• Geomechanics and Engineering
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• 제29권4호
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• pp.435-449
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• 2022

In this paper, unreinforced and geogrid-reinforced soil foundations were modeled by discrete element method and this performed under surface strip footing loads. The effects of horizontal position of geogrid, vertical position, thickness, number, confining pressure have been investigated on the footing settlement and propagation of tensile force along the geogrids. Also, interaction between rectangular tunnel and strip footing with and without presence of geogrid layer has been analyzed. Experimental results of the literature were used to validation of relationships between the numerically achieved footing pressure-settlement for foundations of reinforced and unreinforced soil. Models and micro input parameters which used in the numerical modelling of reinforced and unreinforced soil tunnel were similar to parameters which were used in soil foundations. Model dimension was 1000 mm* 600 mm. Normal and shear stiffness of soils were 5*10⁵ and 2.5 *10⁵ N/m, respectively. Normal and shear stiffness of geogrid were 1*10⁹ and 1*10⁹ N/m, respectively. Loading rate was 0.001 mm/sec. Micro input parameters used in numerical simulation gain by try and error. In addition of the quantitative tensile force propagation along the geogrids, the footing settlements were visualized. Due to collaboration of three layers of geogrid reinforcements the bearing capacity of the reinforced soil tunnel was greatly improved. In such practical reinforced soil formations, the qualitative displacement propagations of soil particles in the soil tunnel and the quantitative vertical displacement propagations along the soil layers/geogrids represented the geogrid reinforcing impacts too.

• Geomechanics and Engineering
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• 제11권2호
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• pp.289-307
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• 2016

A simple hyperbolic shear deformation theory taking into account transverse shear deformation effects is proposed for the free flexural vibration analysis of thick functionally graded plates resting on elastic foundations. By considering further supposition, the present formulation introduces only four unknowns and its governing equations are therefore reduced. Hamilton's principle is employed to obtain equations of motion and Navier-type analytical solutions for simply-supported plates are compared with the available solutions in literature to check the accuracy of the proposed theory. Numerical results are computed to examine the effects of the power-law index and side-to-thickness ratio on the natural frequencies.

• Structural Engineering and Mechanics
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• 제4권2호
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• pp.149-162
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• 1996

A postbuckling analysis is presented for a simply supported, moderately thick rectangular plate subjected to combined axial compression and uniform temperature loading and resting on a two-parameter elastic foundation. The two cases of thermal postbuckling of initially compressed plates and of compressive postbuckling of initially heated plates are considered. The initial geometrical imperfection of the plate is taken into account. The formulations are based on the Reissner-Mindlin plate theory considering the first order shear deformation effect, and including the plate-foundation interaction and thermal effect. The analysis uses a deflection-type perturbation technique to determine the buckling loads and postbuckling equilibrium paths. Numerical examples cover the performances of perfect and imperfect, moderately thick plates resting on Winkler or Pasternak-type elastic foundations. Typical results are presented in dimensionless graphical form.

• Structural Engineering and Mechanics
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• 제49권5호
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• pp.661-672
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• 2014

Laminated Rectangular plates embedded in elastic foundations are used in many mechanical structures. This study presents an analytical approach for transverse bending analysis of an embedded symmetric laminated rectangular plate using Mindlin plate theory. The surrounding elastic medium is simulated using Pasternak foundation. Adopting the Mindlin plate theory, the governing equations are derived based on strain-displacement relation, energy method and Hamilton's principle. The exact analysis is performed for this case when all four ends are simply supported. The effects of the plate length, elastic medium and applied force on the plate transverse bending are shown. Results indicate that the maximum deflection of the laminated plate decreases when considering an elastic medium. In addition, the deflection of the laminated plate increases with increasing the plate width and length.

• Geomechanics and Engineering
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• 제23권3호
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• pp.275-287
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• 2020

Rectangular barrettes have been increasingly used as foundations for many infrastructure projects, but the vertical vibration of a barrette has been rarely addressed theoretically. This paper presents an analysis method of dynamic response for a rectangular barrette subjected to a time-harmonic vertical force with the aid of a modified Vlasov foundation model in multilayered viscoelastic soil. The barrette-soil system is modeled as a continuum, the vertical continuous displacement model for the barrette and soil is proposed. The governing equations of the barrette-soil system and the boundary conditions are obtained and the vertical shaft resistance of barrette is established by employing Hamilton's principle for the system and thin layer element, respectively. The physical meaning of the governing equations and shaft resistance is interpreted. The iterative solution algorithm flow is proposed to obtain the dynamic response of barrette. Good agreement of the analysis and comparison confirms the correctness of the present solution. A parametric study is further used to demonstrate the effects of cross section aspect ratio of barrettes, depth of soil column, and module ratio of substratum to the upper soil layers on the complex barrette-head stiffness and the resistance stiffness.

• Geomechanics and Engineering
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• 제32권2호
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• pp.193-207
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• 2023

In general, the numerous classical approaches available in the literature can anticipate the settlement of shallow foundations. As long as the footings are not in close proximity to other subsurface buildings, the findings achieved using these methods are legitimate and acceptable. However, due to increased urbanisation and land scarcity, footings are frequently built close together. As a result, these footings' settlement behaviour differs from those of isolated footings. A simpler approach for assessing the settlement behaviour of two square or rectangular footings placed in close proximity is presented in this work. A Parametric study has been carried out to examine the interference effect on the settlement of these footings placed in close vicinity on the surface of a homogeneous, isotropic and elastic soil medium. The interaction factors are examined by varying the different aspect ratios (L/B), clear spacing ratio (S/B) and intensity of loading on the right footing with respect to the left footing. Further, variation of the settlement ratio (δ/B) with respect to embedment depth ratio D_f/B is examined. For square and rectangular footings, the interference settlement profile is also investigated by varying the clear spacing ratio (S/B) and the degree of loading. The results were compared to 3D finite element analysis and experimental data that were available.

• Computers and Concrete
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• 제16권2호
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• pp.245-260
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• 2015

In this study, nominal moment-axial load interaction diagrams, moment-curvature relationships, and ductility of rectangular hybrid beam-column concrete sections are analyzed using the modified Hognestad concrete model. The hybrid columns are primarily reinforced with steel bars with additional Glass Fiber Reinforced Polymer (GFRP) control bars. Parameters investigated include amount, pattern, location, and material properties of concrete, steel, and GFRP. The study was implemented using a user defined comprehensive $MATLAB^{(R)}$ simulation model to find an efficient hybrid section design maximizing strength and ductility. Generating lower bond stresses than steel bars at the concrete interface, auxiliary GFRP bars minimize damage in the concrete core of beam-column sections. Their usage prevents excessive yielding of the core longitudinal bars during frequent moderate cyclic deformations, which leads to significant damage in the foundations of bridges or beam-column spliced sections where repair is difficult and expensive. Analytical results from this study shows that hybrid steel-GFRP composite concrete sections where GFRP is used as auxiliary bars show adequate ductility with a significant increase in strength. Results also compare different design parameters reaching a number of design recommendations for the proposed hybrid section.

• Steel and Composite Structures
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• 제20권3호
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• pp.623-649
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• 2016

Most of the early studies on plates vibration are focused on two-dimensional theories, these theories reduce the dimensions of problems from three to two by introducing some assumptions in mathematical modeling leading to simpler expressions and derivation of solutions. However, these simplifications inherently bring errors and therefore may lead to unreliable results for relatively thick plates. The main objective of this research paper is to present 3-D elasticity solution for free vibration analysis of continuously graded carbon nanotube-reinforced (CGCNTR) rectangular plates resting on two-parameter elastic foundations. The volume fractions of oriented, straight single-walled carbon nanotubes (SWCNTs) are assumed to be graded in the thickness direction. In this study, an equivalent continuum model based on the Eshelby-Mori-Tanaka approach is employed to estimate the effective constitutive law of the elastic isotropic medium (matrix) with oriented, straight carbon nanotubes (CNTs). The proposed rectangular plates have two opposite edges simply supported, while all possible combinations of free, simply supported and clamped boundary conditions are applied to the other two edges. The formulations are based on the three-dimensional elasticity theory. A semi-analytical approach composed of differential quadrature method (DQM) and series solution is adopted to solve the equations of motion. The fast rate of convergence of the method is demonstrated and comparison studies are carried out to establish its very high accuracy and versatility. The 2-D differential quadrature method as an efficient and accurate numerical tool is used to discretize the governing equations and to implement the boundary conditions. The convergence of the method is demonstrated and to validate the results, comparisons are made between the present results and results reported by well-known references for special cases treated before, have confirmed accuracy and efficiency of the present approach. The novelty of the present work is to exploit Eshelby-Mori-Tanaka approach in order to reveal the impacts of the volume fractions of oriented CNTs, different CNTs distributions, various coefficients of foundation and different combinations of free, simply supported and clamped boundary conditions on the vibrational characteristics of CGCNTR rectangular plates. The new results can be used as benchmark solutions for future researches.

• 한국소음진동공학회논문집
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• 제19권12호
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• pp.1296-1305
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• 2009

This paper has the object of investigating dynamic stability of stiffened tapered thick plate with concentrated mass on Pasternak foundation by means of finite element method and providing kinematic design data for mat of building structures. Finite element analysis of stiffened tapered thick plate is done by use of rectangular finite element with 8-nodes. In order to analysis plate which is supported on Pasternak foundation, the Winkler foundation parameter is varied with 10, 100, 1000 and the shear foundation parameter is 5, 10, concentrated mass is $0.25m_c$, $1.0m_c$, tapered ratio is 0.25, 0.5. The ratio of In-plane force to critical load is applied as $0.4\sigma_{cr},\;0.6\sigma_{cr},\;0.8\sigma_{cr}$ respectively. This paper analyzed varying tapered ratio.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1997년도 봄 학술발표회 논문집
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• pp.19-26
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• 1997

In this paper, two dimensional analytical infinite elements which can include multiple wave components to model a underlying half-space are developed. Since these elements are expressed clearly and simply using Legendre polynomials of frequencies in frequency domain, these are very economical and efficient in computing the responses of strip foundations in frequency domain and are easily transformed for SSI analysis in time domain. To prove the behavior of the proposed two dimensional analytical infinite elements, vertical, horizontal, and rocking compliances of a rigid strip foundation in layered soils are analyzed and compared with those of Tzong ' Penzie $n^{(17)}$ and with those which calculated by numerical infinite elemen $t^{(1)}$ in frequency domain, and good agreements are noticed between them. As an application for a further study, a new scheme for SSI analysis in time domain are proposed and verified by comparing the displacement responses of the soil with a underlying rock due to a rectangular impulse loading with those of a soil modeled extended FE meshes.soil modeled extended FE meshes.