Elastic Subgrade Research Articles

THREE-DIMENSIONAL THERMO-HYDRO-MECHANICAL DYNAMIC ANALYSIS OF A HALF-SPACE UNDER FRACTIONAL ORDER THEORY OF THERMOELASTICITY

To permit understanding and improvement of subgrade load bearing performance, this paper presents the analysis of a three-dimensional (3D), half-space, elastic subgrade coupling of multi-fields using normal mode analysis (NMA) under Ezzat's fractional order generalized theory of thermoelasticity. Using this method, the analytical equation can be divided into two parts, and the analysis is done with neither integral transformation nor inverse transformation, thereby increasing the speed of decoupling and eliminating the limitation of numerical inverse transformation. The influence of fractional order parameter, load frequency, and permeability coefficient on the thermo-hydro-mechanical dynamic (THMD) coupling media is analyzed for two loading protocols, including thermal impact and normal load. The distributions of the dimensionless vertical displacement, temperature, stress, excess pore water pressure, and strain in the porous structure are analyzed and discussed in detail. The results of the analysis show that the load frequency plays an important role in determining the result values of all dimensionless physical variables. The fractional order parameter only has a significant effect on the calculations of physical variables of the upper surface subjected to thermal impact, and the permeability coefficient mainly affects the stress, strain, and excess pore water pressure. The developed computational method can improve the decoupling speed without any transformation, and it eliminates the limitation of numerical inverse transformation. The method has wide potential application in many engineering fields.

Study on mechanism and application of PFWD for subgrade quality detection: semi-analytical approach and experiment

The mechanism and possible application of Portable Falling Weight Deflectometer (PFWD) for subgrade quality control are investigated by different methods, including semi-analytical simulation, laboratory test, and field test. A layered elastic subgrade model is proposed to consider the stress dependency of subgrade soil under PFWD loads. The elastic modulus of each layer is determined referring to the distribution of stress state along with the depth and laboratory dynamic triaxial test data. It is found that the effective test depth of the PFWD device in the present study is 0.6 m using the analytical model. Furthermore, based on the same static homogeneous elastic half-space theory, the relationship between the test results of PFWD and the Benkelman Beam method is investigated through field tests. Using this relationship, the PFWD is then adopted to evaluate the compaction quality of two sections of the subgrade with different rolling times.

Research of deformation law about guide rails under the action of mining deformation in mine vertical shaft

To lay a foundation for alleviating the influence of mining shaft deformation (MSD) on the guide rail (GR) and monitoring the shaft deformation state, this paper studies the deformation law and mechanism of the guide rail under the MSD. Firstly, a spring is used to simplify the interaction between the shaft lining and surrounding rock soil mass (SRSM) under MSD, and its stiffness coefficient is deduced by the elastic subgrade reaction method. Secondly, a simplified finite element model is established based on spring element, the stiffness coefficient is calculated by the derivation formula, and its effectiveness is verified. Finally, the deformation law and mechanism of GR are analyzed under different types and degrees of MSD, and the deformation characteristics are studied under the disconnection between the shaft, bunton and guide rail. The results show that the established finite element model can better simulate the interaction between the shaft lining and SRSM, and the calculation efficiency is greatly improved. The guide rail deformation (GRD) has a strong ability to characterize MSD and owns the distinctive feature corresponding to different types and degrees of MSD and the connection state. This research can provide reference and guidance for the shaft deformation monitoring and the maintenance and installation of the GR, and also lays a groundwork for studying operation characteristic of hoisting conveyance under MSD.

Study on Design Method of Pile Wall Combination Structure in a Deep Foundation Pit Considering Deformation Induced by Excavation

The technology of pile wall combination in a deep foundation pit is a kind of technology to resist soil and water pressure by using the great stiffness of the retaining pile and basement wall. As a part of basement wall, the retaining pile can reduce the thickness of the basement wall. However, the influence of excavation deformation and the interaction mechanism between the retaining pile and basement wall are ignored in the current design theory of the pile wall combination in a deep foundation pit. Therefore, we proposed a composite structure model of an elastic subgrade beam associated with a continuous beam, and introduced an elastic spring to simulate the interaction between the pile and basement wall. The finite difference equation and calculation method were established to figure out the internal force and displacement of the pile wall combination structure, which was able to accurately calculate the internal force and deformation of the retaining pile during the excavation stage. Based on the above results, further investigation was carried on the interaction between the pile and basement wall during the construction and normal service stage of the basement structure. It was concluded that the basement wall could reduce the lateral displacement on the top of the retaining pile caused by removal of the strut and affect the bending moment of the upper part of the retaining pile among the depth of the basement wall. The bending moment of the basement wall was closely related to the deformation of the retaining pile and changes with the working condition. In addition, the results of factor sensitivity analysis showed that the pile-wall relative stiffness ratio, stiffness of the horizontal beam, and slab of the basement had a significant influence on the interaction between the pile and basement wall.

Numerical Analysis of Laterally Loaded Long Piles in Cohesionless Soil

The capability of piles to withstand horizontal loads is a major design issue. The current research work aims to investigate numerically the responses of laterally loaded piles at working load employing the concept of a beam-on-Winkler-foundation model. The governing differential equation for a laterally loaded pile on elastic subgrade is derived. Based on Legendre-Galerkin method and Runge-Kutta formulas of order four and five, the flexural equation of long piles embedded in homogeneous sandy soils with modulus of subgrade reaction linearly variable with depth is solved for both free- and fixed-headed piles. Mathematica, as one of the world's leading computational software, was employed for the implementation of solutions. The proposed numerical techniques provide the responses for the entire pile length under the applied lateral load. The utilized numerical approaches are validated against experimental and analytical results of previously published works showing a more accurate estimation of the response of laterally loaded piles. Therefore, the proposed approaches can maintain both mathematical simplicity and comparable accuracy with the experimental results.

The method of compensating loads for solving of problems of cyclic symmetrical flexure of anisotropic plates, resting on an elastic subgrade

The purpose of the study - receiving of exact analytical solutions of statics problems of anisotropic plates, resting on an elastic subgrade and subjected to an action of cyclic symmetrical loads. The method of compensating loads is used for solving of the formulated problems. The basic and the compensating solutions are determined. The new approach, connected with the use of Nielsens equation for receiving of the solutions, is applied. For the first time by means of the method of compensating loads the exact analytical solutions of the cycle symmetric flexure of anisotropic circular plates, resting on the elastic subgrade, are received. Various boundary conditions and the loads, distributed along circumferences and over ring surfaces, are considered. The problem of anisotropic infinite plate with the circular opening, resting on the elastic subgrade, is also examined. All the solutions are obtained in the closed form and expressed in terms of Bessel functions.

The effect of subgrade reaction modulus on the nonlinear behavior of reinforced concrete plates

The research investigates the nonlinear behavior of reinforced concrete plates based on soil by using the finite elements method. This investigation has done by using computer program (DARC3) that mean Dynamic Analysis of Reinforced Concrete in 3D which is written in (FORTRAN) language and it is modified in this study to include the effect of elastic subgrade reaction soil using Winkler’s method under effect of different static loads. 20-node isoparametric brick elements are used to represent the nonlinear behavior of reinforced concrete plate, the reinforcement idealized by smeared layer within brick elements, assuming perfect bond between the steel and the concrete. The finite elements results are obtained the load-deflection response. The effects of boundary conditions, plate thickness, type of load and the modulus of vertical subgrade reaction of the soil layer are studied, it is shown that in case of increasing the subgrade reaction values and plate thickness lead to decreasing in the deflection and vice versa. Also it is shown that the fixed boundaries give less deflection than that in case of simply supported boundaries. The results obtained from this study are compared with the previous study, and good agreements results are obtained with percentage (1.52%).

THE ENGINEERING METHOD FOR UNIFYING GROUND FLOOR SLAB SETTLEMENTS

For industrial buildings and logistics centres truck lifts are usually used. Therefore, there are special requirements for flatness tolerance of ground floor. The ground floor settlements differences in selected distances are limited. The article reviews the behaviour of soils and the importance of the actual behaviour assessment of soils during the design of floor slab on elastic subgrade. Particular attention is given to the behaviour of floor slab areas above pile foundations that support the building’s columns. Calculation results show the impact of subgrade stiffness on the behaviour of the floor slab, especially in areas above pile foundations, where the stiffness of subgrade is much higher. The article presents a solution for achieving the required level of settlements’ differences in areas where pile foundations for the building’s columns under the ground slab are used. The paper proposes an efficient engineering method to reduce ground slab settlements differences. The results of performed calculations confirm the efficiency of presented method.

Nonlinear Dynamics of the Rigid Drum for Vibratory Roller on Elastic Subgrades

In this paper, a coupling nonlinear dynamic model of the drum and subgrade is established for the vibratory roller. The dynamic characteristics of the rigid drum of the vibratory roller in the process of vibratory compaction are comprehensively investigated by time history, phase diagram, frequency spectrum, Poincare map, and bifurcation diagram. During the compaction process, the stiffness of the subgrade increases and the motion of the rigid drum of the vibratory roller changes from a single period to multiple periods and finally enters chaos by the way of period doubling. Moreover, the roller parameters also significantly affect the dynamic characteristics of the rigid drum and the compaction effect of the subgrade. Based on detailed numerical results, a parameter adjustment strategy about the roller frequency and nominal amplitude is proposed, which can avoid the “bouncing” of the drum during compaction and improve the compaction efficiency.

Modeling of Utility Tunnels as Thin-Walled Beams on an Elastic Subgrade

In the construction of municipalities and agglomerations, it is necessary to build utility tunnels and other linking underground structural systems. They enable the interconnection of individual buildings for different types of media. For the purposes of the static analysis, the tunnels’ structure can be considered to be a thin-walled beam on an elastic subgrade. The article deals with the analysis of thin-walled beam loaded by bending and torsion. Differential equations and their software solution using the transfer matrix method have been presented. In conclusion, an example of utility tunnels as thin-walled beams on an elastic subgrade has been shown. A solution of a beam using the theory of thin-walled beams has been compared with the solution of shell finite elements using the Finite Element Method.

Analytical formulation and finite-element implementation technique of a rigorous two-parameter foundation model to beams on elastic foundations

ABSTRACT A simple way of computer implementation of an effective two-parameter subgrade model for the routine analysis of flexible foundations on an elastic subgrade is presented. It is based on a rigorous analytical subgrade model recently proposed by one of the authors that takes full account of the soil–structure interaction. The details of both finite element (FE) and analytical implementation of the model to beams are presented. Fully established closed-form relationships are provided for the subgrade parameters. The essence in the method is that the soil shear resistance within the loaded region is transferred to the foundation element as an additional rigidity in form of a geometric stiffness, thereby leaving the Winkler spring bed to take care of the vertical compression as accustomed. Additional edge springs are introduced to account for the edge forces due to the shear continuity extending beyond the edges. By so doing, the attractiveness of the long-enduring Winkler’s model is maintained, whereas the missing shear interaction is taken care of through the introduction of the geometric stiffness and the edge springs. The FE discretisation is thus limited to the foundation unit alone as initially intended. Subject classification codes: soil–foundation interaction

EQUATION DECOMPOSITION METHOD FOR SOLVING OF PROBLEMS OF STATICS, VIBRATIONS AND STABILITY OF THIN-WALLED CONSTRUCTIONS

The work suggests the effective equation decomposition method (EDM) for solving of statics, vibrations and stability problems of thin-walled constructions. This method is based on the partition of the initial problem on the consideration of more simple auxiliary problems. The additional unknown functions are introduced for definition of the sought solutions. The paper shows the method’s advantages on the examples of the boundary value problems for rectangular areas. The problem of anisotropic plate resting on an elastic subgrade and subjected to an action of expanding forces acting in the middle surface and to transverse loads is under study. The plate’s edges are elastically supported. Also free vibrations of the rectangular plates of variable thickness with different boundary conditions were under consideration. The approximate analytical solutions with high exactness are obtained.

A Novel Integrated Approach to Solve Industrial Ground Floor Design Problems

The ground floors of buildings usually have high loads from racks and other storage equipment in industrial buildings and logistics centers. Such types of buildings commonly require lift trucks. Therefore, there are special requirements for flatness tolerance across and along the driving track of truck lifts. Structural design solutions must be optimized and sustainable. The article reviews the behavior of soils and the importance of the actual behavior assessment of soils during the design of the ground floor on the elastic subgrade. The behavior of the ground floor’s areas above pile foundations that support the building’s columns is essential. Calculation results show the impact of subgrade stiffness on the behavior of reinforced concrete (RC) floor slab, especially in areas above pile foundations, where the stiffness of subgrade is much higher. The research provides a solution to achieve the required level of settlement dissimilarity in areas where there are piles underneath a building slab under the columns. The paper proposes a new integrated method for the evaluation of the subgrade reaction coefficient above the pile cap. The proposed method optimizes design time and eliminates the need for specialized geotechnical software. Obtained results confirmed the efficiency of the proposed design method.

Downwards force–displacement response of buried pipelines during dip–slip faulting in sandy soil

In the numerical analysis of underground pipelines against dip-slip faulting, it is common practice to model the problem as a beam surrounded by soil-equivalent nonlinear springs. Previous studies have recognised the importance of the vertical bearing soil springs (VBSS) in the modelling of pipe–fault interaction. Nevertheless, prior studies on VBSS are limited. This study presents an analytical framework for determining a hyperbolic force–displacement (P–y) curve for VBSS in dry sand. This hyperbolic criterion was established based on the ultimate bearing resistance (UBR) of pipe and the elastic subgrade modulus of the soil. Different mechanisms such as flow, arching, bearing, and friction, and various parameters like soil compressibility, pipe–soil relative stiffness, and soil elastic properties have been used in the determination of these two parameters. The P–y curves were verified and calibrated with experimental data. More reliable curves have been obtained compared to the existing methods. A numerical study was also performed to compare the current study with a pipeline seismic design guideline. The results of the current study method are in good agreement with sample experimental data compared to the seismic guideline.

Concrete slab on elastic foundation under one axle load

The paper is dedicated to the dynamical analysis of an isolated concrete slab on an elastic foundation to moving load effect of one axle load. The computational models of one axle load and a slab are mathematically described by the system of ordinary differential equations. The equations of motion are solved numerically in the environment of program system MATLAB. The plate response and dynamic load are monitored at a certain speed and certain initial conditions, depending on the properties of the elastic subgrade.

ANALYSIS OF COMBINED PLATES WITH ALLOWANCE FOR CONTACT WITH ELASTIC FOUNDATION

The paper covers the problems of combined plates with circular base and consisting of a few sections with different laws of thickness variation. Analytical methods of analysis of similar structures are not yet devel­oped. The present work suggests the analytical method for solving of the stated problems, the contact with the elas­tic subgrade is also considered. The above-mentioned approach is shown on the example of the analysis of the bot­tom of the cylindrical reservoir, resting on the elastic subgrade. The inner part of this construction is represented by the ring plate of variable thickness which increases along the direction from the internal boundary. The outer part is represented by the ring plate of the constant thickness. The influence of the elastic basis and the upper part of the reservoir is taken into consideration. The solutions for stresses and deflections of the combined plate are given in closed form in terms of Bessel functions. The conditions of the plate’s sections conjugation are fulfilled.

Temperature and material behaviour effects on dynamic responses of asphalt concrete trackbed

ABSTRACTDeveloping a simulation model for railway subgrades is an important initial step towards a reliable design for a dense-graded asphalt concrete trackbed. This paper presents a comparative simulation study of the dynamic responses in terms of tensile strains and vertical displacements of the elastic and viscoelastic subgrade surface materials affected by different thermal loadings using the finite element method. The simulations for all conditions were performed with a train speed of 350 km/h. The relationship between different thermal loads and dynamic responses of the railway track materials in terms of tensile strain and vertical displacement was defined. This relationship indicated that the resultant tensile strains and vertical displacements for the viscoelastic material were greater than those of the elastic material at the same thermal load.

METHOD OF COMPENSATING LOADS FOR SOLVING OF A PROBLEM OF UNSYMMETRIC BENDING OF INFINITE ICE SLAB WITH CIRCULAR OPENING

Unsymmetric flexure of an infinite ice slab with circular opening is under examination. The men-tioned construction is considered as an infinite plate of constant thickness resting on an elastic subgrade which properties are described by Winkler’s model. The plate’s thickness is variable in the area ajoining to the opening. Method of compensating loads is used. Basic and compensating solutions are received. The obtained solutions are produced in closed form in terms of Bessel functions.

Viscoelastic Nonlinear Multilayered Model for Asphalt Pavements

AbstractFlexible pavements are multilayer structures, typically with a viscoelastic asphalt layer followed by nonlinear unbound/bound layers. Conventionally, multilayered elastic analysis is performed to obtain the response of flexible pavements for design and inverse analyses; however, assuming asphalt pavement to be a linear elastic material is an oversimplification of its actual behavior. It is well known that the responses of asphalt pavements are both rate and temperature dependent. In the present work, a computationally efficient model has been developed to analyze flexible pavements, considering the top layer of linear viscoelastic asphalt concrete (AC), followed by a stress-dependent (nonlinear) base layer, and an elastic subgrade. Constitutive equations are formulated for layered viscoelastic–nonlinear axisymmetric systems. It is shown that the developed model can be used to simulate pavement response under stationary or transient loading. A comparison between the model responses and results obta...

Ring foundation on elastic subgrade: an analytical solution for computer modelling using the Lagrangian multiplier method

In the practice of geotechnical engineering, the case of a ring footing carrying a set of concentrated point loads is a common problem. At times, the induced vertical and angular displacements for the ring footing need to be evaluated at a relatively precise level. By making use of the governing set of equations derived for the case of a general curved beam, expressions that can be easily implemented in modern computing software are derived for the vertical and angular displacements of a ring footing of rectangular cross section as functions of the radial position. The loading case considered is a vertical point load, and the soil is modelled as elastic. Estimates of the displacements have been shown for a common range of practical applications. The behaviour for a set of concentrated loads may be evaluated using the derived equations through direct superposition. Nonlinear finite element analysis is used to evaluate the vertical deflection and angular twist of the ring foundation. Numerical analysis performed for three ring foundations with different radii and cross sections is reported to validate the accuracy of the derived analytical solution. Copyright © 2016 John Wiley & Sons, Ltd.