· · · Institutional Repository

In dit rapport wordt verslag gedaan van een numeriek onderzoek naar steenzettingen op dijken. De steenzetting van een dijk kan door een golfaanval worden beschadigd. Dit wordt veroorzaakt door een opwaartste druk aan de onderzijde, die verantwoordelijk is voor het uitlichten van de stenen. Als er een sterkte-berekening wordt uitgevoerd, blijkt dat er zogenaamde inklemeffecten optreden. Dit is het gevolg van het geometrisch en fysisch niet-lineair gedrag. Er is dus een grotere kracht dan het eigen gewicht nodig om een steen uit de zetting te trekken. Het gunstige effect van deze inklemkrachten kan echter nog moeilijk worden gekwantificeerd en dus niet in de praktijk worden toegepast. Het doel van het afstudeerproject is meer inzicht te verkrijgen in de rol die de verschillende parameters spelen bij het inklemgedrag. Hiertoe wordt steeds de maximaal toelaatbare belasting pmax op het moment van bezwijken van de rij blokken beschouwd.

The Master’s thesis has focussed on the stability of a facetted shell structure. The research contributes to a Ph.D. research currently carried out at the Technical University of Denmark (DTU), which investigates the possibilities to design and build a shell structure from flat glass panels. The structure is a so-called plate (facetted) structure, which is a relatively unknown, though very efficient structure type. By combining this structural typology with laminated float glass, a very transparent structure becomes possible. Since smooth shell structures are prone to buckling, it is very important to assess the behaviour of the glass facetted structure in this respect. During the research different aspects that are important for the stability of the structure have been investigated using a finite element model. Important was for instance the sensitivity of the structure to imperfections. Furthermore, the influence of the stiffness of the joints between the glass facets turns out to play an important role in the behaviour of the structure. Especially the normal stiffness (k_n) is vital, while the bending stiffness (k_m) is less important. Other aspects that have been considered are the robustness of the structure and the influence of the stiffness of the panels. The research has shown that the structural system and its combination with laminated float glass looks very promising.

When analyzing three-dimensional problems with nonlinear finite element analysis (NLFEA) often problems are encountered such as bifurcation and divergence of the solution. In particular, cases subjected to tension softening tend to encourage the emergence of multiple equilibrium paths. In order to overcome these problems the Sequentially Linear Analysis (SLA) method has been developed for three-dimensional solid elements. SLA is an alternative for incremental-iterative solution schemes to model the nonlinear fracture behavior of quasi-brittle materials. It is an attractive method since it avoids the well known convergence and bifurcation problems that are often encountered when using incremental-iterative schemes such as Newton-Raphson. SLA uses a series of linear analyses to model the nonlinear behavior of the structure. By directly specifying a damage increment in each linear analysis, extensive iterations within the load or displacement increment can be avoided. The main objective of this research was to see how the Sequentially Linear Analysis approach could be extended to solid elements, so that it could be used for three-dimensional fracture problems as well. Although three-dimensional geometries such as masonry structures have been analyzed before using SLA, it was always restricted to two-dimensional finite elements only (shell elements). Therefore, first a theoretical constitutive model for three-dimensional stress-strain states has been developed that served as the starting point. Implementation in DIANA was the major second step from which the third and last step could be started: the verification on various fictive and real cases. A single element pull test was used to solve programming errors, whereas the notched beam offered the possibility to check how the newly developed SLA-code would perform for larger models. Both cases showed excellent agreement with the experiment. However, most attention was dedicated to the verification and physical interpretation of a real reinforced concrete slab. The results were critically evaluated, interpreted and compared to results from the experiment and the incremental-iterative Newton-Raphson method. It was concluded that the Sequentially Linear Analysis is able to properly capture the quasi-brittle behavior of the reinforced concrete slab. Especially in comparison to the three-dimensional Newton-Raphson results, SLA turned out to be more robust and accurate.

The increased number of underground infrastructure projects asks for a reliable and efficient assessment of settlement damages to buildings. Currently a three-stage method is in use: the first stage looks into the greenfield deformations, the second stage is a linear elastic 2D method in which greenfield deformations are applied onto a building and the third stage uses finite element methods and 3D models. The goal of this thesis was to improve the second stage by incorporating a non-linear masonry model and a soil-structure interface. A 2D parametric analysis has been performed in which various material and geometrical parameters were varied. The soil model was simplified to a linear-elastic model. The results of the research are twofold. On the one hand there are the results of the parametric analysis showing the effect of incorporating the non-linear masonry model and the soil-structure interface. On the other hand incorporating these two aspects a number of issues came up: the influence of the crack model and convergence criterion, the influence of the building location, the influence of the initial stress and the influence of the participating soil width. For each issue an explanation was sought and the consequences were determined. The results of the parametric analysis showed that including a non-linear material model and a soil-structure interface leads to lower acceptable volume losses. In practice it is generally believed that the current models are already too conservative. The difference between reality and the models must be sought in components that are still missing in the current model.

The tunnel boring process introduces soil settlements. Damage to nearby building could occur if settlements become too large. A reliable damage prediction model is necessary too asses the risks of damage to tunnel induced settlements. A widely used method for damage prediction is the Limiting Tensile Strain Method (LTSM). The LTSM models a masonry building as a weightless, isotropic, linear-elastic, rectangular beam on 2 supports. Although the LTSM is an easy method to use, it has its limitations. For facades for instance the perforation of the wall, which introduces weak spots in the wall and reduces the stiffness, is neglected. In this project the applicability of the LTSM in the case of facades is studied to improve damage predictions in the case of facades. A case study is performed to examine the response of facades in the Daniel Stalpertstraat due to settlements caused by the tunnelling process of the North/Southline. This field data is used to find a calibrated 2D numerical model of the facades. The calibrated numerical model is then subjected to larger settlements to obtain the behaviour of the facades at large settlements. Using linear and nonlinear analyses of the numerical model it is evaluated how accurate and how conservative 4 damage prediction models are. The first two LTSM models were examined: the standard LTSM model with E/G=2.6 and one with E/G=12.5. Based on the findings in the linear analyses also two models based on conventional beam theory were examined for their applicability: portal frame model and Forget-Me-Not model. With linear analyses it is checked how reliable the methods are in terms of strains and deformation under the imposed settlements. With nonlinear analyses the conservativeness of each method in terms of damage is evaluated by comparing the crack with found I the numerical model to the crack width calculated with the damage prediction models. The LTSM with E/G=12.5 gives the best results according to linear numerical analyses results. The LTSM with E/G provided the same curvature and shear distortion as found din the numerical analyses, the strains were approximated with 90%. The Forget-Me-Not model shows the best results according to the nonlinear analyses results. At large settlements this model provides the same results as found in the nonlinear numerical analysis results.

Objective The recently developed material ultra-high performance concrete (UHPC) has compressive strengths of over 150 MPa and a ductile behaviour. It has a higher stiffness and superior durability characteristics in comparison with ordinary concrete. The opportunity emerges to find new optimal structural topologies for this material. The ant system is the first of a family of algorithms that are nowadays all referred to with the term ant colony optimisation (ACO). It is a computational algorithm that is able to solve combinatorial optimisation problems. Its optimisation process is based on the foraging behaviour of ants. ACO is not widely explored for structural design cases. In the city of Apeldoorn a new sports centre called Omnisport is under construction. The centre consists of several halls, one of them containing a cycling and athletics track. The roof of this hall spans an elliptic area of about 120 by 100 metres. This thesis focuses on the creation and evaluation of a structural topology design algorithm, based on the concept of the ant system, for ultra-high performance concrete structures. The algorithm is applied to the design case of the Omnisport sports hall roof. Algorithm A new application for ant colony optimisation is developed in this thesis. Structures are mapped to a binary search space, which forms the link between the structure, ant colony optimisation and the finite element package DIANA. Structures are generated randomly in the first iteration of the routine by assigning material to some elements in a meshed space and leaving others empty. Elements that together form a well-performing structure are more likely to be chosen again in a next iteration. The process is based on a performance that can be any function, and is not necessarily limited to structural information only. In the case considered in the thesis, the UHPC structure is optimised towards a combination of minimum volume, mould surface, pre-stress and the availability of holes for ducts and walking bridges. The algorithm’s multi-objective optimisation process results in a structural topology. Design The algorithm has been applied to the case of the Omnisport hall roof. Based on the results, a preliminary design for the load-bearing structure of the roof in UHPC has been made. A load-bearing structure in this material is found to be possible. The proposed design consists of truss-like supporting elements for the roof. A connection strategy is proposed, member sizes and necessary pre-stress are indicatively determined. Rough cost estimates show that the design is not necessarily more expensive than the current design in steel.

Progressive collapse is a collapse where a local failure leads to a disproportionate collapse. Different terms like initial failure, propagation of failures and disproportionate damage are important aspects of such collapses. In current design practice, a method to measure a structures’ progressive collapse sensitivity in its early design phase and taking into account all aspects of a structures collapse resistance does not exist. The objective of this research is to develop a tool that takes into account all aspects of a progressive collapse and can aid the engineer in assessing a design, in its early design stage, on progressive collapse. At first, the initial failure is elaborated. Different events can cause the failure of elements. The probability an initiating event occurs at a certain element is different for each element. Mitigating measures can limit the chance of occurring for certain events. The initial events are applied on the model in 2 steps. First the location (or: element) of the event is chosen by a random selection method and a distribution of failure chances on the model. Second, the size of the damage is determined by applying a Gaussian curve over the model, both in x- and z-direction. This determines if adjacent elements, related to the removed element in step 1, are removed. The model is calculated by FEA-software. Only linear and first order calculations are considered. These limitations lead to inaccuracies of the results compared with reality. A stability analysis has been performed to determine the buckling lengths of columns with more accuracy. Catenary action is one of the main modelling methods in designing against progressive collapse. This method is implemented into the tool. Iteratively, the forces and deformations are calculated which develop during the occurrence of catenary action.

Recent tunnelling projects have received a great amount of media attention due to settlement induced damage. Due to the simplified approach of existing risk assessment methods, a new assessment system is in development, which can account for three-dimensional structural aspects of buildings. The aim of this study is to investigate the influence of the position and geometry of masonry buildings on the development of damage, while undergoing tunnelling induced settlements. In line with previous research, three-dimensional finite element analyses are used as a tool to perform a parametric study. A parametric study consists of an evaluation of the parameters position, aspect-ratio, grouping and orientation. The position parameter is divided into three characteristics: the sagging zone, a combined settlement profile and the hogging zone. The aspect-ratio parameter is also divided into three characteristics: shallow buildings, square buildings and deep buildings. The grouping effect parameter also distinguishes three characteristics: small and large isolated buildings and grouped buildings. The orientation parameter includes seven different increasing angles of the building main axis with respect to the tunnelling axis. The maximum measured crack width in the buildings gives input for a classification of damage, according the system of Burland et al. (1977). An average trend in the damage classification indicates the sensitivity to tunnelling induced settlements of the parameters. Both during and after tunnelling, a position of the building in the combined settlement profile appears to be the most sensitive to differential settlements. Buildings far away from the tunnelling axis generally obtain no more than slight damage. Structures with a low aspect-ratio seem on average to obtain equal amounts of damage as buildings with an aspect-ratio of 1. Structures with a higher aspect-ratio are less affected, both during and after tunnelling. Grouping of the buildings seems to be an influential parameter. Small isolated buildings obtain far less damage than large or grouped buildings. In relation to the numerical analyses, the empirical Limiting Tensile Strain Method (LTSM) seems to overestimate the damage for an isolated small building, but underestimate the damage in large or grouped buildings. For buildings in the sagging zone, a building with a low orientation angle is the least sensitive to differential settlement, while the maximum measured crack width increases by increasing the angle. The difference in maximum crack width can grow to a factor 3. A building in the combined settlement profile or in the hogging zone displays opposite behaviour. Cases with low orientation angles are the most susceptible to damage, while increasing the angle to 90 degrees lowers the maximum measured crack width. The difference in results can grow up to a factor 2.

Recent years have witnessed the realization of multiple concrete curved surface structures. The often complex geometry of these structures led to new challenges in the final design and production phase: design of the reinforcement is one of these challenges. Current reinforcement modelling software is not capable of properly dealing with NURBS curves and surfaces. The absence of proper reinforcement tools for curved surface structures renders the structural engineer less effective in designing the reinforcement. This can lead to missing out on potential through ill-informed design decisions. The computational strategy proposed in this thesis provides a way of improving the design process of reinforcement in curved surface structures. It includes all necessary steps of raising an architectural curved surface model to production level in terms of reinforcement. Three design aspects have been distinguished: geometrical control, structural analysis, and production. Corresponding to these design aspects, three concepts have been developed: the SolidModel, FEM Analysis visualization and Rebar DNA which help to control them. The developed Reinforcement Toolbox supports the strategy by offering structural engineers a tool which can be used to control the design aspects of reinforcement in curved surface structures. It sets out to help remove the current split between draftsman and structural engineer by offering a design environment which offers the possibility to simultaneously model and verify reinforcement for curved surface structures. Functional requirements which emerged from the computational strategy formed important input for the developed architecture of the Reinforcement Toolbox. Use cases helped to identify different scenarios in which the software application is likely to be used. The system architecture of the Reinforcement Toolbox has been developed with strong attention to the multifaceted design process of reinforcement in curved surface structures. It builds on existing 3D modelling software, Rhinoceros and Grasshopper, by adding custom components. The Reinforcement Toolbox has been developed using Microsoft Visual Studio 2008 and written in C#. In accordance to the possibilities offered by this object oriented programming language, the Reinforcement Toolbox uses a collection of custom objects which can be considered the building blocks of the Toolbox. For the first version of the Reinforcement Toolbox several components have been developed. Together they offer the necessary functionality for a structural engineer or CAD draftsman to design longitudinal reinforcement groups and reinforcement meshes for curved surface structures. A first version of the Reinforcement Toolbox has been developed and tested. It can be applied to both complex curved surface structures as well as non-complex structures, making it a widely applicable design tool. Users can apply the Reinforcement Toolbox at their own discretion within any given stage of the reinforcement process either to quickly research different reinforcement design alternatives, or use it to build extensive reinforcement models. The parametric reinforcement models are easily adaptable to design changes, which makes them valuable throughout the entire reinforcement process. The Toolbox has been designed considering user friendliness, and freedom of use. The modular setup allows users to combine components at their own discretion allowing for the intended freedom when designing reinforcement. It has been demonstrated to a group of structural engineers, who recognize the potential it can bring to the reinforcement process, especially when its current functionality and scope will be expanded.

This thesis focuses on assessing the crack width and durability at the outside of an immersed tunnel in case of fire inside the tunnel. Previous research (for instance Nieman [20]) addressed only the heating phase of a tunnel while also the inevitable cooling phase may have a large influence on the crack width. A user supplied code was written to calculate both the heating and cooling phase and handle the different reversibilities of the material properties. The material model is based on an explicit strain model where some simplifications had been made such as uniaxiality and the omission of the Poisson ratio. This material model is validated on some small models; the tunnel calculations are performed by making use of the geometry of the Wijkertunnel. The results of the tunnel calculations showed good agreement with the results of TNO 2007 [26] for the own weight and pressure loading. During the heating phase the results start to deviate from [26]; partly due to differences in the material model (load induced thermal strains reduces compressive stresses in the walls), partly due to instabilities in the calculation process. The load induced thermal strain decreases the thermal strain under compressive stresses and first time heating. One analysis could follow the complete fire, heating and cooling phase. During the heating and cooling phase the convergence behaviour was poor which is partly due to the complex material behaviour. The material model should be improved to obtain a more stable calculation process. During the cooling phase the tensile stresses increased in the roof and decreased in the walls of the heated tunnel tube as expected. The crack width at the outside of the tunnel is cumulative over a specific area. A lower limit is calculated and a crack width of more than 1 mm is found. This could influence the durability of the tunnel. To support this indication more calculations should be performed. The effect of the load induced thermal strain shows in a decrease of the tensile stresses in vertical direction in the walls and the compressive stresses in the side wall which are present for a longer time. In the mid wall an increase in compressive stress can be seen as a consequence of the net shrinkage which is a consequence of the load induced thermal strain during the cooling phase. It is possible to analyse the crack width during a fire. However more tests need to be performed to get a better understanding about the behaviour of the material properties during heating (high temperatures) and cooling. The code must be validated more thoroughly and only when the deformations of the walls can be explained for sure, a good assessment of the crack width after a heating and cooling phase can be made. In this thesis a foundation is laid for assessing the crack width in immersed tunnels during a heating and cooling phase. No such model existed until now. This model should be perfected, particular with respect to convergence, in order to obtain a more stable calculation and reliable results.