An elasto-plastic critical state framework for unsaturated soil.

Data from a series of controlled suction triaxial tests on samples of compacted speswhite kaolin were used in the development of an elasto–plastic critical state framework for unsaturated soil. The framework is defined in terms of four state variables: mean net stress, deviator stress, suction and specific volume. Included within the proposed framework are an isotropic normal compression hyperline, a critical state hyperline and a state boundary hypersurface. For states that lie inside the state boundary hypersurface the soil behaviour is assumed to be elastic, with movement over the state boundary hypersurface corresponding to expansion of a yield surface in stress space. The pattern of swelling and collapse observed during wetting, the elastic–plastic compression behaviour during isotropic loading and the increase of shear strength with suction were all related to the shape of the yield surface and the hardening law defined by the form of the state boundary. By assuming that constant–suction cross–sections of the yield surface were elliptical it was possible to predict test paths for different types of triaxial shear test that showed good agreement with observed behaviour. The development of shear strain was also predicted with reasonable success, by assuming an associated flow rule.

Micromechanical analysis of cohesive granular materials using the discrete element method with an adhesive elasto-plastic contact model

An adhesive elasto-plastic contact model for the discrete element method with three dimensional non-spherical particles is proposed and investigated to achieve quantitative prediction of cohesive powder flowability. Simulations have been performed for uniaxial consolidation followed by unconfined compression to failure using this model. The model has been shown to be capable of predicting the experimental flow function (unconfined compressive strength vs. the prior consolidation stress) for a limestone powder which has been selected as a reference solid in the Europe wide PARDEM research network. Contact plasticity in the model is shown to affect the flowability significantly and is thus essential for producing satisfactory computations of the behaviour of a cohesive granular material. The model predicts a linear relationship between a normalized unconfined compressive strength and the product of coordination number and solid fraction. This linear relationship is in line with the Rumpf model for the tensile strength of particulate agglomerate. Even when the contact adhesion is forced to remain constant, the increasing unconfined strength arising from stress consolidation is still predicted, which has its origin in the contact plasticity leading to microstructural evolution of the coordination number. The filled porosity is predicted to increase as the contact adhesion increases. Under confined compression, the porosity reduces more gradually for the load-dependent adhesion compared to constant adhesion. It was found that the contribution of adhesive force to the limiting friction has a significant effect on the bulk unconfined strength. The results provide new insights and propose a micromechanical based measure for characterising the strength and flowability of cohesive granular materials. 

Web crippling behaviour of cold-formed steel channel sections with offset web holes subjected to interior-two-flange loading

Cold-formed steel sections are often used as wall studs or floor joists; such sections often include web holes for ease of installation of the services. Cold-formed steel design codes, however, do not consider the effect of such web holes. In this paper, a combination of experimental tests and non-linear elasto-plastic finite element analyses are used to investigate the effect of such holes on web crippling under interior-two-flange (ITF) loading conditions; the cases of both flange fastened and flange unfastened are considered. A good agreement between the experimental tests and finite element analyses was obtained. The finite element model was then used for the purposes of a parametric study on the effect of different sizes and position of holes in the web. It was demonstrated that the main factors influencing the web crippling strength are the ratio of the hole depth to the depth of the web, and the ratio of the distance from the edge of the bearing to the flat depth of web. Design recommendations in the form of web crippling strength reduction factors are proposed, that are conservative to both the experimental and finite element results.

Effect of column base strength on steel portal frames in fire

This paper presents the findings of a project part sponsored by an ICE Research and Development grant on portal frames in fire. The research reported here has also lead to a sucessful research grant from the IStructE. The paper describes a non-linear elasto plastic dynamic finite element model that captures the collapse of a portal frame in fire. It demonstrates that current guidance on the column base stiffness and strength, to prevent collapse, may in some cases be unconservative.

F. E.-assisted design of the eaves bracket of a cold-formed steel portal frame

Non-linear large-displacement elasto-plastic finite element analyses are used to propose design recommendations for the eaves bracket of a cold-formed steel portal frame. Owing to the thinness of the sheet steel used for the brackets, such a structural design problem is not trivial as the brackets need to be designed against failure through buckling; without availability of the finite element method, expensive laboratory testing would therefore be required. In this paper, the finite element method is firstly used to predict the plastic moment capacity of the eaves bracket. Parametric studies are then used to propose design recommendations for the eaves bracket against two potential buckling modes of failure:

Effects of elevated temperatures on bolted moment-connections between cold-formed steel members

Experimental investigations at ambient temperature into the behaviour of bolted moment-connections between cold-formed steel members have previously been described. Full-scale joint tests have demonstrated that the channel-sections being connected are susceptible to premature failure, the result of web buckling caused by the concentration of load transfer from the bolts. The results of tests on bolted lap joints have been used to propose design recommendations for the shear strength in bearing of the bolt-hole. For both types of test, the results of non-linear elasto-plastic finite element analyses have been shown to have good agreement. No consideration, however, has been given to the behaviour of such connections at elevated temperatures. This paper describes non-linear elasto-plastic finite element parametric studies into the effects of elevated temperatures on bolted moment-connections between cold-formed steel members. Two issues at elevated temperatures are investigated:

Cold-formed steel sections with web openings subjected to web crippling under two-flange loading conditions - part I: Tests and finite element analysis

The results of 82 web crippling tests are presented, with 20 tests conducted on channel sections without web openings and 62 tests conducted on channel sections with web openings. The tests consider both end-two-flange and interior-two-flange loading conditions. In the case of the tests with web openings, the hole was located directly under the concentrated load. The concentrated load was applied through bearing plates; the effect of different bearing lengths is investigated. In addition, the cases of both flanges fastened and unfastened to the support is considered. A non-linear elasto-plastic finite element model is described, and the results compared against the laboratory test results; a good agreement was obtained in terms of both strength and failure modes.

Pull-out forces in shear connectors in composite beams with large web openings

Composite beams with large web openings are often used, and their design is controlled by Vierendeel bending at the four corners of each opening, which is assisted by local composite action with the floor slab. Development of this Vierendeel bending resistance may be limited by pull-out failure of the shear connectors. In this paper, a non-linear elasto-plastic finite element model of a composite beam with web openings was used to investigate this mode of pull-out failure. A test was performed on a typical composite slab in which the shear connectors were subject to pure tension and the failure load was 67 kN, which is approximately 70% of the longitudinal shear resistance. The results of the finite element model are compared against those obtained using the established design theory, that does not limit the vertical pull-out resistance of the shear connectors. It is shown that the local bending resistance due to composite action should be reduced when limited by pull-out of the shear connectors. A parametric study investigated the effect of openings of 600 to 1200 mm length. A simple model is developed to establish the Vierendeel bending resistance, when limited by pull-out of the shear connectors.

Calculated and observed long term performance of Leneghans embankment

This paper presents the finite element (FE) analysis of the consolidation of the foundation of an embankment constructed over soft clay deposit which shows significant time dependent behaviour and was improved with prefabricated vertical drains. To assess the capability of a simple elastic viscoplastic (EVP) model to predict the long term performance of a geotechnical structure constructed on soft soils, a well documented (Leneghans) embankment was analyzed to predict its long term behaviour characteristics. Two fully coupled two dimensional (2D) plane strain FE analyses have been carried out. In one of these, the foundation of the embankment was modelled with a relatively simpler time dependent EVP model and in the other one, for comparison purposes, the foundation soil was modelled with elasto-plastic Modified Cam-clay (MCC) model. Details of the analyses and the results are discussed in comparison with the field performance. Predictions from the creep (EVP) model were found to be better than those from Elasto-plastic (MCC) analysis. However, the creep analysis requires an additional parameter and additional computational time and resources. © 2011 Taylor & Francis.

Cold-formed steel portal frames in fire: Full-scale testing and finite element analysis

A full-scale, non-uniform natural fire test on a cold-formed steel portal frame building is described. The results of the test are used to validate a non-linear, elasto-plastic, finite element shell idealisation, for the purposes of later forming the basis of a performance-based design approach for cold-formed steel portal frames at elevated temperatures.

The Collapse Behaviour of Cold-formed Steel Portal Frames at Elevated Temperatures

This paper describes the results of non-linear elasto-plastic implicit dynamic finite element analyses that are used to predict the collapse behaviour of cold-formed steel portal frames at elevated temperatures. The collapse behaviour of a simple rigid-jointed beam idealisation and a more accurate semi-rigid jointed shell element idealisation are compared for two different fire scenarios. For the case of the shell element idealisation, the semi-rigidity of the cold-formed steel joints is explicitly taken into account through modelling of the bolt-hole elongation stiffness. In addition, the shell element idealisation is able to capture buckling of the cold-formed steel sections in the vicinity of the joints. The shell element idealisation is validated at ambient temperature against the results of full-scale tests reported in the literature. The behaviour at elevated temperatures is then considered for both the semi-rigid jointed shell and rigid-jointed beam idealisations. The inclusion of accurate joint rigidity and geometric non-linearity (second order analysis) are shown to affect the collapse behaviour at elevated temperatures. For each fire scenario considered, the importance of base fixity in preventing an undesirable outwards collapse mechanism is demonstrated. The results demonstrate that joint rigidity and varying fire scenarios should be considered in order to allow for conservative design.

A DEM study of silo discharge of a cohesive solid

Bulk handling of powders and granular solids is common in many industries and often gives rise to handling difficulties especially when the material exhibits complex cohesive behaviour. For example, high storage stresses in a silo can lead to high cohesive strength of the stored solid, which may in turn cause blockages such as ratholing or arching near the outlet during discharge. This paper presents a Discrete Element Method study of discharge of a granular solid with varying levels of cohesion from a flat-bottomed silo. The DEM simulations were conducted using the commercial EDEM code with a recently developed DEM contact model for cohesive solids implemented through an API. The contact model is based on an elasto-plastic contact with adhesion and uses hysteretic non-linear loading and unloading paths to model the elastic-plastic contact deformation. The adhesion parameter is a function of the maximum contact overlap. The model has been shown to be able to predict the stress history dependent behaviour depicted by a flow function of the material. The effects of cohesion on the discharge rate and flow pattern in the silo are investigated. The predicted discharge rates are compared for the varying levels of cohesion and the effect of adhesion is evaluated. The ability of the contact model to qualitatively predict the phenomena that are present in the discharge of a silo has been shown with the salient feature of mixed flow from a flat bottomed hopper identified in the simulation.

Experimental and discrete element modelling of cohesive iron ore fines

In this study, the behaviour of iron ore fines with varying levels of adhesion was investigated using a confined compression test and a uniaxial test. The uniaxial test was conducted using the semi-automated uniaxial EPT tester in which the cohesive strength of a bulk solid is evaluated from an unconfined compression test following a period of consolidation to a pre-defined vertical stress. The iron ore fines were also tested by measuring both the vertical and circumferential strains on the cylindrical container walls under vertical loading in a separate confined compression tester - the K0 tester, to determine the lateral pressure ratio. Discrete Element Method simulations of both experiments were carried out and the predictions were compared with the experimental observations. A recently developed DEM contact model for cohesive solids, an Elasto-Plastic Adhesive model, was used. This particle contact model uses hysteretic non-linear loading and unloading paths and an adhesion parameter which is a function of the maximum contact overlap. The model parameters for the simulations are phenomenologically based to reproduce the key bulk characteristics exhibited by the solid. The simulation results show a good agreement in capturing the stress history dependent behaviour depicted by the flow function of the cohesive iron ore fines while also providing a reasonably good match for the lateral pressure ratio observed during the confined compression K0 tests. This demonstrates the potential for the DEM model to be used in the simulation of bulk handling applications.

Finite-element investigation of cold-formed steel portal frames in fire

This paper presents the results of a full-scale site fire test performed on a cold-formed steel portal frame building with semi-rigid joints. The purpose of the study is to establish a performance-based approach for the design of such structures in fire boundary conditions. In the full-scale site fire test, the building collapsed asymmetrically at a temperature of 714°C. A non-linear elasto-plastic finite-element shell model is described and is validated against the results of the full-scale test. A parametric study is presented that highlights the importance of in-plane restraint from the side rails in preventing an outwards sway failure for both a single portal and full building geometry model. The study also demonstrates that the semi-rigidity of the joints should be taken into account in the design. The single portal and full building geometry models display a close match to site test results with failure at 682°C and 704°C, respectively. A design case is described in accordance with Steel Construction Institute design recommendations. The validated single portal model is tested with pinned bases, columns protected, realistic loading and rafters subject to symmetric uniform heating in accordance with the ISO 834 standard fire curve; failure occurs at 703°C.