Dynamic Characteristics of Infinite and Finite Railways to Moving Loads

Some fundamental dynamic characteristics of a railway subjected to a harmonic or constant moving load are established and presented in this paper. The railway is modeled as an infinite or finite Timoshenko beam on viscoelastic foundation. The dynamic-stiffness matrices characterized by the complex wave numbers are employed to deal with this problem. The relationship between the forced frequency and the resonant velocity of the moving load, and the resonant frequency of the railway are especially emphasized and intensively discussed. The fundamental dynamic characteristics of a railway modeled as a Bernoulli-Euler Beam on viscoelastic foundation are also included for comparison.     

Substructure Simulation of Inhomogeneous Track and Layered Ground Dynamic Interaction under Train Passage

The vibrations in track and ground induced by train passages are investigated by the substructure method with due consideration to dynamic interaction between an inhomogeneous track system comprising continuous rails and discrete sleepers, and the underlying viscoelastic layered half space ground. Initially, the total system is divided into two separately formulated substructures, i.e., the track and the ground. The rail is described by introducing the Green function for an infinite long Euler beam both for moving axle loads action from a train and for reactions from sleepers. The ground is formulated by the layer transfer matrix approach for wave propagation along the depth. Subsequently, these substructures are integrated to meet the displacement compatibility and force equilibrium via inertia of sleepers and stiffness of railpad springs. The dynamic equations are solved in the frequency–wave-number domain by applying the Fourier transform procedure. Based on the assumption of a constant train speed, the time domain response is evaluated from the inverse Fourier transform computation. The dispersive characteristics of the layered ground and the moving axle loads lead to significantly different response features, depending on the train speed. The response is classified as quasistatic for a low speed, whereas it is dynamic for a high-speed situation. An illustrative case study is presented for Swedish X-2000 train track properties and ground profile.     

Seismic Performance of RC Bridge Column under Repeated Ground Motions

Seismic performance of reinforced concrete bridge column under repeated earthquake ground motions is investigated through shake-table experimentation on a scale model. The specimen is subjected to a series of simulated ground motions at different levels of shaking intensity. The deformation and damage evolution of the test column is addressed in terms of selected mechanical quantities including the effective stiffness, hysteretic energy dissipation, residual displacement, and dominant vibration frequency. The test column, designed according to the AASHTO seismic design specifications, survived successive ground motions by virtue of its outstanding energy-absorption and ductility capacity. Analysis of the experimental data indicates that structural degradation of the column closely correlates with its decreasing effective stiffness and increasing hysteretic energy dissipation. The residual displacement measured at the column top after each shaking event increases with the growth of damage in the column. A frequency-domain analysis of the vibration response of the column during successive ground motions indicates that increase in the structural degradation of the column results in a decrease in the dominant vibration frequency of the column.     

Train-Induced Vibration Control of High-Speed Railway Bridges Equipped with Multiple Tuned Mass Dampers

This paper deals with the applicability of multiple tuned mass dampers (MTMDs) to suppress train-induced vibration on bridges. A railway bridge is modeled as an Euler-Bernoulli beam and a train is simulated as a series of moving forces, moving masses, or moving suspension masses. According to the train load frequency analysis, resonant effects will occur as the modal frequencies of a bridge are close to the multiple of the impact frequency of the train load to the bridge. An MTMD system is then designed to alter the bridge dynamic characteristics to avoid excessive vibrations. Numerical results from simply supported bridges of the Taiwan High-Speed Railway (THSR) under real trains show that the proposed MTMD is more effective and reliable than a single TMD in reducing dynamic responses during resonant speeds, as the train axle arrangement is regular. It is also found that the inner space of a bridge box-girder of the THSR is wide and deep enough for installation and movement of MTMDs.     

Parameter Identification Procedure for Heterogeneous Viscoelastic Composites Using Iterative Functions

This paper presents a new numerical procedure for the determination of the viscoelastic compliance properties of a matrix phase from a simple three-point bending test on a composite beam. The composite is modeled as elastic inclusions randomly dispersed throughout a viscoelastic matrix. It is also assumed that the spatial distribution of the inclusions in the composite is known or can be determined. Zevin’s method of iterative functions is proposed for the determination of the matrix properties. Following a detailed explanation of the proposed scheme, a numerical verification is performed using three-dimensional finite-element (FE) analysis simulations. The proposed scheme was applied to the experimentally obtained creep compliance of the asphalt concrete beam. The obtained viscoelastic properties of the asphalt binder matrix phase were used as input into the FE model to simulate the behavior of the composite beam. An excellent comparison between the experimental data and the predicted beam deflections was observed. This shows that the proposed method is robust and it can be implemented to solve identification problems for viscoelastic composite materials.     

Field Monitoring of Roller Vibration during Compaction of Subgrade Soil

A field investigation was carried out with an instrumented vibratory roller compactor to explore the relationship between vibration characteristics and underlying soil properties, namely soil stiffness. The roller was outfitted with instrumentation to monitor drum and frame acceleration, as well as eccentric excitation force. Multiple consecutive passes were performed over six test beds on an active earthwork construction site to capture changes in roller vibration during compaction. Using lumped parameter vibration theory, soil stiffness was extracted from the roller data (drum and frame acceleration and drum phase lag). Both drum acceleration and drum phase lag were found to be very sensitive to changes in underlying soil stiffness. The drum–soil natural frequency of the coupled roller–soil system varied considerably and increased with compaction-induced soil stiffening. Phase lag always decreased with increasing soil stiffness, whereas drum acceleration trends depended on whether the excitation frequency was less than or greater than resonance. Roller-determined soil stiffness was found to be a function of the eccentric force, and heterogeneity in moisture, lift thickness, and underlying stiffness has a considerable affect on roller vibration behavior. When used as a proof roller, the instrumented roller identified soft areas in the embankment that were not identified by a static proof roll test.     

Concentrations of Pressure Between an Elastically Supported Beam and a Moving Timoshenko-Beam

The present paper is concerned with the motion of an elastically supported beam that carries an elastic beam moving at constant speed. This problem provides a limiting case to the assumptions usually considered in the study of trains moving on rail tracks. In the literature, the train is commonly treated as a moving line-load with space-wise constant intensity, or as a system of moving rigid bodies supported by single springs and dampers. In extension, we study an elastically supported infinite beam, which is mounted by an elastic beam moving at a constant speed. Both beams are considered to have distributed stiffness and mass. The moving beam represents the train, while the elastically supported infinite beam models the railway track. The two beams are connected by an interface modeled as an additional continuous elastic foundation. Here, we follow a strategy by Stephen P. Timoshenko, who showed that a beam on discrete elastic supports could be modeled as a beam on a continuous elastic Winkler (one-parameter) foundation without suffering a substantial loss in accuracy. The celebrated Timoshenko theory of shear deformable beams with rotatory inertia is used to formulate the equations of motion of the two beams under consideration. The resulting system of ordinary differential equations and boundary conditions is solved by means of the powerful methods of symbolic computation. We present a nondimensional study on the influence of the train stiffness and the interface stiffness upon the pressure distribution between train and railway track. Considerable pressure concentrations are found to take place at the ends of the moving train.     

Dynamic Stiffness of Foundations on Inhomogeneous Soils for a Realistic Prediction of Vertical Building Resonance

The aim of this contribution is a practice-oriented prediction of environmental building vibrations. A Green’s functions method for layered soils is used to build the dynamic stiffness matrix of the soil area that is covered by the foundation. A simple building model is proposed by adding a building mass to the dynamic stiffness of the soil. The vertical soil-building transfer functions with building-soil resonances are calculated and compared with a number of measurements of technically induced vibrations of residential buildings. In a parametrical study, realistic foundation geometries are modeled and the influence of incompressible soil, deep stiff soil layering, soft top layers, and increasing soil stiffness with depth is analyzed. All these special soil models reduce the resonant frequency compared to a standard homogeneous soil. A physically motivated model of a naturally sedimented soil has a stiffness increasing with the square root of the depth and yields a foundation stiffness that decreases with foundation area considerably stronger than the relatively insensitive homogeneous soil. This soil model is suited for the Berlin measuring sites and reproduces satisfactorily the experimental results.     

Performance of Geosynthetic-Encased Stone Columns in Embankment Construction: Numerical Investigation

This paper presents the results of a numerical investigation into the performance of geosynthetic-encased stone columns (GESCs) installed in soft ground for embankment construction. A three-dimensional finite-element model was employed to carry out a parametric study on a number of governing factors such as the consistency of soft ground, the geosynthetic encasement length and stiffness, the embankment fill height, and the area replacement ratio. The results indicate among other things that additional confinement provided by the geosynthetic encasement increases the stiffness of the stone column and reduces the degree of embankment load transferred to the soft ground, thereby decreasing the overall settlement. It is also shown that the geosynthetic encasement has a greater impact for cases with larger stone column spacing and/or weaker soil. Also revealed is that unlike isolated column loading conditions, full encasement may be necessary to ensure maximum settlement reduction when implementing GESCs under an embankment loading condition. Practical implications of the findings are discussed in detail.     

Nonlinear Interaction of Soil–Pile in Horizontal Vibration

This paper presents a new model for analyzing a nonlinear soil–pile interaction subject to horizontal shaking of a vertical circular pile embedded in a soil layer of finite thickness. The pile rests on bedrock with either a pinned or a clamped support. The soil mass is assumed composing of a “semi-nonlinear” inner soil zone around the pile and a linear viscoelastic soil zone outside the inner zone. When the inner soil behaves linearly, the present solutions are identical to those obtained by Nogami and Novak in 1977. Numerical results show that soil resistance of less slender piles developed against the vibration is larger than that of more slender piles. Soil resistance depends more strongly on the size of the nonlinear inner zone when the pile is vibrating at a frequency higher than the natural frequency of the soil. Soil nonlinearity, in general, results in a smaller damping and stiffness of the soil–pile system, except at high frequency. At higher vibration frequency, the situation can be very complicated. The exact value of the dynamic stiffness of the soil–pile system depends on elastic shear wave speed, soil nonlinearity, vibration frequency, slenderness ratio of the pile, magnitude of vibration, and tip conditions of the pile. Generally speaking, the dynamic stiffness is smaller than the static stiffness. The normalized dynamic stiffness for pile with a pinned tip is, in general, larger than that with a clamped tip, while the reverse is true for the damping.     

Passively Cooled Railway Embankments for Use in Permafrost Areas

Permafrost (permanently frozen ground) underlies approximately 25% of the world’s land surface. Construction of surface facilities in these regions presents unique engineering challenges due to the alteration of the thermal regime at the ground surface. Even moderate disturbance of the preexisting ground surface energy balance can induce permafrost thawing with consequent settlement and damage to roadway or railway embankments. Railway embankments are particularly susceptible to thaw settlement damage because of the need to maintain the alignment and even grade of the rails. The present work examines the heat transfer and thermal characteristics of railway embankments constructed of unconventional, highly porous materials. It is possible to produce a passive cooling effect with such embankments because of the unstable density stratification and resulting natural convection that can occur during winter months. The convection enhances the upward transport of heat out of the embankment during winter, thus cooling the lower portions of the embankment and underlying foundation soil. Numerical results have been obtained with an unsteady two-dimensional finite-element model that is capable of solving the coupled governing equations of pore air flow and energy transport. The numerical results are obtained for conditions typical of those found in railway configurations which allow open exchange of air between the embankment structure and the surrounding ambient air mass.     

Dynamic Response of Elevated High-Speed Railway

The study of the dynamic response of the elevated railway for the high-speed train in the Taiwan area at the preliminary design stage is presented. Two types of the elevated reinforced concrete railway, they being the simple-span and the three-equal-span box girders supported on piers; three types of the high-speed train, namely, the French T.G.V., the German I.C.E., and the Japanese S.K.S.; and the maximum operation speed 350 km∕h are under investigation. The general dynamic stiffness matrix of a damped Timoshenko beam is employed for the structural analysis. The influence line of any dynamic response (also called the dynamic influence line) of the elevated railway subjected to the high-speed train, considered as a series of the moving loads, is calculated by the mode-superposition method. A preliminary design of the section of the railway is proposed for this study.     

Dynamic Stiffness and Damping of a Shallow Foundation from Forced Vibration of a Field Test Structure

Foundation impedance ordinates are identified from forced vibration tests conducted on a large-scale model test structure in Garner Valley, California. The structure is a steel moment frame with removable cross-bracing, a reinforced concrete roof, and a nonembedded square slab resting on Holocene silty sands. Low-amplitude vibration is applied across the frequency range of 5–15?Hz with a uniaxial shaker mounted on the roof slab. We describe procedures for calculating frequency-dependent foundation stiffness and damping for horizontal translational and rotational vibration modes. We apply the procedures to test data obtained with the structure in its braced and unbraced configurations. Experimental stiffness ordinates exhibit negligible frequency dependence in translation but significant reductions with frequency in rotation. Damping increases strongly with frequency, is stronger in translation than in rocking, and demonstrates contributions from both radiation and hysteretic sources. The impedance ordinates are generally consistent with numerical models for a surface foundation on a half-space, providing that soil moduli are modestly increased from free-field values to account for structural weight, and hysteretic soil damping is considered.     

Three-Dimensional Model for Analysis of Stiffness and Hygroexpansion Properties of Fiber Composite Materials

A three-dimensional model for stiffness and hygroexpansion of fiber and particle composite materials is presented. The model is divided into two steps, first a homogenization of a single fiber with a coating representing the matrix material, then a network mechanics modeling of the assembly of coated fibers that constitutes the composite material. The network modeling is made by a fiber orientation integration including a linear and an exponential interpolation between the extreme case of homogenous strain and the extreme case of homogenous stress. A comparison between the modeled prediction and measurement data is made for stiffness, Poissons ratio, and hygroexpansion. The matrix material is assumed to have isotropic properties and the fiber or particle material may have arbitrary orthotropic properties.     

Natural history of paroxysmal nocturnal hemoglobinuria in adolescents,adults, and children: the Mexican experience

The mechanical properties of a contracting smooth muscle can be changed by changing its length. A viscoelastic material model was developed to predict the length-dependent stiffness changes when a constrained muscle is allowed to shorten under a constant external force. Three-dimensional finite element simulations were carried out to estimate the stiffness changes and compared to available experimental data. A good agreement was found indicating that the viscoelastic material model developed gives a valid representation of the length dependent stiffness changes of a smooth muscle. Sensitivity analysis was carried out to determine the relative effects of material constants in the model on the length dependent stiffness.     

Deformation Characteristics of Ventiduct Embankment on Qinghai-Tibet Railway

The Qinghai-Tibet railway, the highest railway in terms of elevation, was built under the harshest of weather conditions in the world. A new technique, called the ventiduct embankment, was used for the first time in railway construction in the Qinghai-Tibet permafrost region of China to overcome the specific difficulties of the permafrost plateau. To evaluate its effectiveness, several full-scale test embankments were constructed at a representative field site, the Qingshuihe experimental section. The effectiveness of the ventiduct embankment structure has been verified by comparing it with the performance of the nearby control embankment in terms of permafrost table, settlement, and thaw depth. These observations are presented in this paper. The ventiduct embankment structure based on this study has been adopted in Qinghai-Tibet permafrost railway construction.     

Three-Dimensional Linear Behavior of Bituminous Materials: Experiments and Modeling

The linear viscoelastic properties of bituminous mixtures are used to design pavement structure. Usually, only complex moduli E* (complex Young modulus) or G* (complex shear modulus) characterizing the stiffness of the materials in one direction (1D) are measured by classical tests. In this paper, the three-dimensional (3D) behavior is investigated. The complex Poisson's ratio (ν*) is introduced. Its evolution with temperature and frequency is studied for a bitumen, a mastic, and a mix. Experimental results show that the time–temperature superposition principle is applicable in the 3D case. The same shift factor applies for E* and ν*. The Di Benedetto–Neifar model developed at Ecole Nationale des Travaux Publics de l’Etat to simulate so far the 1D thermo-elastoviscoplastic behavior of bituminous materials has been extended to simulate their 3D isotropic behavior. Calibration of the model and comparison between simulations in the linear viscoelastic domain and experimental data are proposed.     

In Situ Test on Cooling Effectiveness of Air Convection Embankment with Crushed Rock Slope Protection in Permafrost Regions

An experimental air convection embankment (ACE) was constructed in Beiluhe on the Qinghai-Tibet Plateau during 2001–2003, using coarse (5–8 and 40–50 cm), poorly graded crushed rock fill material on the slope of embankment with thick ground ice permafrost foundation, which should be called the air convection embankment with crushed rock slope protection (ACE–CRSP). The highly permeable ACE–CRSP installation was designed to test the cooling effectiveness of ACE–CRSP concept in an actual railway project. Ground temperature data were collected from test sections on the railway with thermistor sensor strings. The results showed that the mean ground temperature under the layer of the crushed rock with coarse particle diameter of 40–50 cm was lower than that under one with finer particle diameter of 5–8 cm, and the fluctuating range of temperature under the former was bigger than that under the latter. It was obvious that the maximum thaw depth was raised under the layer of crushed rock with coarse particle diameter of 40–50 cm, which resulted from the stronger cooling effectiveness of air convection during the winter. The amount of heat exchange also showed that the absorbed cooling energy of the foundation, under the layer of the crushed rock with coarse diameter, was larger than that with finer diameter.So, we believe that the cooling effectiveness of the crushed rock layer with coarse diameter was stronger than that one with finer diameter.     

Design Charts for Piles Supporting Embankments on Soft Clay

This paper describes the development and application of design charts for piled embankment designs. It outlines the computational approach adopted, the geotechnical profiles used, and the application of the design procedure using the charts. The soil profile used for the charts is representative of a Malaysian soft clay profile, involving a more or less normally consolidated soil, with a strength and stiffness that varies linearly with depth. Such a profile is typical of the ground conditions in a variety of countries in the Southeast Asian region. The design charts address the issues of pile capacity, settlement due to embankment load, settlement due to a temporary piling construction platform, and lateral response of piles near the edge of the embankment. The charts consider variations in ground conditions, embankment height, pile length, and pile spacing. An illustrative example is given to demonstrate the use of the charts.