• Magazine of the Korean Society of Agricultural Engineers
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• v.34 no.1
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• pp.49-56
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• 1992

This study was carried out to investigate the mechanical behaviour of the plate on a Winkler's foundation according to the soil-structures relative stiffness and the applicability of the conventional analysis method. For the above purpose, Winkler's constant of 4, 15, 25 and 100kg/$cm^2$/cm was considered and the plate thickness of 20, 30, 50, 100 and 150cm was adopted. Results obtained from the numerical examples are summarized as follow: 1. The effects of elastic foundation is considerable for plates with small flexural rigidity. 2. As the Winkler's constant increases, the bending moment in the plate becomes localized near the loading point. 3. The stresses evaluated by the conventional method not correct even for rigid ground such as rock. 4. If the relative stiffness of the plate is very large, for example the plate thickness is larger than 100cm, the conventional analysis method can be justified for the design purposes. 5. On assumption the flexural rigidity of the plate is infinite, the interaction of soil and plate can be ignored in design consideration. The numerical examples in this paper show that when the plate thickness is more than 100cm, the effects of elastic foundation almost disappear. In practical design, soil-plate interaction should be taken into account, because the 100cm-thickness of the plate will not be practical value in usual sites.

• Magazine of the Korean Society of Agricultural Engineers
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• v.29 no.2
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• pp.39-52
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• 1987

This study was to investigate the effects of soil-structure relative stiffness on the structural characteristics of the cylindrical tank supported by soil. A standard example model of the farm silo rested on the Winkler's subsoil model was used for the analysis of soil-structure coupled system. In this paper, Winkler's constants 4,15 and l00kg/cm$^2$/cm were considered and the bottom plate thicknesses of the farm silo 20, 30, 50,100 and 150cm were adopted. For the given model the effects of bottom plate thickness were the most conspicuous at weakest Winkler's constant 4kg/ cm$^2$/cm. While when Winkler's constant is l00kg/cm$^2$/cm, the effect of the bottom plate thickness is almost negligible. On the other hand, when the bottom plate thickness is more than 100cm, the effects of elastic foundation were aknost disappeared. In design practice, it is hoped that the thicknesses of bottom plate should be determined reasonably because of it's considerable effect on the structural characteristics as the lOOcm thickness of bottom plate will not be practical value in usual sites.

• Journal of the Earthquake Engineering Society of Korea
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• v.28 no.4
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• pp.165-170
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• 2024

This study investigated the impact of soil-structure interaction on multi-degree-of-freedom structures using the shallow-foundation Winkler model, known as the BNWF model. The model's period was determined through eigenvalue analysis and compared to results obtained from FEMA's formula. Results indicated that considering the soil, the structure's period increased by up to 8.7% compared to the fixed-base model, aligning with FEMA's calculations. Furthermore, with adequate ground acceleration, roof displacement increased by 3.4% to 3.8%, while base shear decreased by 4% to 10%. However, roof displacement and base shear increased in some earthquake scenarios due to spectral shape effects in regions with extended structural periods. Foundation damping effects, determined through the foundation's moment-rotation history, grew with higher ground acceleration. This suggests that accounting for period elongation and foundation damping can enhance the seismic design of multi-degree-of-freedom structures.

• Computational Structural Engineering
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• v.1 no.1
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• pp.103-112
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• 1988

In this study, the earthquake response of building structures with foundation uplift was investigated. The Winkler foundation model and two-spring model are widely used to represent the interaction between foundation mat and soil. While the analysis using the Winkler foundation model results in more accurate prediction, it requires a complex procedure and longer computation time. In this study, an equivalent two-spring model(S model) is proposed. The S model can represent the Winkler foundation model more accurately and the analysis using the S model is simpler and more effective. The S model is derived by simplifying the nonlinear moment-rotation relationship of foundation mat. The dynamic responses predicted by the S model gave a good agreement to those of the Winkler foundation model.

• Earthquakes and Structures
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• v.12 no.2
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• pp.165-175
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• 2017

This paper studies soil properties uncertainty and its implementation in the seismic response evaluation of structures. For this, response sensitivity of two 4- and 12-story RC shear walls to the soil properties uncertainty by considering soil structure interaction (SSI) effects is investigated. Beam on Nonlinear Winkler Foundation (BNWF) model is used for shallow foundation modeling and the uncertainty of soil properties is expanded to the foundation stiffness and strength parameters variability. Monte Carlo (MC) simulation technique is employed for probabilistic evaluations. By investigating the probabilistic evaluation results it's observed that as the soil and foundation become stiffer, the soil uncertainty is found to be less important in influencing the response variability. On the other hand, the soil uncertainty becomes more important as the foundation-structure system is expected to experience nonlinear behavior to more sever degree. Since full This paper studies soil properties uncertainty and its implementation in the seismic response evaluation of structures. For this, response sensitivity of two 4- and 12-story RC shear walls to the soil properties uncertainty by considering soil structure interaction (SSI) effects is investigated. Beam on Nonlinear Winkler Foundation (BNWF) model is used for shallow foundation modeling and the uncertainty of soil properties is expanded to the foundation stiffness and strength parameters variability. Monte Carlo (MC) simulation technique is employed for probabilistic evaluations. By investigating the probabilistic evaluation results it's observed that as the soil and foundation become stiffer, the soil uncertainty is found to be less important in influencing the response variability. On the other hand, the soil uncertainty becomes more important as the foundation-structure system is expected to experience nonlinear behavior to more sever degree. Since full probabilistic analysis methods like MC commonly are very time consuming, the feasibility of simple approximate methods' application including First Order Second Moment (FOSM) method and ASCE41 proposed approach for the soil uncertainty considerations is investigated. By comparing the results of the approximate methods with the results obtained from MC, it's observed that the results of both FOSM and ASCE41 methods are in good agreement with the results of MC simulation technique and they show acceptable accuracy in predicting the response variability.

• Coupled systems mechanics
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• v.1 no.2
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• pp.115-131
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• 2012

Paper presents an improved solution algorithm based on Finite Element Method to analyse piled raft foundation. Piles are modelled as beam elements with soil springs. Finite element analysis of raft is based on the classical theory of thick plates resting on Winkler foundation that accounts for the transverse shear deformation of the plate. Four node, isoparametric rectangular elements with three degrees of freedom per node are considered in the development of finite element formulation. Independent bilinear shape functions are assumed for displacement and rotational degrees of freedom. Effect of raft thickness, soil modulus and load pattern on the response is considered. Significant improvement in the settlements and moments in the raft is observed.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1995.04a
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• pp.53-56
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• 1995

Despite the recent development of structural analysis programs for the CRCP pavements over Westergaard's equations and finite element techniques, the Winkler foundations which are modelled by series of vertical springs at the nodes are generally used for the computer modelling of subbases under the concrete slab. Herewith, two parameter of soil foundation model is adopted as the most convenient mathematical model to enable deflections outside the loaded area to be effected and to upgrade the Winkler foundations. This paper highlights the derivations of finite element method for the two-parameter soil foundation model in the concrete pavements.

• Geomechanics and Engineering
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• v.32 no.1
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• pp.69-84
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• 2023

This paper proposes a novel frame element on Winkler-Pasternak foundation for analysis of a non-ductile reinforced concrete (RC) member resting on foundation. These structural members represent flexural-shear critical members, which are commonly found in existing buildings designed and constructed with the old seismic design standards (inadequately detailed transverse reinforcement). As a result, these structures always experience shear failure or flexure-shear failure under seismic loading. To predict the characteristics of these non-ductile structures, efficient numerical models are required. Therefore, the novel frame element on Winkler-Pasternak foundation with inclusion of the shear-flexure interaction effect is developed in this study. The proposed model is derived within the framework of a displacement-based formulation and fiber section model under Timoshenko beam theory. Uniaxial nonlinear material constitutive models are employed to represent the characteristics of non-ductile RC frame and the underlying foundation. The shear-flexure interaction effect is expressed within the shear constitutive model based on the UCSD shear-strength model as demonstrated in this paper. From several features of the presented model, the proposed model is simple but able to capture several salient characteristics of the non-ductile RC frame resting on foundation, such as failure behavior, soil-structure interaction, and shear-flexure interaction. This confirms through two numerical simulations.

• Geomechanics and Engineering
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• v.5 no.5
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• pp.379-399
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• 2013

In practice, analysis of laterally loaded piles is carried out using beams on non-linear Winkler springs model (often known as p-y method) due to its simplicity, low computational cost and the ability to model layered soils. In this approach, soil-pile interaction along the depth is characterized by a set of discrete non-linear springs represented by p-y curves where p is the pressure on the soil that causes a relative deformation of y. p-y curves are usually constructed based on semi-empirical correlations. In order to construct API/DNV proposed p-y curve for clay, one needs two values from the monotonic stress-strain test results i.e., undrained strength ($s_u$) and the strain at 50% yield stress (${\varepsilon}_{50}$). This approach may ignore various features for a particular soil which may lead to un-conservative or over-conservative design as not all the data points in the stress-strain relation are used. However, with the increasing ability to simulate soil-structure interaction problems using highly developed computers, the trend has shifted towards a more theoretically sound basis. In this paper, principles of Mobilized Strength Design (MSD) concept is used to construct a continuous p-y curves from experimentally obtained stress-strain relationship of the soil. In the method, the stress-strain graph is scaled by two coefficient $N_C$ (for stress) and $M_C$ (for strain) to obtain the p-y curves. $M_C$ and $N_C$ are derived based on Semi-Analytical Finite Element approach exploiting the axial symmetry where a pile is modelled as a series of embedded discs. An example is considered to show the application of the methodology.

• Structural Engineering and Mechanics
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• v.68 no.1
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• pp.121-130
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• 2018

This study deals with optimum geometry design of laterally loaded piles in a Winkler's medium through the Fully Stressed Design (FSD) method. A numerical algorithm distributing the mass by means of the FSD method and updating the moment by finite elements is implemented. The FSD method is implemented here using a simple procedure to optimise the beam length using an approach based on the calculus of variations. For this aim two conditions are imposed, one transversality condition at the bottom end, and a one sided constraint for moment and mass distribution in the lower part of the beam. With this approach we derive a simple condition to optimise the beam length. Some examples referred to different fields are reported. In particular, the case of laterally loaded piles in Geotechnics is faced.