Elastic Half-space Foundation Research Articles

Comparative study on dynamic responses of ballasted and ballastless tracks at critical velocity

High-speed railways are becoming ubiquitous worldwide, demanding increased operational speeds. Yet, as trains near critical speeds, dynamic stress and embankment displacement escalate, jeopardizing safety. While significant strides have been made in studying these critical speeds, capturing the dynamic characteristics of all track responses remains elusive. This study presents a coupled train-track-ground model employing a 2.5D finite element approach integrated with a nonlinear soil model to investigate the influence of embankment and foundation properties on the critical speeds for both ballasted and ballastless tracks. The research resulted in the development of unified Dynamic Amplification Factor curves that consistently represent the dynamic behavior of various tracks as observed in multiple studies. Additionally, the applicability of simplified theoretical models for calculating critical speeds, such as the elastic half-space foundation and track-foundation models, was assessed. The findings suggest that the simplified models are suitable only under specific conditions. This research provides valuable perspectives on optimizing train speeds and ensuring the safety of diverse track types.

Bending Analysis of Stepped Rectangular Plates Resting on an Elastic Half-Space Foundation

In this paper, the bending behavior of rectangular plates with stepped thickness resting on an elastic half-space foundation is investigated through an analytic method. Combined with the bending theory of the rectangular thin and moderately thick plate, the stepped rectangular plate is divided into upper and lower plates, and the Fourier series is used to obtain the analytical solution of the deflection of the plate and the interaction force between the plate and foundation. The influence of the elastic modulus of the plate, plate theory, and the dimension of the plate on the deflection of the stepped rectangular plate is also discussed. The results show that the analytical solution is basically the same as the existing research results, and it is also verified by the analysis results of the models established by ABAQUS software. The deflection at the center of the stepped rectangular plate increases with the increase of the elastic modulus of the upper plate and the decrease of the side length of the upper plate, while the plate theory has little effect on the deflection of the plate. This method not only overcomes some of the disadvantages of numerical methods but also eliminates the assumptions of the Winkler foundation model and the two-parameter foundation model, thus obtaining a more reasonable and accurate bending performance of the stepped rectangular plate resting on the elastic half-space foundation.

Influence analysis of the selection of foundation model on fatigue stress evaluation results of cement concrete pavement-based on GPR and FWD

• The internal structural condition of the pavement was analyzed by FWD and GPR. • The applicability of different foundation models to cement pavement was analyzed. • The specific influence of h c , E c , E t on load and temperature stress was analyzed. This study showed a method of selecting appropriate foundation models for fatigue stress analysis of cement concrete pavement. Based on the strength and damage conditions of the base and the correlation between the crack rate of the base ( C b ) and modulus of the base ( E t ), the integrity and stiffness of the base were evaluated. Moreover, the applicability of the base to the Winkler foundation model and the elastic half-space foundation model for each road section was clarified based on the evaluation results. The cement concrete pavement's load stresses and temperature stresses under different technical conditions were calculated by combining the parameters of the thickness of the cement concrete surface layer ( h c ), modulus of the cement concrete surface layer ( E c ), and E t of each road section and the compatible foundation models. The effects of the changes of parameters h c , E c , and E t on the load and temperature stresses of cement concrete surface layers under different foundation models were also investigated. It was observed that the effects of E c and E t on the temperature stresses of the cement concrete surface layer are more pronounced compared to h c . h c is the parameter that has the most significant influence on the internal load stress of the cement concrete surface layer. The Winkler foundation model is more sensitive to the change in h c , and the Elastic half-space foundation model is more sensitive to the change of E c and E t . No matter what kind of technical condition the pavement is and what type of foundation model is adopted, the influence degree of each structural parameter on the load stress of the cement concrete surface layer is not different obviously, and the influence ratio is relatively stable. However, for the temperature stress, under different pavement technical conditions, the changing amplitude of temperature stress caused by the changes of h c , E c , and E t is significantly different, and the greater the h c is, the greater the influence of the changes of h c , E c , and E t on the temperature stress is.

Impact response of reinforced concrete slabs in elastic half space

The analysis of the mechanical behaviour of reinforced concrete slabs on elastic foundation under impact loads is of great significance in the construction and protection of concrete pavements in airports. Based on the Elastic Half-space Foundation Model and Concrete Damage Plasticity Model, the displacement and stress fields of reinforced concrete slabs under impact loading are numerically simulated by explicit nonlinear finite element method. The result can be used to design and evaluate the safety of foundations and reinforced concrete slabs under impact loads.

Time Effects on Settlement of Rigid Pile Composite Foundation: Simplified Models

The behavior of pile composite foundation is studied using the flexibility method. During the analysis, determination of the flexibility matrix (settlement) is critical. However, conventional methods of Winkler and elastic half-space foundation models are incapable of considering the time effects of soil consolidation and creep. The foundation model of Zaretsky and Tsytovich [1965] can be used to evaluate settlement for unsaturated soils, but the complexity of numerical integration over an arbitrary loading area hinders its application. In this paper, a novel scheme is proposed for numerical integration by rotating the loading surface using the equiareal transformation technique. Therefore, a simplified closed-form solution is developed to calculate time dependent settlement for foundation soils. The efficacy of the proposed technique is demonstrated using illustrative examples of an elastic half-space, a rigid raft foundation without piles, and rigid pile composite foundations with multiple piles under surface loading. Furthermore, parametric study is conducted to evaluate the sensitivity of model parameters. The permeability [Formula: see text] and Poisson’s ratio [Formula: see text] are found to be important, whereas pore pressure coefficient [Formula: see text] and degree of saturation [Formula: see text] are less significant in the calculation.

A study on launch site ground of vehicle-mounted missile based on elastic layer theory

With the widespread use of the vehicle-mounted missile launching system, the research of launch site ground becomes very important. The loading of missile launch system under the supporting disk is similar to inverted bell, and its radius and size of the missile launching are much more than a car. So the ready-made equivalent modulus formula under the action of circular uniformly distributed loading is not suitable for the calculation of launch site ground of vehicle-mounted missile. Therefore, based on the elastic layered system and the Gauss–Legendre numerical calculation method, a new calculation method of equivalent modulus is proposed, as well as the regression formulation for calculation of equivalent modulus of foundation is also shown. Based on the above analysis, a launch site ground mechanical model is presented. The thin plate model on elastic half-space foundation was formulated taking into account normal direction and the double-layer elastic system model was proposed for in tangential direction. Validity of the model was done by coring the programming calculation with the finite element numerical simulation for selected cases.

A New Form of the General Solution of the Elastic Space Axisymmetric Problem in Pavement Mechanics

In order to analyze the stress and displacement of pavement, a new form of the general solution of the elastic space axisymmetric problem is proposed by the method of mathematics reasoning. Depending on the displacement function put forward by Southwell, displacement function is derived based on Hankel transform and inverse Hankel transform. A new form of the general solution of the elastic space axisymmetric problem has been set up according to a few basic equations as the geometric equations, constitutive equations, and equilibrium equations. The present solution applies to elastic half-space foundation and Winkler foundation; the stress and displacement of pavement are obtained by mathematical deduction. The example results show that the proposed method is practically feasible.

A Semi-Analytical Solution of Single-Phase Elastic Foundation Three-Dimensional Static Characteristics

Based on the single-phase elastic soil medium control equations and boundary conditions [1], by using the weighted residual method, a semi-analytical theory of elastic foundation three-dimensional static response was established. When the uniformly distributed loads were applied on the elastic half space foundation, the change rules of vertical displacement, lateral displacement, lengthways displacement were analyzed numerically, and compared with the theoretical solution [2]. The result shows that foundation displacements are completely symmetrical or antisymmetrical about x = 0 plane and y = 0 plane. The maximum vertical displacement appears in the center of load range, the maximum lateral and lengthways displacements appear at the edge of load range, and the displacements get smaller far from the loads.

A BEM solution for plates on elastic half-space with unilateral contact

The method developed to analyze the stress and deflection of plates on unilateral foundation is different from the traditional method. The behavior of plates on unilateral foundation belongs to that of free-boundary problems. It has been proved effective to solve the problems of free-boundary using the linear complementary equation method. In this paper, a boundary element–linear complementary equation is derived according to contact theory. This equation is used to analyze plate-bending on elastic half-space foundation, especially considering the impact on the internal force and displacement of plate, which is caused by the neighboring loads acting on the foundation around the plate. The effectiveness of the method is illustrated by numerical results.

The seismic responses of structure-viscoelastic foundation systems in time domain and power spectra

This paper predicts the seismic responses of building-embedded foundation systems, using the seismic records of Lotung (Taiwan) — large scale seismic test (LSST), in time domain and power spectra. The seismic responses of the structure founded on the elastic half-space foundation are overestimated resulting in underestimating the soil damper. Accordingly, an analytical model of viscoelastic half-space, as the hysteretic damping effect of nonlinear soil, is developed. The proposed model can simulate the seismic behavior of the records of LSST of three strong earthquakes that hit the eastern coast of Taiwan in 1986.

Infinite spline boundary element method and its application to structure-foundation interaction

In view of the infinity behaviors of 3-D Kelvin solution, we constructed an infinite spline boundary element which has fine precision in the analysis of the half space foundation subjected to uniform pressure on the circular domain. We also analysed a square plate resting on elastic half space foundation. The results indicate that this model not only fits for the coupled analysis of foundation and structures but also has the advantage of fewer degrees of freedom and fine precision.