Rigid-plastic Finite Element Method Research Articles

Bearing Capacity of a Shallow Foundation above the Soil with a Cavity Based on Rigid Plastic Finite Element Method

Based on the Rigid Plastic Finite Element Method (RPFEM), this study investigates the performance of the footing on the soil with a cavity. The RPFEM is used in plane strain conditions and necessitates only a few materials to predict the bearing capacity: the unit weight of the soil, the cohesion, the shear resistance angle, and the dilation angle. Considering diverse soil types, including cohesive and intermediate soils, the findings are presented through dimensionless 2D charts in which the horizontal axis X and vertical axis Y are normalized to parameters R and H, representing the horizontal and vertical dimensions of the plastic mechanism beneath the footing in the absence of the soil cavity. Analyzing geometric factors such as footing width B and cavity characteristics (shape, size, and location), the study reveals that the farther the cavity, the less it impacts the footing performance. The distribution of the normalized bearing capacity across the (X, Y) space elucidates the expansion and variation of the influence zone. Equations incorporating the mentioned geometric parameters and soil shear strengths are proposed and verified with data in the literature. In cohesive soils, the influence zone predominantly extends vertically, following the expansion of the slip surface in no void condition. Conversely, for intermediate soils, the zone of influence exhibits a dependency on the shear resistance angle, resulting in an extension in one direction more than the other. Illustrating typical failure mechanisms, the study delves into detailed discussions to enhance comprehension of how the cavities affect the bearing capacity of the footing.

Effect of footing roughness on ultimate bearing capacity of rigid strip footing on sandy soil slope

This study investigates the ultimate bearing capacity of a rigid strip footing on a sandy slope using the Rigid Plastic Finite Element Method (RPFEM). To accurately represent a wide range of frictional conditions at the footing roughness, a new interface element was introduced, capable of accommodating both perfectly rough and perfectly smooth conditions. A new constitutive equation is introduced to model these interface elements, which had a significant influence on the failure mode of the strip footing. Moreover, the study focuses on assessing critical parameters, including the internal friction angle of the sandy ground, as well as slope geometry parameters (slope angle b, edge distance L, and slope height H). The RPFEM results illustrate that increasing the edge distance positively influences the bearing capacity, while a higher slope angle exerts a negative effect. Notably, variations in slope height produce consistent outcomes, regardless of the frictional conditions.

Effect of foundation surface roughness on ultimate bearing capacity of an eccentrically loaded foundation

The study extensively investigated the ultimate bearing capacity (UBC) of an eccentrically loaded foundation under two scenarios (horizontal sandy soil and sandy soil slope), utilizing the Rigid Plastic Finite Element Method (RPFEM). To precisely simulate a diverse range of frictional conditions on the foundation surface roughness, a novel joint element is introduced, capable of accommodating both perfectly rough and perfectly smooth foundations. A novel constitutive equation is presented to model these joint elements, significantly influencing the failure mechanism of the shallow foundation. The study also examines the impact of the friction strength ϕ on the normalized vertical load V/Vult. The RPFEM results reveal that the friction strength ϕ substantially influences the V/Vult ratio for sandy soil slopes, while its effect is found to be negligible for horizontal sandy soil.

Ultimate bearing capacity of rigid strip footings on c-ϕ soil subjected to combined eccentric and inclined loading

The present study calculated the maximum bearing capacity of a strip footing against eccentrically inclined coupled loading on c-ϕ soil, by means of the plane strain rigid plastic finite element method (RPFEM). The influence of soil strengths and footing width on the V-H and H-M failure envelopes (presenting the vertical load V, horizontal load H, and moment M) was thoroughly surveyed to assess the uniqueness of the V-H-M failure envelope. Based on the obtained results, the V-H-M failure envelope was found to be distinct for each value of normalized cohesion c/γB and internal friction angle ϕ. A novel equation, which is a function of c/γB and ϕ, was achieved to predict the failure envelope of the V-H-M limit load space.

Limit load space of rigid strip footing on sand slope subjected to combined eccentric and inclined loading

The stability of a footing-on-slope system under coupled eccentric and inclined loading is a significant concern in urban areas, especially in geotechnical engineering. To evaluate the ultimate bearing capacity of an eccentrically inclined loaded footing placed on a sand slope, the rigid plastic finite element method (RPFEM) was employed, and several analyses were conducted. Due to the asymmetry of the footing-slope system, an interface element was introduced to accurately calculate the contact stress between the footing and the soil for two eccentric directions, namely, positive and negative eccentricities. The study focused on assessing the influence of the soil strengths, such as the internal friction angle and soil unit weight, the footing width, and the slope geometry, including slope angle, slope height, and edge distance, on the three-dimensional V-H-M limit load space (vertical load – horizontal load – moment) to determine the uniqueness of this limit load space. In particular, the influence of the combination of two eccentric directions and two horizontal load directions, namely, positive horizontal load and negative horizontal load, on the V-H-M limit load space was investigated. The obtained results of the RPFEM indicated that the positive eccentricity and positive horizontal load had a positive effect on improving the bearing capacity of the strip footing on the slope crest. However, the results also showed a negligible effect on the bearing capacity as the edge distance increased up to a certain threshold value. The applicability of the V-H-M limit load space was thoroughly examined for several loading paths, and it was discovered to be unique for each soil strength and slope geometry parameter.

Modified ultimate bearing capacity formula of strip footing on sandy soils considering strength non-linearity depending on stress level

Most of the contemporary ultimate bearing capacity (UBC) formulas assume a linear yield function in shear stress-normal stress space. However, experimental investigations have corroborated the non-linearity in the failure envelopes of sandy soils. This study focused on the assessment of the stress level effect on the UBC of surface strip footings ascribed to the soil unit weight (γ), footing size (B), and uniform surcharge load (q). The rigid plastic finite element method (RPFEM) was employed for the analysis. The analysis method was validated against the centrifuge test results from the published references in the case of various sandy soils with different relative densities. The RPFEM, using the mean confining stress dependence property of Toyoura sand, is utilized in non-linear finite element analysis of model sandy soil. The normalized ground failure domains in the case of the non-linear shear strength model are gleaned smaller than those in the case of the linear shear strength one. The numerical results are compared with the guidelines of the Architectural Institute of Japan (AIJ) and the Japan Road Association (JRA). The modification coefficients are ascertained for the frictional bearing capacity factor (Nγ) and surcharge bearing capacity factor (Nq), and a modified UBC formula is proposed. The performance of the proposed UBC formula is examined against the analysis results and various prevailing UBC guidelines.

Limit load space of rigid strip footing on cohesive-frictional soil subjected to eccentrically inclined loads

In geotechnical engineering, the stability of strip footings under eccentrically inclined coupled loads is a major concern. The objective of this paper was to estimate the ultimate bearing capacity of a rigid strip footing, subjected to eccentrically inclined loads resting on cohesive-frictional soil, using the rigid plastic finite element method (RPFEM). In the numerical analysis, an interface element was introduced to properly evaluate the interaction between the footing base and the soil. The footing base was assumed to be rigid and rough, as it most often is in reality. Focus was placed on the effect of the soil properties (cohesive strength c, internal friction angle ϕ, and unit self-weight γ) and footing width B on the loading planes of the V-H-M limit load space (vertical load-horizontal load-moment) in order to consider the uniqueness of this limit load space. In particular, the effect of the two directions of the horizontal load, namely, positive and negative horizontal loads, on the V-H-M limit load space was clarified. The numerical results of the RPFEM showed that the negative horizontal load had a positive effect on supporting a higher bearing capacity than the positive horizontal load in the presence of a small eccentricity length. However, the results also showed a negligible effect on the bearing capacity for both directions of the horizontal load in the presence of a large eccentricity length. New equations were proposed to determine the V-H-M limit load space, predicted as functions of c/γB and ϕ, by taking into account the direction of the horizontal load. The applicability of the V-H-M limit load space was widely examined for several loading paths with different prescribed loads for V, H, and M. Consequently, the limit load space of the strip footing was clearly found to be unique for each value of c/γB and ϕ.

End bearing capacity of a single incompletely end-supported pile based on the rigid plastic finite element method with non-linear strength property against confining stress

An Incompletely End Supported Pile (IESP) is a pile in a soft soil layer underlain by a hard soil layer that does not reach the bottom hard layer in practice. This study estimates the end bearing capacity of IESP by using an inhouse Rigid Plastic FEM code (RPFEM), considering shear strength non-linearity of soil against confining pressure, and soil-foundation interaction. The effect of the distance between the pile tip and the bottom hard soil layer (d/B) on the end-bearing capacity of IESP was mainly investigated for three types of soil: cohesive soils, cohesionless soils and intermediate soils. Also, theratio (r) of the end bearing capacity of the pile when it reaches the bottom hard layer to that of the pile when the bottom layer has no influence was was considered. By considering the shear strength non-linearity, the end bearing capacity was accurately estimated. The estimations were consistent with previous analytical, experimental and numerical solutions. It is found that the end bearing capacity inversely decreases with the distance d/B and becomes constant around d/B = 3. Based on the results, a formula for estimating the end bearing capacity of IESP is proposed. Comparisons with methods in existing literature confirmed the reliability of the proposed equation.

Ultimate Bearing Capacity of Rigid Footing on Two-Layered Soils of Sand–Clay

Abstract This study widely investigates the ultimate bearing capacity of a rigid footing on the free surface of sand overlying clay using the rigid-plastic finite-element method (RPFEM). Interface ...

Influence of die parameters on internal voids during multi-wedge-multi-pass cross-wedge rolling

The formation of internal voids in workpieces during cross-wedge rolling affects die design and limits their widespread applications. This article investigated the formation of internal voids during the multi-wedge-multi-pass rolling production of connecting rods. A three-dimensional numerical simulation model of cross-wedge rolling (CWR) was established using the rigid-plastic finite element method, and a density change model of the porous material was developed to characterize the degree of internal void formation in the connecting rod during CWR. The optimal die parameters (forming angle, spreading angle, and distribution coefficient of area reduction) were determined by determining their relationship to the density. The stress and strain of characteristic points near the loose longitudinal sections were used to study the void formation mechanisms. The accuracy of the numerical simulations was verified by rolling experiments, which showed no void formation in the internal sections of the connecting rod after production, confirming the feasibility of using this scheme to prevent void formation.

Limit load space of rigid footing under eccentrically inclined load

In geotechnical engineering, the stability of rigid footings under eccentrically inclined loads is an important issue. This is because the number of superstructures has increased and the situation of structures being subjected to eccentrically inclined loading is occurring more and more frequently. The objective of this paper was to evaluate the bearing capacity of a rigid footing on the free surface of uniform sandy and clayey soils under the action of eccentric and inclined loading using a finite element analysis by assuming that the soils follow the Drucker-Prager yield function. In the two-dimensional analysis of the footing-soil system, the rigid plastic finite element method (RPFEM) was applied to calculate the ultimate bearing capacity of the eccentric-inclined loaded footing. In the numerical analysis, an interface element was introduced to simulate the footing-soil system with the rigid plastic constitutive equation developed by the authors. The footing was considered to be rigid and rough, as it most often is in reality. This study thoroughly considered the effect of the soil properties on load inclination factors iγ and ic in order to investigate the validity of the current design methods. In particular, the effects of the horizontal load in two directions on the ultimate bearing capacity of the footing and the failure envelopes in the V-H-M space were clarified, namely, positive and negative horizontal loads. The results showed that the positive horizontal load had a negative effect on the bearing capacity, while the negative horizontal load had the opposite effect in the presence of eccentrically inclined loading. The failure mode of the footing-soil system was clearly seen in the difference between the two directions of horizontal load. Through a series of numerical analyses, new equations were proposed for load inclination factors iγ and ic, and for the failure envelopes in the V-H-M space, taking into account the direction of the horizontal load. The obtained limit load space was proved to be rational in comparison to those given in the literature. Furthermore, the applicability of the limit load space to different loading paths, and moreover, to the independently prescribed loads of V, H, and M, was examined. Consequently, the failure envelope for each type of soil in the V-H-M space was clearly seen to be unique.

Numerical Simulation of Material Plastic Deformation Using the Drawing Forming Process of Contoured Internal Surface Tubes

Production of multi-rifled seamless steel tubes employing cold draw process using multi-rifled mandrel is quite a modern technology. The important characteristic of the tube drawing process, unlike the tube with internal rifling, is the corner filling which influences the dimension accuracy of the internal shape of the tube. In this study, the influence of drawing tool dimensions and mandrel shape on to final rifling filling was investigated. Draw process has been simulated by using the three-dimensional rigid-plastic finite element method (FEM) by using DEFORM 3D software. The results of numerical simulation show that the shape of drawing tools and process conditions have a significant influence on the forming process and final shape and properties of the workpiece.

Ultimate bearing capacity of rigid footing under eccentric vertical load

In geotechnical engineering, the stability of rigid footings under eccentric vertical loads is an important issue. This is because the number of superstructure buildings has increased and the situation of structures being subjected to eccentric vertical loading is occurring more and more frequently. In this study, focus is placed on the ultimate bearing capacity of a footing against the eccentric load placed on two types of soil, namely, sandy soil and clayey soil, using a finite element analysis. For the sandy soil, the study newly introduces an interface element into the footing-soil system in order to properly evaluate the interaction between the footing and the soil, which greatly affects the failure mechanism of the footing-soil system. For the clayey soil, the study improves the analysis procedure by introducing a zero-tension analysis into the footing-soil system. Two friction conditions between the footing and the soils are considered; one models a perfectly rough condition and the other models a perfectly smooth condition. For a two-dimensional analysis of the footing-soil system, the rigid plastic finite element method (RPFEM) is applied to calculate the ultimate bearing capacity of the eccentrically loaded footing. The RPFEM is extended in this work to calculate not only the ultimate bearing capacity, but also the distribution of contact stress along the footing base. The study thoroughly investigates the effect of the eccentric vertical load on the ultimate bearing capacity in the normalized form of V/Vult and e/B where e is the length of the eccentricity and B is the width of the footing. Vult indicates the ultimate bearing capacity of the centric vertical load. The failure envelope in the plane of V/Vult and M/BVult is further investigated under various conditions for the sandy and clayey soils. M is the moment load induced by the eccentric vertical load. This study examines the applicability of the failure envelope obtained for the eccentric vertical load to the cases where two variables, V and M, are independently prescribed. The obtained results are coincident and indicate the wide applicability of the failure envelope in the normalized V-M plane in practice. Finally, in a comparison with previous researches, the numerical data in the present study lead to the derivation of new equations for the failure envelopes of both sandy and clayey soils.

ASSESSING THE ULTIMATE BEARING CAPACITY OF FOOTING IN A TWO-LAYERED CLAYEY SOIL SYSTEM USING THE RIGID PLASTIC FINITE ELEMENT METHOD

Ultimate bearing capacity formulae for foundations are specified in the guideline published by the Architectural Institute of Japan for the design of building foundations. The rigid plastic finite element method was developed by Tamura and Ohtsuka to estimate the ultimate bearing capacity of footing. Unlike deformation analysis, this method employs limited soil constants; it uses only the strength parameters of cohesion c and friction angle φ as it considers the limit state directly and disregards the deformation of the building and ground. A series of rigid plastic finite element analyses were conducted to compare the ultimate vertical and inclined bearing capacities of spread foundations between the simulation results and the theoretical formula for a two-layered clayey soil system. The change in the failure mode of the ground was discussed using the geometrical ratio between the width of the footing and the height of the surface layer. The strength ratio of the surface and second ground layer was clearly shown to affect the formation of failure mode. The applicability of the rigid plastic finite element method for the assessment of the ultimate bearing capacity of a two-layered clayey soil system was successfully demonstrated.

ULTIMATE VERTICAL BEARING CAPACITY OF CLAYEY SQUEEZE BREAKDOWN USING RIGID-PLASTIC FINITE ELEMENT METHOD

The relations of ultimate bearing capacity for foundations are specified in the guideline published by the Architectural Institute of Japan for design of building foundations. The rigid-plastic finite element method developed by Tamura and Ohtsuka has been employed to estimate the ultimate bearing capacity of footings. The characteristic of this method is that, in contrast to deformation analysis, it applies limited soil constants; only the strength parameters, such as cohesion and friction angle, are used since the method deals with the limit state directly by disregarding the deformation of the building and ground. In this study, a series of rigid plastic finite element analyses were performed to compare the ultimate bearing capacities of spread foundation for clayey squeeze breakdown obtained by simulations and the formulae of the Architectural Institute of Japan. The change in the failure mode of the ground was discussed considering the geometrical ratio between the width of the footing and the surface clay layer. In addition, inclined load was considered for clayey squeeze breakdown. The applicability of rigid plastic FEM to the assessment of ultimate vertical bearing capacity of clayey squeeze breakdown was demonstrated.

Application of three-node triangular element with drilling and strain degrees of freedoms to rigid plastic finite element method and verification of its validity

Application of three-node triangular element with drilling and strain degrees of freedoms to rigid plastic finite element method and verification of its validity

Group effect on ultimate lateral resistance of piles against uniform ground movement

In earthquake engineering, pile foundations are designed to withstand the lateral loading that results from large displacements due to ground movement caused by strong earthquakes. The distress and failure of superstructures occurs when the lateral load exceeds the ultimate lateral resistance of the piles. The aim of this study is to estimate the ultimate lateral resistance of piles especially in terms of the group effect induced by the pile arrangement. Several experimental and numerical analyses have been conducted on pile groups to investigate the group effect when the groups are subjected to uniform large horizontal ground movement. However, the ultimate lateral resistance of the pile groups in these studies was calculated by applying load to the piles. The present study directly assesses the ultimate lateral resistance of pile groups against ground movement by systematically varying the direction of the ground movement. Although the load bearing ratio of each pile in a pile group, defined as the ratio of the ultimate lateral resistance of each pile in a pile group to that of a single pile, is an important design criterion, it was difficult to assess in past works. This study focuses on the load bearing ratio of each pile against ground movement in various directions. The use of the finite element method (FEM) provides options for simulating the pile-soil system with complex pile arrangements by taking the complicated geometry of the problem into account. The ultimate lateral resistance is examined here for pile groups consisting of a 2 × 2 arrangement of four piles, as well as two piles, three piles, four piles, and an infinite number of piles arranged in a row through case studies in which the pile spacing is changed by applying the two-dimensional rigid plastic finite element method (RPFEM). The RPFEM was extended in this work to calculate not only the total ultimate lateral resistance of pile groups, but also the load bearing ratio of the piles in the group. The obtained results indicate that the load bearing ratio generally increases with an increase in pile spacing and converges to almost unity at a pile spacing ratio of 3.0 with respect to the pile diameter. Moreover, the group effect was further investigated by considering the failure mode of the ground around the piles.

Influence of punch geometry on surface deformation and tribological conditions in backward extrusion

The main goal of this study is to examine the influence of process conditions such as reduction and punch face angle in backward extrusion, especially for surface stresses such as surface expansion, contact pressure and sliding velocity and distance. Extensive analysis has been performed for the forming efficiency and flow mode. The simulation has been conducted by applying rigid-plastic finite element method. It was found that the relative movement at the contact interface increases with decrease in punch face angle and with increase in reduction such that sliding mode is expected for smaller punch face angles with larger reductions.

Numerical simulation of cold forging process to investigate folding defect in enclosed dies

In the precision forging industries, improving product quality and reducing product cost are important cases. Enclosed-die forging is one of the precision forging processes. In this paper, the cold forging process in the enclosed dies by using kinematical mechanism to create precision parts is considered. The numerical simulation techniques by using the rigid-plastic finite element method (FEM) as software QForm 2D have been applied to investigate defect as a folding defect in this paper. Based on the finite element simulations, forming characteristics such as deformation patterns (gridlines distortion), distributions of effective strain and stress at several stages of process as single-ended and double-ended with different forming parameters to avoid folding defect in cold forging process have been investigated. The lower die velocity vs. geometric ratio by using this numerical simulation method has been determined.

Implementation of VPSC polycrystal model into rigid plastic finite element method and its application to Erichsen test of Mg alloy

A methodology on the multiscale simulation of metal forming processes is presented, which fully integrates the visco-plastic self-consistent (VPSC) polycrystal model into rigid plastic finite element method (FEM). To accurately predict the material behavior of a magnesium alloy from the microstructural level, the VPSC crystal plasticity model was used as a constitutive equation in this methodology. An optimization program VPSC-GA was developed in order to calculate the hardening parameters for each slip and twin mode of a single crystal from a couple of simple tension/compression tests. The existing constitutive equation for rigid plastic FEM is modified using the deviatoric stress components and the derivatives of them with respect to strain rate components. The stiffness matrix and the load vector were derived based on a new approach and implemented into DEFORMTM-3D via a user subroutine which handles stiffness matrix in elemental level. An application to the Erichsen tests of magnesium alloys was done and the stretch formability of two different Mg alloy sheets was analyzed using the results of both experiment and simulation.