Winkler Theory Research Articles

Simulation Research on Local Settlement of Kiln Foundation Based on Winkler Theory

The masonry structure is one of the main types of modern industrial buildings in China because of its local materials and simple economy. However, these buildings often suffer damage and cracks due to uneven settlement of the foundation and disrepair, which affects the safe and normal use of the structure. It is urgent to maintain and strengthen the structure to restore the safety of the structure. This paper takes Baoji Shenxin Yarn Factory - Kiln Factory as the actual engineering background, and use the finite element software ABAQUS based on Winkler’s theory to establish a finite element calculation model that can more conveniently respond to the effects of different foundation settlements. Through the simulation analysis, the influence law of the local settlement of the kiln foundation on the overall structural force state was obtained, which can provide an important reference basis for the maintenance and reinforcement of the structure.

Nonlinear energy sink vibration suppression and parameter optimization of a finite-length beam on the elastic medium based on the modified Winkler theory

Nonlinear energy sink vibration suppression and parameter optimization of a finite-length beam on the elastic medium based on the modified Winkler theory

A Simple Approach for the Dynamic Analysis of a Circular Tapered Pile under Axial Harmonic Vibration

The tapered pile offers sustainable use of construction materials due to its higher axial and lateral capacity and better performance owing to its geometry. This paper develops a semi-analytical solution of the vertical dynamic impedance of the tapered pile based on the dynamic Winkler theory and transfer matrix method. The accuracy and reliability of the proposed approach are verified by comparing the impedance functions of cylindrical and tapered piles obtained from the analytical solution and finite element analysis. A parametric study is performed to investigate the influence of the taper angle on the vertical dynamic impedance and resonant frequency. The results reveal that the taper angle has a significant influence on the vertical dynamic impedance, while it does not affect the oscillation period of the dynamic impedance and the resonant frequency. Besides, the vibration performance of the tapered pile is better than that of a cylindrical pile with the same volume. For a fixed-volume tapered pile, varying the pile length while keeping the pile tip diameter constant yields a better dynamic impedance than varying the pile tip diameter while keeping the pile length constant. Finally, the vertical displacement amplitude of the tapered pile decreases as the taper angle increases, especially for high-frequency excitation.

Influence of soil-structure interaction modeling on the behavior of multi-story plane steel frames with shallow footing foundations

Traditionally, structural analysis is based on the hypothesis that supports are indeslocable due to simplicity. However, the conventional design in which settlements of foundation elements are disregarded can lead to physical results that are incompatible with reality. This work aims to analyze the influence of the consideration of soil-structure interaction (SSI) on the responses of steel structural elements obtained by a static second order analysis. Furthermore, it is evaluated the responses obtained by different types of procedures for the consideration of soil stiffness in the structural analysis. Solid elements considering linearly elastic material parameters and spring elements based on the Winkler theory are employed. The analyses were performed with the commercial software SAP2000. Plane steel frames models were analyzed, either considering conventional supports or taking into account the soil-structure interaction. Shallow footing foundations are considered. Three frames with the same characteristics, but with a different number of floors were analyzed, showing the influence of the height increase and the building stiffness on the SSI results. It has been shown that the consideration of the effects of soil-structure interaction on structural analysis of buildings can have a significant influence on the stress distribution, displacements and structural behavior. In addition, it is concluded that the structural capacity of steel frames can be affected by the type of support adopted and by changes on the way the model considers soil deformation.

Influence of the Primary Key Stratum on Surface Subsidence during Longwall Mining

The surface subsidence caused by mining influences the mine environment and construction safety. In this paper, strata movement and surface subsidence were combined. Based on elasticity and Winkler theory, a prediction method of surface subsidence was established with the primary key stratum as the research object. Using the Tingnan Coal Mine as an example, the mining subsidence of the second panel was predicted. Comparing the predicted results with the measured results, the causes of errors were analyzed and the field of application of the model was clarified. Besides, the geological and mining factors affecting surface subsidence were also analyzed. The results show that the mining subsidence is the surface manifestation of the strata movement. Surface subsidence is affected by the mining area, load, and flexural rigidity of the primary key stratum, foundation modulus of the goaf, and the rock mass. The research results have significance for the planning of the coal resources and the prevention of geological disasters.

Evaluation of the lateral bearing characteristics of composite caisson-pile foundation considering the scour-hole dimensions

Based on the nonlinear Winkler theory, a simplified method for evaluating the lateral bearing capacity of the caisson-pile foundation (CCPF) considering the effect of scour-hole dimensions was proposed. The reliability of this method was verified by the results from a model test. The influences of the scour-hole dimensions on the lateral bearing characteristics of the foundation were discussed. The results show that the influence degree of each individual factor on the ultimate lateral bearing capacity of the foundation was in the order of the scour depth, the scour width and the scour slope angle. In the meantime, as the slope angle decreases or the scour width increases, the decrease of the ultimate lateral bearing capacity becomes stable. Furthermore, the scour width effect on the ultimate lateral bearing capacity could be ignored when the width is greater than or equal to the caisson diameter, and the effect of scour slope angle could be ignored when the scour slope angle is less than 5°. The effect of scour width and scour slope angle on the bearing capacity of the foundation shows a similar trend when the scour depth varies differently. The results can provide a technical guide for the CCPF design.

Analysis of Lateral Dynamic Response of Caisson Foundation in Layered Clayey Soils considering Scour-Hole Dimensions

As a cross-sea or river deep-water foundation, it is clear that the caisson foundation will be subjected to significant lateral dynamic loads due to winds or waves and suffer from scouring under its long-term effect. In order to obtain the scour effect on the dynamic response of the foundation, an analytical model describing the scour-hole effect in terms of scour depth, scour width, and slope angle was constructed. Combined with the nonlinear Winkler theory, a method for the dynamic response of the caisson foundation considering the scour-hole dimensions was proposed. Comparisons against the results from the dynamic FEM demonstrate the reliability of this method. The effects of the scour width, slope angle, and scour depth on the dynamic response of the caisson were discussed. The results show that the scour depth affects the dynamic displacement and resonant frequency of the foundation most, whereas the scour width does less and the slope angle does the least; the dynamic response of caisson can be approximated as the case of the slope angle 5° and the scour width 5B when the slope angle is less than 5° and the scour width is greater than 5B, respectively; the effects of scour width and slope angle on the dynamic response of caisson have the similar change pattern in the displacement and resonant frequency when the scour depth is different. However, the effect of amplitude on dynamic response shows a nonlinear increase trend when the scour depth is relatively large.

Non-linear Analysis of Laterally Loaded Piles Using "p-y" Curves

In this paper, we analyze the behavior of a monopile under lateral loading. Specifically, this work focuses on the examination of the static stiffness coefficients of a monopile vertically embedded in a homogeneous or multilayer soil of random geometry and random mechanical properties. To solve the problem, a semi-analytical, closed form solution is developed, based on Winkler's theory. In this model, simulation of the mechanical behavior of the soil is achieved via non-linear p-y springs positioned along the axis of the pile, in conjunction with shape functions which describe the lateral movement of the pile. By iterative application of the proposed method the lateral stiffness coefficients at the pile head are calculated with satisfactory accuracy. The results of the proposed method converge satisfactory enough with real data and other theoretical results coming from sophisticated numerical analysis methods.

Seismic Response of Steel Braced Vertically Irregular RC Frame Considering Soil Structure Interaction

Bracing system is one of the structural system which forms an integral part of the frame. Steel bracings have been used extensively as a structural system to resist seismic loads in the recent times due to their passive energy dissipation property. Steel bracing being economical and easy to erect assists to enhance the strength and retrofitting properties of a structure and their effective performance in controlling seismic effects on the structures during earthquake. In the present study the effect of soil structure interaction (SSI) on multi-storied vertically irregular RC buildings on a horizontal soil profile with varying underlying soil types using concentric chevron bracing is investigated. A G+4 story vertically irregular building (with bracing and without bracing) is analyzed as per IS 1893:2002 using ANSYS.v19 software with fixed and flexible foundation. The soil structure interaction effects on the flexible foundation are analyzed and the effectiveness of the chevron braced frame on the seismic performance of the building is studied. Two different combination of the soil profile for the same building with bracing and without bracing and for free headed and fixed headed flexible foundation condition has been analyzed in response spectrum method for Winkler theory. The performance of the building is evaluated in terms of displacement, storey drift and bending moment along the pile and time period. It was found that the chevron bracing with fixed headed flexible foundation significantly contributes to the structural stiffness and reduces the displacement compared to the bare frame and also the SSI effect considering the water table showed more displacement when compared to the structure on saturated hard soils. Time period increases when SSI was considered.

Internal Force Analysis and Field Test of Lattice Beam Based on Winkler Theory for Elastic Foundation Beam

As a new flexible supporting structure, prestressed anchor cable lattice beams have been widely used in high-slope support engineering and have achieved good results. However, theoretical research on the internal force analysis of lattice beams is far behind engineering practice. Based on the theory of the Winkler elastic foundation model, a mechanical model of a prestressed anchor cable lattice beam at the tension stage was established. Considering the nonhomogeneous lattice beam materials, a calculation method was given and applied to engineering examples. A calculation method of the measured moment was introduced in the field test conducted in the Zhouqu County “8·8” debris flow disaster reconstruction project. Comparisons between the test results and the theoretical results were performed. The results showed that the theoretical results of the distribution trend of the lattice beam moment were consistent with the test results, which verified the rationality of the proposed calculation method. The inertia moment of the beam section solved by the transformed section method was more realistic. The results of the transformed section method could improve the bending resistance of the lattice beam and reduce the reinforcement ratio. The greater the anchoring force was, the more obvious the lifting effect was. The anchoring force was an important influencing factor of the internal force of the lattice beam. The greater the anchoring force was, the greater the lattice beam moment was, and they showed the same proportional change phenomenon. Compared with the theoretical moment, the measured moment obtained by the test was smaller, which indicated that the lattice beam of the tested slope was safe at the present stage.

An analytical study on the elastic-plastic pure bending of a linear kinematic hardening curved beam

In this study, an analytical solution is presented for elastic-plastic pure bending of a linear kinematic hardening curved beam with rectangular cross section both in monotonic loading and unloading. Compared to exact plane plasticity solution (already reported in the literature in loading) which needs solution of a system of equations, the proposed method is based on the hyperbolic strain distribution on the cross section which yields a simple approximate solution. To this end, we employ Winkler's theory, and assume plane cross sections remain plane after loading proved by the exact elasticity and plasticity solutions for pure bending of curved beams with rectangular cross section. At the loading stages, the equations required to obtain the location of the neutral axis, the location of inner and outer elastic-plastic borders, the stress distribution on the cross section, and moment-curvature relation are presented. At the unloading stages, taking reverse yielding of some fibers into account, the stress distribution on the cross section after unloading and final curvature of the curved beam are also determined. Finally, the results are validated and compared with the exact plane plasticity and finite element results.

Anchored piles in Santiago's gravel: modeling results for displacement curve

This study describes the method of discontinuous and anchored machine bored piles. The main advantage of this method is its faster and safer execution in comparison with hand-dug piles (rectangular section), the most widely used method for soil retaining in the gravel of Santiago. This paper shows the results of displacement versus height obtained by a numerical modeling (software Plaxis 2D), in the case of anchored machine bored piles used for the construction of the Faculty of Physical and Mathematical Sciences, Universidad de Chile. As part of monitoring of excavation, measurements of displacements were obtained for two piles at different stages by preinstalled inclinometers in the piles. Furthermore, the study shows the results for the displacement using rod construction module (software GGU-Retain), and through Winkler's theory (software CYPE: Embedded retaining walls), considering the most representative stages and the redistribution of soil pressure that is indicated in the Chilean Norm NCh.3206 for the model done on GGU-Retain. The results of the performed modellings are graphically compared with the measured field values.

A continuous contact force model of planar revolute joint based on fitting method

Both the process of eliminating the clearance in joints and the contact–impact process involve movement of a clearance mechanism, which may reduce transmission accuracy and lengthen the response time. An appropriate continuous contact force model is able to describe the contact phenomena of a joint with clearance in a facile manner. However, two main problems still should be solved in building the continuous contact force model. First, the elastic force parts in previous continuous contact force models for a revolute joint were established by amending the force exponent of the Hertz spherical contact model or by the modified Winkler contact model. Nevertheless, the force exponent is usually given by experience, and the thickness of the elastic layer in the Winkler theory is difficult to determine. Second, for the previous damping force parts of a revolute joint, the hysteretic damping coefficients were obtained by substituting the stiffness coefficient with the contact stiffness of revolute joint directly instead of using the energy conservation method for the complicated form of elastic force model. A feasible continuous contact force model based on a fitting method was proposed to avoid these problems. According to the experimental results, the continuous contact force model can be used to predict the contact characteristics of a planar revolute joint in a facile manner.

Nonlinear Analysis of Single Model Piles Subjected to Lateral Load in Sloping Ground

Uncertainty associated due to soil-pile interface and unreliable assessment of the pile bearing capacity constructed in sloping ground have been cited as barriers to the wide utilizations of the deep foundations in sloping ground. Extensive studies were conducted concerning the failure mechanism of laterally loaded piles penetrated in horizontal ground. However, the number of studies regarding the pile in sloping ground is scarce in literatures. In this research, a detailed of numerical modelling using Winkler theory is discussed on the basis of finite element and experimental tests for models input parameters to examine the behaviour of the model piles penetrated in sandy soil subjected to lateral load. An Aluminium of open-ended model piles were utilized embedded in dense dry sloping sand of 1.5 horizontal to 1 vertical (1.5H: 1V). Three piles aspect's ratio of (18, 24 and 30) were selected to examine the behaviour of both flexible and rigid pile. The results revealed that lateral soil stiffness, effective passive wedge, flexural rigidity, EI, pile slenderness’ ratio (lc/d) and sand morphology as confirmed by scanning electronic microscopy, SEM observation play a key-role on the factors effecting the pile capacity and its lateral response.

An analytical approach to the deflection analysis of woven preforms and composites under tensile loading using the Winkler theory of curved beams

In this article, a new analytical approach for the deflection analysis of yarns in woven materials under tensile loading is presented. A unit cell of a warp yarn surrounded by adjacent weft yarns is modeled using curved beams. Next, using the Winkler theory of curved beams, the warp yarn strain energy under tensile loading is derived; followed by the implementation of the variational method to obtain the governing equations as well as related boundary conditions. The exact displacement field solution was found and using the continuity of deflection condition at crossover points, the normal inter-yarn contact force was estimated. In the proposed analytical approach, shear forces and potential slippage of yarns at contact points are neglected. The validation of the solution was checked by comparing results of a benchmark example on steel textile preforms to two sets of finite element simulations. For further evaluation of the approach, the uniaxial extension response of a polypropylene/glass woven fabric composite with a noncircular yarn cross section is also considered under large deformation and predictions are compared to earlier data in the literature.

Development of a higher order finite element on a Winkler foundation

Analyzing thick plates as a construction component has been of interest to structural engineering research for several decades. In particular, thick plates resting on elastic foundations are more specific. Mindlin's plate theory for thick plate analysis and the Winkler theory for elastic foundation analyses have wide applications. The current research considers analysis of isotropic plates on a Winkler foundation according to Mindlin's plate theory. The analysis uses a higher order plate element to avoid shear locking phenomena in the plate. The main features of this element are representation of real displacement functions of the plate perfect and shear locking do not occur at the plates modeled with this element. Derivation of the equations for finite element formulation for thick plate theory uses fourth-order displacement shape functions. A computer program using the finite element method, coded in C++, analyzes the plates resting on an elastic foundation. The analysis involves a 17-noded finite element. The study's graphs and tables assist engineers' designs of thick plates resting on elastic foundations. The study concludes with the computer-coded program, which allows effective use for the shear locking-free analysis of thick Mindlin plates resting on elastic foundations.

Deflection Analysis of Woven Composite Planes under In-Plane Loading

Deflection analysis of yarns of a bi-axial woven composite plate under tensional loading is investigated in this article. A unit part of the warp yarn which is limited by two adjacent weft yarns is modeled by a curved beam. Using the Winkler theory of curved beams, the strain energy under the tensile loading is derived. Initial shape of yarns is chosen to be arc shaped. The deflection analysis is accomplished by making use of energy method. First, the external work of the horizontal (or tensile) force and also the vertical contacting force is evaluated. Second, using the variational method the governing equations and boundary conditions are derived and then solved to find out the displacement fields exactly. Finally, making use of the continuity of the deflection of two contacting yarns at the contacting point the vertical contacting force is obtained. It must be mentioned that shear forces and slipping of contacting yarns are disregarded here. The validation of the work is performed by comparison of results with the semi circle beam (yarn) which is found in some usual text books.

Designing the cross-section of curved beams for equal magnitude of peak bending stresses

The paper discusses the problem of designing the cross-section of curved beams to achieve any desired ratio of the stress arising at the inner radius to that arising at the outer radius. A general design equation is developed which identifies the cross-sectional profiles enforcing that condition when the beam undergoes flexural and axial loads. Based on Winkler's theory for circumferential stresses, the equation shows the extent to which trapezoidal and triangular cross-sections can develop equal peak stresses for an assortment of loading conditions. Several three-dimensional finite element analyses of reference configurations are performed that confirm the theoretical findings.

Recommendations for the use of the coefficient of subgrade reaction

It has only been recently that computers were available to analyze the combined of structure and foundation, introducing more accuracy in structural analysis. Obviously, this technique involves the soil modeling as necessary. The model of the coefficient of subgrade reaction has been often used for this task. At last, the accuracy of the model depends on the agreement between predictions and soil behavior. The appropriate use of Winkler theory and the suitable determination of k are essential conditions for a good analysis. Unfortunately, manuals are not sufficiently concerned with this problem. The limits of this theory, some formulations for the determination of the k values and a few improvements of the model are described in this paper.

Pure bending of an I-section beam having initial curvature

From the two ‘approximate’ theories of bending—Elementary Theory and Winkler available to designers for the determination of bending stresses in beams having initial curvature, the Winkler approximate solution is the one closer to the exact solution development by Golovin.Timoshenko and Goodier show a comparison of stresses resulting from the three theories for a beam having rectangular cross-section. It is shown here that the values of bending stresses given by Winkler theory are very close to Golovin's exact results. The difference between the two theories lies in the range of 0·1–3·1 % increasing with the ratio, c/a, of the outer to inner radius of curvature of the beam. The above close relationship between the two theories for a beam of rectangular cross-section is also reported by Ford.