• Advances in Computational Design
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• v.3 no.1
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• pp.49-69
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• 2018

This paper shows an optimal design for reinforced concrete rectangular combined footings based on a criterion of minimum cost. The classical design method for reinforced concrete rectangular combined footings is: First, a dimension is proposed that should comply with the allowable stresses (Minimum stress should be equal or greater than zero, and maximum stress must be equal or less than the allowable capacity withstand by the soil); subsequently, the effective depth is obtained due to the maximum moment and this effective depth is checked against the bending shear and the punching shear until, it complies with these conditions, and then the steel reinforcement is obtained, but this is not guaranteed that obtained cost is a minimum cost. A numerical experimentation shows the model capability to estimate the minimum cost design of the materials used for a rectangular combined footing that supports two columns under an axial load and moments in two directions at each column in accordance to the building code requirements for structural concrete and commentary (ACI 318S-14). Numerical experimentation is developed by modifying the values of the rectangular combined footing to from "d" (Effective depth), "b" (Short dimension), "a" (Greater dimension), "${\rho}_{P1}$" (Ratio of reinforcement steel under column 1), "${\rho}_{P2}$" (Ratio of reinforcement steel under column 2), "${\rho}_{yLB}$" (Ratio of longitudinal reinforcement steel in the bottom), "${\rho}_{yLT}$" (Ratio of longitudinal reinforcement steel at the top). Results show that the optimal design is more economical and more precise with respect to the classical design. Therefore, the optimal design presented in this paper should be used to obtain the minimum cost design for reinforced concrete rectangular combined footings.

• Coupled systems mechanics
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• v.13 no.4
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• pp.311-335
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• 2024

This work aims to show a model to estimate the minimum cost (Thickness and area of steel in X and Y directions) for design a circular isolated footing with eccentric column that considers that the surface in contact with the ground works partially under compression. The formulation is shown by integration to find the moments, the bending shears and the punching shear using the pressure volume under the footing. Some researchers show the minimum cost design for circular isolated footings for an eccentric column assuming that the contact area works completely in compression, others consider the contact surface with the ground working partially in compression for a column in the center of the base. Three numerical examples are developed to obtain the complete design, which are: Example 1 for a column in the center of the base,Example 2 for a column at a distance of 1.50 m from the center of the base in the X direction, Example 3 for a column at a distance of 1.50 m from the center of the base in both directions. Also, a comparison of the new model against the model proposed by other authors is presented. The comparison shows that the new model generates a great saving of up to 43.74% for minimum area and 48.44% for minimum cost design in a column located in the center of the base, and when the column is located at a distance of radius/2 starting from the center of the base in the X direction generates great savings of up to 45.24% for minimum area and 31.80% for minimum cost design. Therefore, it is advisable to use the model presented in this study.

• Geomechanics and Engineering
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• v.4 no.3
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• pp.191-208
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• 2012

Due to rapid industrialisation, large scale infrastructure development is taking place worldwide. This includes railways, high speed highways, elevated roads etc. To meet the demands of society and industry, many innovative techniques and materials are being developed. In developed nations like USA, Japan etc. for railways applications, new material like geocells, geogrids are being used successfully to enable fast movement of vehicles. The present research work was aimed to develop design methodologies for improvement of grounds subjected to cyclic loads caused by moving vehicles on roads, rail tracks etc. Deformation behavior of ballast under static and cyclic load tests was studied based on square footing test. The paper presents a study of the effect of geo-synthetic reinforcement on the (cumulative) plastic settlement, of point loaded square footing on a thick layer of granular base overlying different compressible bases. The research findings showed that inclusion of geo-synthetics significantly improves the performance of ballasted tracks and reduces the foundation area. If the area is kept same, higher speed trains can be allowed to pass through the same track with insertion of geosynthetics. Similarly, area of machine foundation may also be reduced where geosynthetics is provided in foundation. The model tests results have been validated by numerical modeling, using $FLAC^{3D}$.

• Proceedings of the Korean Geotechical Society Conference
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• 2009.03a
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• pp.210-221
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• 2009

A new foundation type which is called Top-Base method has been used frequently in engineering practices in Korea. In this study, the settlement behavior of concrete Top-Base foundation on soft ground is investigated since the consolidation settlement of the embedding depth and the effect of footing dimensions are not included in current Korean criterion (2007). To obtain detailed information, the model tests of the Top-Base foundation are performed using the PLAXIS 3D finite element analysis. It is shown that in-situ measurements and finite element analysis of the behavior of foundations indicate that consolidation settlement is reduced up and bearing capacity of the foundation increases up to 50%~100%, compared to the primary non-treated ground. Based on this study, it is found that the Top-Base foundation prevents the lateral deformation of soft ground and reduces its negative dilatancy to the surface settlement, and that the foundation creates rather uniform stress distribution under it to increase its bearing capacity. It is also found that the total settlement of Top-Base foundation was highly dependent on the consolidation settlement and footing configurations.

• Geomechanics and Engineering
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• v.12 no.2
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• pp.223-238
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• 2017

In this study, bearing capacities and settlement profiles of six irregularly shaped footings located on sand have been experimentally and analytically investigated under the effect of axial loading. The main variable considered in the study was the geometry of the footings. The axial loads were applied from the center of gravities of the test specimens. Consequently, the effect of footing shape on the variation of the bearing capacities and settlement profiles have been investigated in this paper. The three dimensional finite element analyses of the test specimens were conducted using the PLAXIS 3D software. The finite element model results are in acceptable agreement with the results obtained using experimental investigation. In addition, the usability of the finite element technique by design engineers to determine the bearing capacities and settlement profiles of irregularly shaped footings was investigated. From the results of the study, it was observed that the geometric properties of the footings significantly influenced the variation of the bearing capacities and settlement profiles.

• Structural Engineering and Mechanics
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• v.81 no.3
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• pp.379-394
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• 2022

Shallow footings usually belonged to the category of thick plate structures. For accurate analysis of thick plates, the contribution of out-of-plane components of the stress tensor should be considered in the formulation. Most of the available shallow footing models are based on the classical plate theories, which usually neglect the effects of the out-of-plane stresses. In this study, a mixed-field plate finite element model (FEM) is developed for the analysis of shallow footings rested on soil foundations. In addition to displacement field variables, the out-of-plane components of the stress tensor are also assumed as a priori unknown variables. For modeling the interaction effect of the soil under and outside of the shallow footings, the modified Vlasov theory is used. The tensionless nature of the supporting soil foundation is taken into account by adopting an incremental, iterative procedure. The equality requirement of displacements at the interface between the shallow footing and soil is fulfilled using the penalty approach. For validation of the present mixed FEM, the obtained results are compared with the results of 3D FEM and previous results published in the literature. The comparisons show the present mixed FEM is an efficient and accurate tool for solving the problems of shallow footings rested on subsoil.

• Geomechanics and Engineering
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• v.25 no.3
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• pp.195-205
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• 2021

Time effect on the deformation and strength characteristics of geogrid reinforced sand retaining wall has become an important issue in geotechnical and transportation engineering. Three physical model tests on geogrid reinforced sand retaining walls performed under various loading conditions were simulated to study their rate-dependent behaviors, using the presented nonlinear finite element method (FEM) analysis procedure. This FEM was based on the dynamic relaxation method and return mapping scheme, in which the combined effects of the rate-dependent behaviors of both the backfill soil and the geosynthetic reinforcement have been included. The rate-dependent behaviors of sands and geogrids should be attributed to the viscous property of materials, which can be described by the unified three-component elasto-viscoplastic constitutive model. By comparing the FEM simulations and the test results, it can be found that the present FEM was able to be successfully extended to the boundary value problems of geosynthetic reinforced soil retaining walls. The deformation and strength characteristics of the geogrid reinforced sand retaining walls can be well reproduced. Loading rate effect, the trends of jump in footing pressure upon the step-changes in the loading rate, occurred not only on sands and geogrids but also on geogrid reinforced sands retaining walls. The lateral earth pressure distributions against the back of retaining wall, the local tensile force in the geogrid arranged in the retaining wall and the local stresses beneath the footing under various loading conditions can also be predicted well in the FEM simulations.

• The Bulletin of The Korean Astronomical Society
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• v.42 no.2
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• pp.78.3-78.3
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• 2017

The positions of galaxies in comoving Cartesian space varies under different cosmological parameter choices, inducing a redshift-dependent scaling in the galaxy distribution. The shape of the two-point correlation of galaxies exhibits a significant redshift evolution when the galaxy sample is analyzed under a cosmology differing from the true, simulated one. In our previous works, we can made use of this geometrical distortion to constrain the values of cosmological parameters governing the expansion history of the universe. This current work is a continuation of our previous works as a strategy to constrain cosmological parameters using redshift-invariant physical quantities. We now aim to understand the redshift evolution of the full shape of the small scale, anisotropic galaxy clustering and give a firmer theoretical footing to our previous works.

• Coupled systems mechanics
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• v.12 no.5
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• pp.461-479
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• 2023

The paper deals with the finite element modelling of the free vibration and structural behavior of a particular four-floor reinforced concrete structure subjected to static equivalent seismic loads and supported by a shallow foundation system called SNSF (Spider Net System Footing). The two FE models are a simple 2D Matlab model and a detailed 3D model based on solid elastic elements using Altairworks (Hypermesh and Optistruct). Both models can simulate the soil structure interaction. We concentrate on the behavior of a representative cell involving two columns on five levels. The influence of the boundary conditions on the external vertical planes of the domain are duly studied. The Matlab model appears relevant for a primary estimation of frequencies and stiffness of the whole structure under vertical and lateral loads.

• Geotechnical Engineering
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• v.12 no.2
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• pp.71-84
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• 1996

In order to investigate the influence of slanting angle of reticulated root piles(RRP) on their bearing capacities, model tests of compressive and uplift loads on RRP with different slanting angles, which were installed in sandy soils with a relative density of 47%, were carried out. Each pile which is made of a steel bar of 5mm in diameter and 300mm in length, is coated with sand to be 6.5mm in diameter. One set of RRP consists of 8 piles which are installed in circular patterns forming two concentric circles, each of which has 4 piles. Slanting angles of RRP for load tests are 0$^{\circ}$, 5$^{\circ}$, 10$^{\circ}$, 15$^{\circ}$, 20$^{\circ}$, and 25$^{\circ}$. In addition, compressive load tests on circular footing whose diameter is the same as the outer circle of RRP were carried out. Test results show that maximum load bearing capacities of RRP by regression analysis are obtained at about 12$^{\circ}$ and 13$^{\circ}$ of slanting angles for compressive and uplift load tests, respectively. Maximum compressive bearing capacity is estimated to be 13oA bigger than that of the vertical RRP and 95% bigger than that of surface footing. Maximum uplift capacity is estimated to be 21% bigger than that of the vertical RRP. And it can be appreciated that increasing the slanting angle makes the load -Settlement behavior more ductile.