Moving Surface Loads Research Articles

Micro‐Mechanical Analysis for Residual Stresses and Shakedown of Cohesionless‐Frictional Particulate Materials Under Moving Surface Loads

AbstractResidual stresses and shakedown have been successfully presented by two‐dimensional numerical experiments based on the discrete element method (DEM), wherein a cohesionless‐frictional material under moving surface loads was replicated through irregular‐shaped particles. With surface loads below the shakedown limit, both permanent deformations and residual stresses cease to accumulate and the numerical structure shakes down after a number of load passes. Corresponding micro‐mechanical analyses indicate that strong forces and normal forces make a dominant contribution to residual stresses. Besides, averaged magnitudes of interparticle forces and corresponding total contact numbers initially change with load passes, and their final variation trends will differ as the structure shakes down or not. Furthermore, polar distributions of interparticle forces and contacts have been presented, and variations of their preferential orientations were emphasised. Lastly, the fabric tensor and anisotropy of resultant forces were studied, presenting the anisotropy weakening of macro‐stress fields, induced by developments of residual stresses.

Micro-mechanical analysis of residual stresses in cohesive-frictional particulate materials under moving surface loads

Micro-mechanical analysis of residual stresses in cohesive-frictional particulate materials under moving surface loads

Seismometer Records of Ground Tilt Induced by Debris Flows

ABSTRACT A change in surface loading causes the Earth’s surface to deform. Mass movements, such as debris flows, can cause a tilt large enough to be recorded by nearby instruments, but the signal is strongly dependent on the mass loading and subsurface parameters. Specifically designed sensors for such measurements (tiltmeters) are cumbersome to install. Alternatively, broadband seismometers record translational motion and also tilt signals, often at periods of tens to hundreds of seconds. Their horizontal components are thereby the most sensitive to tilt. In this study, we show how to obtain tilt caused by the passing by of debris flows from seismic measurements recorded within tens of meters of the flow and investigate the usefulness of this signal for flow characterization. We investigate the problem on three scales (1) large-scale laboratory experiments at the U.S. Geological Survey debris-flow flume, where broadband seismometers and tiltmeters were installed for six 8–10 m3 experiments, (2) the Illgraben torrent in Switzerland, one of the most active mass wasting sites in the European Alps, where a broadband seismometer placed within a few meters of the channel recorded 15 debris-flow events with volumes up to 105 m3, and (3) Volcán de Fuego, Guatemala, where a broadband seismometer recorded two lahars. We investigate how the tilt signals compare to debris-flow parameters such as mean normal stresses, usually measured by expensive force plates, and debris-flow height. We model the elastic ground deformation as the response of an elastic half-space to a moving surface load. In addition, we use the model with some simplifications to determine the maximum debris-flow heights of Volcán de Fuego events, where no force plate measurements are available. Finally, we address how and under what assumptions the relatively affordable and straightforward tilt measurements may be utilized to infer debris-flow parameters, as opposed to force plates and other complicated instrument setups.

Shakedown analysis and its application in pavement and railway engineering

This paper has been prepared in memory of Professor Scott Sloan. It first presents a brief review of the development of shakedown analysis methods for pavement and railway engineering problems. In particular, it describes a new lower-bound method using the concept of critical residual stress fields and an upper-bound method using a nonlinear programming technique, which were developed by the authors, and then extended and applied to solve various shakedown problems in pavement and railway engineering. Moreover, this paper summarises and compares shakedown solutions for pavement and railway engineering problems, whilst highlighting the key factors that influence the shakedown limits. In addition, this paper proposes a simple, unified shakedown limit equation for pavements and railways under repeated moving surface loads. The equation includes three terms, which represent the resistances from cohesion, self-weight of the underlying soil, and self-weight of any superficial rigid layers, respectively, in a format analogous to Terzaghi’s bearing capacity equation. Numerical results indicate that the coefficient in the cohesion term Ncsd depends on the soil friction angle; while the coefficient in the self-weight term Nγsd is controlled by the soil friction angle and a dimensional factor γa/c. Values of Ncsd and Nγsd for a typical rolling point contact problem are also presented and interpreted, which explain the different contribution ratios from the soil self-weight to the shakedown limits of pavement and railway problems.

Probabilistic shakedown analysis of cohesive soil under moving surface loads considering wheel-soil interface friction

Probabilistic shakedown analysis is performed on spatially varied cohesive soil medium under two-dimensional moving surface load in the present study by combining lower bound finite element limit analysis, random field modelling, and Monte-Carlo simulation technique. The efficiency of the analysis is substantially increased by substituting the linearised yield criterion with a second-order conic function. Log-normally distributed random field of undrained shear strength is generated by Karhunen-Loève expansion method. Probabilistic design charts are presented in terms of mean shakedown limit and probability of failure of pavement for different wheel-soil interface frictions. The results show that an increase in wheel-soil interface friction decreases the effect of spatial variability, thereby reducing the probability of failure of the pavement. Distribution of elastic, residual, and total stresses within the soil mass is obtained to further understand the shakedown behaviour of soil mass under moving loads.

Fully coupled thermo-mechanical finite element modeling of friction stir processing of super duplex stainless steel

In the present paper, a 3D thermo-mechanical finite element model (FEM) was developed to simulate friction stir processing (FSP) of super duplex stainless steel (SDSS SAF 2507). It aims to study the developed bead residual stresses and thermal history of the processed material. The model was built and solved in the Abaqus environment by considering the temperature dependency of the mechanical and physical properties of the investigated material. The Gaussian moving heat source was adopted to simulate the heat generated by the tool-workpiece interaction and was applied with the help of a developed user subroutine. Similarly, the tool forging force was incorporated as a moving surface load. For validation purposes, FSP was experimentally performed at a fixed rotational speed of 400 rpm, traverse speed of 100 mm/min, and tilt angle of 2°. During the process, the tool-workpiece temperature was measured using an infrared camera. After processing, the developed residual stresses within the processed zone were measured using the drill hole technique. The numerical results were found to agree with measured temperatures and residual stresses. FEM was then used to estimate the temperature history, the residual stress distribution, and the deformation contours in the processed SDSS SAF 2507. The numerically estimated results revealed a broadening in the plasticized zone within the plunging area. Moreover, developed stresses were found to stabilize within 40 mm from the starting point, i.e., two shoulder advancements. According to the estimated temperature history, the sigma phase was predicted not to form.

Centrifuge and numerical modeling of moving traffic surface loads on pipelines buried in cohesionless soil

Abstract The main aim of this research was to investigate the mechanism of deformation of buried pipe under traffic moving load and the suitability of the modified Spangler-Iowa formula, coupled with the Boussinesq theory of load transmission through elastic media in predicting the deformation of these buried structures. This study employed reduced-scale physical model tests in a geotechnical centrifuge, numerical back-analysis using ABAQUS software and a numerical prediction for a hypothetical case. The hypothetical case consisted of a steel pipe buried in cohesionless soil under moving surface loads. Nine centrifuge tests were carried out for three different embedment ratios in dense, medium and loose sand. The tests results demonstrated that the formulas used for pipeline projects, the modified Spangler-Iowa formula together with the Boussinesq theory, are somewhat conservative for all densities analyzed and that the degree of conservatism increases with both embedment ratio and with the stiffness of the soil the pipe rests.

Geotechnical centrifuge and numerical modelling of buried pipelines

Mechanical response of buried pipes subjected to vehicle live loads acting on the ground surface has been exhaustively studied in the past decades. However, it remains an open subject especially for cases where the load is not necessarily positioned over the centre of the crown. Simplifications regarding loading transmission based on the theory of elasticity and the lack of soil–pipe interaction in the analyses have been blamed for possible lack of adherence between the predicted and the observed behaviour of such structures. Herein, both numerical and physical modelling were used to capture the important features of the mechanical behaviour of buried pipelines under live moving surface loads. The physical models were tested under modified gravity in a centrifuge, which allowed the calibration of a three-dimensional numerical finite-element model. Three different models were tested in the geotechnical centrifuge, corresponding to three different cover heights: 1D, 1·5D and 2D, where D is the pipe diameter. The results showed that pipe deformations, caused by live vehicle loads applied at distances greater than twice the diameter of the pipe, are negligible. The diametrical deformations did not exceed the 2% limit suggested by regulation associations. The highest value found in this study was 0·2%.

An analytical solution to investigate the dynamic impact of a moving surface load on a shallowly-buried tunnel

In order to investigate the dynamic impact of a moving surface load on a shallow-buried tunnel, an analytical model of a tunnel embedded in an elastic half-space was proposed. The half-space and the tunnel structure were modeled as visco-elastic media and the moving surface load was simplified as a moving point load on the ground surface. Based on the fundamental solution for the isotropic elastic half-space system in Cartesian and cylindrical coordinates, the dynamic response of a shallowly-buried tunnel in a half-space generated by a moving surface load was obtained. The transformations between plane wave and cylindrical wave functions were used to facilitate the application of boundary conditions at the ground surface and the tunnel interface. It was found that the vibration of the shallowly-buried tunnel increases significantly as the load moving speed increases, and reaches a maximum value at a critical load velocity. The tunnel vibration can be greatly reduced as the buried depth increases, and can satisfy the requirement of vibration specification (ISO 04866-2010) after it exceeds the critical depth. The critical depth increases exponentially with the increase of the moving speed of the surface load.

Three-dimensional shakedown analysis of ballasted railway structures under moving surface loads with different load distributions

Shakedown of ballasted railway structures was analyzed based on Melan's shakedown theorem, in which the wheel/rail contact was approximated by Hertz (circular and elliptical contact areas), uniform and trapezoidal load distributions, separately. The shakedown solutions incorporating to the three-dimensional finite element model calculated shakedown multiplier by means of a self-equilibrated critical residual stress field. The shakedown multiplier for multi-layered ballasted railway structure was determined as the minimum one among all layers. The results showed that elliptical Hertz and uniform load yielded the largest and smallest shakedown limits, respectively, with the maximum difference of approximately 64%. The shakedown limits always occurred at ballast layer for relatively small frictional coefficient, whilst occurred at rail for low rail's yield stress with large frictional coefficient. As expected, the shakedown limits decreased as the ballast stiffness and thickness increased, especially for relatively small frictional coefficient; while increased with raising rail's yield stress. The material properties and thickness should therefore be optimally designed so as to provide a maximum resistance to the structure failure and reduce the material costs.

Shakedown analysis for design of flexible pavements under moving loads

In this paper, a numerical method based on shakedown theory has been developed to calculate shakedown load limits of flexible pavements under moving surface loads. The shakedown results can serve as a design basis for flexible road pavements for the prevention of excessive plastic deformation. This numerical method utilises elastic stress fields obtained from finite element analyses and calculates optimum shakedown multiplier for each pavement layer by means of a self-equilibrated critical residual stress field. Finally, the shakedown load limit of a flexible pavement is found as the minimum shakedown multiplier among all layers. The results of numerical analyses examine the effect of surface frictional coefficient, material properties and layer thicknesses on the shakedown load limits, and meanwhile provide an insight into the differences between two-dimensional and three-dimensional pavement models. A simple design procedure using the shakedown method is also developed for layered, flexible road pavements.

Three-dimensional shakedown solutions for anisotropic cohesive-frictional materials under moving surface loads

Previous work on three-dimensional shakedown analysis of cohesive-frictional materials under moving surface loads has been entirely for isotropic materials. As a result, the effects of anisotropy, both elastic and plastic, of soil and pavement materials are ignored. This paper will, for the first time, develop three-dimensional shakedown solutions to allow for the variation of elastic and plastic material properties with direction. Melan's lower-bound shakedown theorem is used to derive shakedown solutions. In particular, a generalised, anisotropic Mohr–Coulomb yield criterion and cross-anisotropic elastic stress fields are utilised to develop anisotropic shakedown solutions. It is found that shakedown solutions for anisotropic materials are dominated by Young's modulus ratio for the cases of subsurface failure and by shear modulus ratio for the cases of surface failure. Plastic anisotropy is mainly controlled by material cohesion ratio, the rise of which increases the shakedown limit until a maximum value is reached. The anisotropic shakedown limit varies with frictional coefficient, and the peak value may not occur for the case of normal loading only.

Residual stresses and shakedown in cohesive-frictional half-space under moving surface loads

‘Shakedown’ is used to refer to a state of structures under repeated loading conditions at which the material behaviour becomes purely elastic after some initial plastic deformation. Residual stresses developed in a structure due to the initially occurred plastic deformation play an important role in helping the structure to reach the shakedown state. A better understanding of residual stresses in cohesive-frictional half-space under moving surface loads is urgently needed if shakedown theory is applied to solve pavement or railway problems. This paper is focused on residual stresses in cohesive frictional materials by using finite element analysis to investigate the development of residual stresses in a cohesive-frictional half-space under repeated moving surface loads. These numerical results illustrate how residual stresses affect the behaviour of cohesive frictional materials under repeated loading conditions.

Three-dimensional shakedown solutions for cohesive-frictional materials under moving surface loads

Pavement and railtrack design is of huge importance to society and yet the theoretical basis for most current design methods is still very simplistic and crude (Brown, 1996; Yu, 2006). This paper is part of a concerted effort at the Nottingham Centre for Geomechanics to develop improved theoretical foundations for pavement and railtrack design. It is mainly concerned with the development of rigorous lower-bound solutions for shakedown of cohesive-frictional materials under three-dimensional moving traffic loads. Compared with previous studies, two important aspects are taken into account. First, this paper considers a more general case of elliptical contact area between traffic and material surface, as most previous lower-bound studies considered the traffic load is applied through an infinite long roller. Secondly, by introducing a critical self-equilibrated residual stress field, this shakedown problem is reduced to a formulation in terms of a load parameter only. By using a simple optimisation procedure, the maximum load parameter leads to a lower-bound shakedown limit to this problem. Results for the special case of circular contact area are also presented in analytical form, which can then be readily applied for practical design.

A Shakedown Limit under Hertz Contact Pressure

In his "Contact Mechanics" book, Professor K. L. Johnson described an analytical lower bound shakedown approach to predict the shakedown load limit under repeated Hertz moving surface loads. Based on Bleich-Melan shakedown theorem, this problem will be revisited in this paper using finite element techniques and mathematical programming.

A long-wave model for the surface elastic wave in a coated half-space

The paper deals with the three-dimensional problem in linear isotropic elasticity for a coated half-space. The coating is modelled via the effective boundary conditions on the surface of the substrate initially established on the basis of an ad hoc approach and justified in the paper at a long-wave limit. An explicit model is derived for the surface wave using the perturbation technique, along with the theory of harmonic functions and Radon transform. The model consists of three-dimensional ‘quasi-static’ elliptic equations over the interior subject to the boundary conditions on the surface which involve relations expressing wave potentials through each other as well as a two-dimensional hyperbolic equation singularly perturbed by a pseudo-differential (or integro-differential) operator. The latter equation governs dispersive surface wave propagation, whereas the elliptic equations describe spatial decay of displacements and stresses. As an illustration, the dynamic response is calculated for impulse and moving surface loads. The explicit analytical solutions obtained for these cases may be used for the non-destructive testing of the thickness of the coating and the elastic moduli of the substrate.

Using complex potentials to determine the reaction of a prestressed two-layer elastic half-space to a moving load

Complex potentials in common form for compressible and incompressible elastic bodies are used to formulate and solve the problem of stationary motion of a prestressed two-layer elastic half-space under a moving surface load. The results presented are similar to those obtained earlier using the Fourier transform

Dynamic Crack Extension Along the Interface of Materials That Differ in Thermal Properties: Convection and Thermal Relaxation

Moving surface loads cause crack extension at a constant subcritical speed between perfectly bonded materials. The materials differ only in thermal properties and are governed by coupled thermoelastic equations that admit as special cases Fourier heat conduction and thermal relaxation with one or two relaxation times. Convection from the crack surfaces is allowed and for the latter two models is itself influenced by thermal relaxation. A dynamic steady state of plane strain is assumed. Fourier heat conduction is shown to dominate away from the crack edge at low speeds; solution behavior at the crack edge at high speeds depends upon the particular thermal model. Thermal mismatch is seen to cause solution behavior similar to that for the isothermal bimaterial, and so insight into the case of general material mismatch is provided.

Bounds for shakedown of cohesive-frictional materials under moving surface loads

In this paper, shakedown of a cohesive-frictional half space subjected to moving surface loads is investigated using Melan’s static shakedown theorem. The material in the half space is modelled as a Mohr–Coulomb medium. The sliding and rolling contact between a roller and the half space is assumed to be plane strain and can be approximated by a trapezoidal as well as a Hertzian load distribution. A closed form solution to the elastic stress field for the trapezoidal contact is derived, and is then used for the shakedown analysis. It is demonstrated that, by relaxing either the equilibrium or the yield constraints (or both) on the residual stress field, the shakedown analysis leads to various bounds for the elastic shakedown limit. The differences among the various shakedown load factors are quantitatively compared, and the influence of both Hertzian and trapezoidal contacts for the half space under moving surface loads is studied. The various bounds and shakedown limits obtained in the paper serve as useful benchmarks for future numerical shakedown analysis, and also provide a valuable reference for the safe design of pavements.

Analysis of ground motion due to moving surface loads induced by high-speed trains

A three-dimensional time domain boundary element (BE) approach for the analysis of soil vibrations induced by high-speed moving loads is presented in this paper. An attenuation law is included in the formulation. By doing so, internal material damping can be taken into account. The characteristics of the BE model required for the study of travelling load problems are analysed. Thus, mesh size, type of elements, internal damping representation and the complete numerical approach are validated. Existing analytical solutions for some simple problems are used as a reference. Experimental results measured in a simple soil dynamic load problem are also accurately reproduced by the proposed model. The analysis of the type of BE mesh required for a good representation of high-speed train effects is carried out using different discretizations under the sleepers and the free field near the track. All these analyses allow to define a model very well suited for the study of soil vibration effects due to high-speed train passage. Vibrations produced by an Alstom (Thalys-AVE) train travelling at 256 and 300 km/h speed are evaluated at different locations near the track. Results show that the proposed numerical procedure and attenuation law allow for a realistic representation of the effects of the different passing loads. The BE approach presented in this paper can be used for actual analyses of high-speed train-induced vibrations. Layered soils, ballast or coupled vibrations of nearby structure can be included in the model in a straightforward manner.