing capacity of a helical pile increased with increasing the diameter and spacing of the helix. However, the ultimate bearing capacity computed using conventional methods did not show this trend. Then, the transition from the cylindrical shear to the individual bearing failure mechanism occurred at a spacing ratio (i.e., helical plate spacing divided by its diameter) of about two. Ultimately, the load transfer curves indicate that the helical plates mainly supported the applied load.

Modelling of Hybrid Steel-SMA Shear Walls with Local Strain and Reinforcement Considerations

The incorporation of Super-elastic (SE) Shape Memory Alloys (SMAs), such as Nitinol (Nickel-Titanium), presents a method of passively improving the damage resiliency of traditional reinforced concrete structural elements. This resiliency can be of particular use in seismic applications owing to the super-elastic behavior allowing for increased recentering. Currently available experimental data on hybrid slender shear walls incorporating both steel and SE-SMAs has demonstrated the recentering improvements while also highlighting that use of SE-SMAs tend to cause the formation of a predominant crack that controls the response. The ability to more accurately predict this behaviour through numerical modelling would allow for better understanding of the salient parameters affecting the response of hybrid slender shear walls. The paper herein presents a numerical modelling methodology that considered the impacts of local strain concentration as a result of a singular predominant crack formation during reverse-cyclic loading. This modelling was performed in VecTor2, a non-linear two-dimensional finite element program, in conjecture with experimental data of a hybrid steel-SMA slender shear wall and a steel-only reinforced concrete companion wall. The use of a tension stiffening constitutive model which considered local fracture was found to improve the displacement prediction capabilities of models. Additional considerations which were investigated included local reinforcement properties to reflect conditions at the wall base and accounting for the impact of strain gauge instrumentation on the location of rupture of the reinforcement. The results provide insight into the numerical modeling that captures the local strain and reinforcement conditions present in hybrid steel-SMA and reinforced concrete slender shear walls.

Simulation of hard rock pillar failure using 2D continuum-based Voronoi tessellated models: The case of Quirke Mine, Canada

The Quirke Mine, ON, Canada, is a typical example of a mine that experienced a chain reaction of pillar failure. In this mine, the rib pillars were initially laid out with their long axis parallel to the dip direction of the orebody. In the central part of the mine, the pillars were re-aligned at 45° to the orebody true dip. This realignment resulted in adverse shear loading conditions that led to their failure. In this study, a two-dimensional finite element program was used to simulate the failure of Quirke Mine pillars under compressive and shear loading conditions. The pillars were simulated as a heterogeneous material, consisting of randomly generated Voronoi blocks. The calibration of this model, referred to as a Voronoi Tessellated Model (VTM), was conducted against the rock mass strength estimated based on a tri-linear, brittle failure criterion. The calibrated VTM was then employed to investigate the pillar behavior during drift development and stope excavation. It was found that the pillar under shear loading experiences higher confinement loss and tensile stress at its core and, therefore, fails at a lower stress level than that under compression. The simulated pillar failure process was found to agree with documented field observations.

Effects of Unidirectional In Situ Stress on Crack Propagation of a Jointed Rock Mass Subjected to Stress Wave

This paper proposes a large-scale experiment combined with multiple cement mortar blocks to simulate stress wave propagation across a jointed rock mass under unidirectional in situ stress. Two identical mortar block models with smooth, dry, and unfilled joints were poured. The stress waves in Model 1 and Model 2 were generated by an electric spark source and a blast-induced source, respectively. The effects of these two excitation sources on stress wave propagation were compared through crack propagation experiments. The experimental results show that the peak value of the transmitted strain wave decreases as the in situ stress increases. The unidirectional in situ stress has a certain inhibitory effect on the stress wave propagation. It also indicates that for Model 1 with the electric spark source, no cracks on the upper surface, but a Livingstone blasting crater at the bottom is generated. For Model 2 with the blast-induced source, cracks on the upper surface and a blasting crater at the bottom are produced. The results verify the similarity between the electric spark source and the explosive source. The two-dimensional finite element program (ANSYS/LS-DYNA) was applied to further simulate the crack propagation of a jointed rock mass under different in situ stresses. The results of numerical simulation verify that the in situ stress has a clear guiding effect on the crack propagation.

Strength and failure mechanism of highly interlocked jointed pillars: Insights from upscaled continuum grain-based models of a jointed rock mass analogue

An optimum design of mine pillars necessitates a reliable estimation of the rock mass strength. It is known that the Hoek-Brown failure criterion, with its strength parameters obtained using the Geological Strength Index, tends to underestimate the confined strength of interlocked jointed hard rock masses. Therefore, geomechanical designs based on this approach could lead to oversized pillars due to the underestimation of the pillar core strength. In this study, a two-dimensional finite element program was used to investigate the strength and failure mechanisms of jointed pillars. For this purpose, a previously calibrated grain-based model of heat-treated marble, an analogue for a highly interlocked jointed rock mass, was upscaled to simulate jointed pillars of various width-to-height ratios. The simulation results showed that the slope of the pillar stability curve obtained from this approach is steeper than those of existing continuum and discontinuum models of jointed pillars. This is attributed to the high degree of block interlock leading to higher rock mass strength at the pillar core. It is demonstrated that this modeling approach provides more realistic results in terms of pillar failure process compared to other continuum models, in which the rock mass is simulated as a homogeneous material.

Numerical evaluation of backfill compaction behind the face of reinforced soil walls

The effects of the compaction conditions and backfill material behind the face of reinforced soil walls (RSWs) were numerically investigated. The analyses were carried out using a two-dimensional finite-element computer program considering different backfill materials in the zone 1 m behind the wall face and different compaction conditions. The results of the analyses were compared with data from a 16.7 m high well-instrumented, steel-reinforced soil wall constructed in 1999 in the USA. The results illustrate the importance of the compaction conditions and the backfill material near the wall facing on the performance of RSWs both at the end of construction and post-construction.

Design of Initial Shotcrete Lining for a Mine Shaft Using Two-Dimensional Finite Element Models Considering Excavation Advance Rate

Shotcrete is widely used as a temporary support element in the construction of underground mine excavations, tunnels, and shafts. It is sprayed on the excavation walls to provide safe working conditions for mine personnel and equipment until the permanent support is installed. Therefore, the ability of the shotcrete liner to resists falls of ground is of paramount importance. In this paper, a two-dimensional finite element program is used to simulate a three-dimensional excavation advance and a shotcrete liner that is used as temporary support in a mine shaft. The mechanical properties of the shotcrete are determined based on existing empirical equations by considering the shaft advance rate. The study uses three methods to analyze the stability of the initial shotcrete liner. The first method pertains to the calculation of the load factor of safety based on the convergence confinement method. In the second method, the shotcrete liner is simulated using a structural element with elastic properties, and its stability is analyzed using support capacity diagrams. In the third method, a material model is used to explicitly simulate the shotcrete liner with elastic perfectly-plastic material behavior. This method allows for capturing the progressive yielding of the shotcrete liner during the excavation advance. The results of numerical simulations are then used to calculate a strain factor of safety for the shotcrete liner by dividing the lateral strain capacity of the shotcrete by the radial strain of the liner due to the shaft convergence. The study infers that the strain factor of safety for the 100 mm shotcrete liner is greater than unity although its load factor of safety is less than unity. Therefore, it is concluded that the 100 mm shotcrete liner can be used as temporary support until the installation of the final concrete liner.

Effect of construction and design factors on the behaviour of nailed-soil structures

This study numerically evaluates the influence of excavation execution procedures in combination with the nail stiffness, facing stiffness and inclination, surcharge width and position and excavation near to the bottom on the behaviour of nailed-soil structures under working stress conditions. The numerical analyses are carried out using the two-dimensional finite-element program Plaxis 2D 2015. Data from a full-scale physical model of soil nailing constructed by the French national research project, Clouterre, is first used for the validation of the analyses. In the parametric study, two different excavation execution procedures are investigated. The first procedure represents the execution of small-width incremental excavation, starting from one side of the wall and progressing along the same level to the other side. In the second procedure, which can occur in the field, each level is fully excavated, and then nail installation and shotcreting are performed. The results show the effect of each execution procedure, in combination with the other factors mentioned, on the behaviour of the soil-nailing structure and indicate the first procedure to be the optimum construction process.

Monte Carlo Simulations of Coupled Transient Seepage Flow and Soil Deformation in Levees

The purpose of this research is to compare the results from two different computer programs of flow analysesof two levees at Port Arthur, Texas where rising water of a flood from Hurricane Ike occurred on the levees. The first program (Program 1) is a two-dimensional (2-D) transient finite element program that couples the conservation of mass flow equation with accompanying hydraulic boundary conditions with the conservation of force equations with accompanying x and y displacement and force boundary conditions, thus yielding total head, x displacement, and y displacement as unknowns at each finite element node. The second program (Program 2) is a 2-D transient finite element program that considers only the conservation of mass flowequation with its accompanying hydraulic boundary conditions, yielding only total head as the unknown at each finite element node. Compressive stresses can be computed at the centroid of each finite element when using the coupled program. Programs 1 and 2 were parallelized for high performance computing to consider thousands of realisations of the material properties. Since a single realisation requires as much as one hour of computer time for certain levees, the large realisation computation is made possible by utilising HPC. This Monte Carlo type analysis was used to compute the probability of unsatisfactory performance for under seepage, through seepage, and uplift for the two levees. Respective hydrographs from the flood resulting from Hurricane Ike were applied to each levee. When comparing the computations from the two programs, the most significant result was the two programs yielded significantly different values in the computed results in the two clay levees considered in this research.

P-y-ẏ curves for dynamic analysis of offshore wind turbine monopile foundations

The well-known p-y curve method provides soil-structure interaction that is independent of the load rate. In this paper an improved p-y curve method is proposed by considering the influence of the excitation frequency. For this purpose, a two-dimensional finite-element program is developed for analysis of a segment of an offshore monopile foundation placed in different depths. The intended use of the model is analyzes of offshore wind turbines in operation where small-magnitude cyclic response is observed in addition to the quasi-static response from the mean wind force. The response to small-magnitude cyclic loading is analyzed by employing coupled equations based on the u-P formulation, i.e. accounting for soil deformation as well as pore pressure. Thus, the paper has focus on the effects of drained versus undrained behavior of the soil and the impact of this behavior on the stiffness and damping related to soil-structure interaction at different load frequencies. In order to enable a parameter study with variation of the soil properties, the constitutive model is purposely kept simple. Hence, a linear poroelastic material model with few material parameters is utilized. Based on the two-dimensional model, linear p-y-ẏ curves are extracted for the lateral loading of monopiles subjected to cyclic loads. The developed code is verified with findings in the literature.

Simulation of Behavior of In-Service Metal Culverts

As part of an experimental program, a large number of in-service culverts were tested to investigate the influence of several parameters on field performance of culverts. These parameters included cover depth, load application, size, shape, and other properties of corrugated metal culverts. Response of 14 test culverts was simulated using a two-dimensional finite element program and a three-dimensional finite difference program. Deflections predicted from the two-dimensional analyses were larger than the deflections measured in the field. However, the experimental and calculated thrust forces were similar. Deflections and thrust forces predicted from the three-dimensional analysis were similar to the experimental results. The critical factors affecting the response of the culverts include cover depth, culvert size, metal thickness, and elastic modulus and other properties of backfill soil. The influence of these parameters on the culvert behavior is investigated through numerical simulations using the established modeling properties.

Finite element analysis of a concrete slab under various non-uniform support conditions

A two-dimensional finite element program was utilised to study the effects of a non-uniform subgrade support on the tensile stresses in a concrete slab. A total of 12 subgrade support conditions were created including uniform and non-uniform support. The modulus of subgrade reaction (k-value) for different support areas was arbitrarily assigned either a soft (50 psi/in., 13.5 MPa/m) or stiff (500 psi/in., 135 MPa/m) value. Three axle types (single, tandem and steer-drive), three linear temperature differentials (none, negative and positive), two loading paths (edge and wheel path) and multiple longitudinal wheel positions were considered in the analysis. The theoretical analyses showed that several non-uniform subgrade support cases had a profound impact on the peak tensile stresses in a slab. In particular, a stiff subgrade with soft edges and a subgrade with randomly assigned soft and stiff locations significantly increased the peak tensile stresses relative to a uniformly soft support condition by at least 30%.

The use of finite-element based programs in the study of atmospheric phenomena

The academic problem described in this paper concerns the measures to protect an idealized building against atmospheric discharges. The proposed lightning protection system contains a Franklin rod and two down conductors connected to the ground. The problem is analyzed computationally employing a two-dimensional finite element program. Two numerical models are used to investigate the distributions of electric potential and electric field around the building. Numerical results show that, by using the proposed lightning protection system, the mean value of the electric field close to the building increases more than four times. The paper also presents a theoretical description on fair-weather and storm conditions.

Plastic Deformation Theory Application in Finite Element Analysis

In the present study, the constitutive law of the deformation theory of plasticity has been derived. And that develop the two-dimensional and three-dimensional finite element program. The results of finite element and analytic of plasticity are compared to verify the derived the constitutive law of the deformation theory and the FEM program. At plastic stage, the constitutive laws of the deformation theory can be expressed as the linear elastic constitutive laws. But, it must be modified by iteration of the secant modulus and the effective Poisson’s ratio. Make it easier to develop finite element program. Finite element solution and analytic solution of plasticity theory comparison show the answers are the same. It shows the derivation of the constitutive law of the deformation theory of plasticity and finite element analysis program is the accuracy.

Load-Transfer Efficiencies of Rigid Airfield Pavement Joints Based on Stresses and Deflections

Load-transfer efficiency (LTE) of jointed concrete pavement is typically measured by the ratio of unloaded and loaded slab deflection. However, the maximum tensile stress in a slab is one of the critical mechanical responses that influences the performance of the jointed concrete pavement. Therefore, stress-based load-transfer efficiency, defined as stress reduction in the loaded slab because of the presence of an adjacent unloaded slab, is often considered an appropriate way to quantify LTE. Strain gauge data from full-scale tests collected by the Federal Aviation Administration were analyzed to compute the stress-based LTE of joints under moving loads. The effect of static aircraft gear loads and slab size on the LTE of joints was analyzed by using a two-dimensional finite-element program. FEM-calculated stress-based LTE under static aircraft loading on average was 38% lower than that measured under moving loads. LTE values were similar under various gear positions, gear configurations, and different slab sizes.

Investigation on Behavior of Rock-Socketed Retaining Piles for Deep Excavation

In the soil-rock mixed areas where the soils overlie on the rock layer, the rock-socketed retaining piles have been widely used for deep excavations. Up to date, little attention has been paid to performance of the rock-socketed piles used for deep excavation. Therefore, using the two-dimensional finite element program, Plaxis2D, a typical deep excavation engineering supported by rock-socketed piles with the whole embedded portion in rock is analyzed to investigate behavior of the rock-socketed retaining piles in detail. Computation results have shown that for rock-socketed retaining piles used in deep excavations, there exists an ultimate or a maximum rock-socketed depth which can be estimated by the pile diameter. For the ultimate rock-socketed depth, in the final excavation step, the first zero bending moment point of the rock-socketed part of the pile generally locates near the top surface of the rock layer. When the excavated surface is located at the top surface of the rock layer, the corresponding shear force distribution of the rock-socketed pile has an extremum at the same position.

Direct damage-controlled design of plane steel moment-resisting frames using static inelastic analysis

A new direct damage-controlled design method for plane steel frames under static loading is presented. Seismic loading can be handled statically in the framework of a push-over analysis. This method, in contrast to existing steel design methods, is capable of directly controlling damage, both local and global, by incorporating continuum damage mechanics for ductile materials in the analysis. The design process is accomplished with the aid of a two-dimensional finite element program, which takes into account material and geometric nonlinearities by using a nonlinear stress-strain relation through the beam-column fiber modeling and including P-δ and P-Δ effects, respectively. Simple expressions relating damage to the plastic hinge rotation of member sections and the interstorey drift ratio for three performance limit states are derived by conducting extensive parametric studies involving plane steel moment-resisting frames under static loading. Thus, a quantitative damage scale for design purposes is established. Using the proposed design method one can either determine damage for a given structure and loading, or dimension a structure for a target damage and given loading, or determine the maximum loading for a given structure and a target damage level. Several numerical examples serve to illustrate the proposed design method and demonstrate its advantages in practical applications.

Damage and Fracture Analysis of Brittle Structural Elements Reinforced with Carbon Fiber Sheets

A constitutive equation for elasto-plastic damageable solids is formulated by using Drucker-Prager's equivalent stress to analyze the damage failure behavior of concrete structural elements reinforced with carbon fiber sheets. The forumulated constitutive equation is implemented in the two-dimensional finite element program to simulate the experimental results. The constitutive equation is identified by using the uniaxial, compressive and tensile test results for concrete and carbon fiber sheets. The finite element analyses are carried out for real-scaled cantilever RC slabs with and without carbon fiber sheets. The calculated results are compared with the experimental results to illustrate the validity of the proposed method of analysis.

Heat transfer behavior in the impingement zone under circular water jet

In this study an iterative and sequential inverse heat transfer analysis procedure is developed and implemented into a two-dimensional finite element program. The developed program is used to determine the heat fluxes at the stagnation points of stationary hot plates cooled by impingement water jets in an industry scale test facility. Analysis of data shows that the heat transfer behavior at the stagnation is mainly affected by water temperature and hardly affected by water flow rate with mild effect from steel grade. The features of boiling curves and the typical values obtained are in good agreement with data in the literature.

Material Models for the Finite Element Analysis of Materials Exhibiting a Pronounced Bauschinger Effect

Realistic material models have been developed on the basis of the experimental investigation of reverse loading with actual Bauschinger effect and implemented into a two-dimensional finite element computer program. The developed program is capable of treating the elastoplastic deformation behavior of thick-walled cylinders during both loading and unloading phases. Strain hardening may occur during loading, and reverse yielding may occur during unloading at a yield strength significantly reduced due to the Bauschinger effect. Three different models for the reverse hardening are presented. Strain hardening during reverse yielding may have a different slope than for forward loading, and it may also be nonlinear. The intended application is for autofrettage analysis of thick-walled cylinders. Being a numerical solution, it will also be very useful for finite element analysis of residual stress experimental procedures and also in the determination of more accurate stress intensity factors for autofrettaged cylinders that had undergone reverse yielding due to the Bauschinger effect.