Flexural shear failure is a brittle failure mode that can occur in reinforced concrete (RC) beams without stirrups due to the combination of flexural and shear stresses. The failure mode begins with vertical flexural cracks at the bottom of the RC beam central span area due to flexural tensile stresses, followed by diagonal cracks. During stabilization, a diagonal crack enlarges, leading to flexural shear failure. The failure mode is brittle due to the significant bearing capacity reduction making it more difficult to predict.

Accurately predicting the capacity of concrete structures is important for ensuring their safety, especially in the case of brittle failures. Various design codes are available to design and assess such structures, but an advanced numerical method called the Non-Linear Finite Element Analysis (NLFEA) is an alternative to these codes. NLFEA allows for more detailed and accurate modeling of the structure behavior by considering material, geometry, and boundary conditions nonlinearity. By using NLFEA, engineers can optimize their design and gain a deeper understanding of the behavior of RC beams without stirrups. The NLFEA model requires several modeling decisions to accurately simulate the structures’ behavior.

Sensitivity analysis on different modeling aspects is crucial to obtain a numerical model that can accurately simulate the RC beam. To be considered accurate, the numerical model should simulate approximately the same damage progression, failure mode, and failure load compared to the experiments. The sensitivity analysis is performed to modeling aspects with uncertainties identified during the literature review. These uncertainties are in the constitutive model, finite element discretization, and analysis procedure modeling aspects. Sensitivity analysis on various modeling aspects is per-formed using four experimental beams with distinct geometrical sizes, while some material configura-tions differ. This research investigates whether, using sensitivity analysis, a numerical model can be obtained that accurately simulates flexural shear failure for RC beams without stirrups.

The total strain crack models’ crack orientation sensitivity analysis shows that the rotating crack orientation can suffer from over-rotation, which causes delamination of the concrete cover. Over-rotation also shows a strong correlation with many non-converged steps. In addition, the fixed crack orientation simulates a more realistic representation of the experimental failure mode. The compression-compression confinement sensitivity analysis shows that this modeling aspect does not influence simulations for cases with flexural shear failure much and can thus be excluded. A slightly lower failure load is simulated with the confined numerical model for one of the four cases. The sensitivity analysis on the FIB bond-slip relation and Shima bond-slip relation reveals that the former has a lower initial stiffness when using the same material configurations for their modeling assumptions. Due to the lower initial stiffness, there is a higher relative displacement between the concrete and reinforcement. In some cases, this results in either increased convergence problems, a higher possibility of dowel failure, a lower failure load, or a combination of them.

For the fourth sensitivity analysis modeling aspect, the full Newton-Raphson (NR) iteration scheme simulations are slightly more representative of the experiment than the Secant iteration scheme. This result is obtained despite the full NR scheme having more convergence problems during the initial crack. In addition, for a few cases, the Secant iteration scheme simulates symmetrical flexural shear failure due to failing to include material nonlinearity.

Sensitivity analysis of the reinforcement elements shows that simulations with truss elements are more accurate than beam elements. The beam elements models show compatibility issues when combined with plane stress elements. The interface elements fail to correctly tie the beam elements’ extra rotational degree of freedom to the transitional degree of freedom. This incompatibility results in convergence problems. Also, higher relative displacements and a higher stiffness after the initial crack is noticed in some cases compared to the experiment. The final sensitivity analysis reveals that the element size sensitivity increases with an increase in the geometrical beam size. Too-large element sizes decrease the accuracy of simulations. In contrast, too-small element sizes increase the computational cost but can also simulate irregular crack patterns not representative of the experiment. A formula is introduced from the sensitivity analysis for beams up to a depth of 1200 mm to predict an appropriate element size.

The sensitivity analysis reveals that the most accurate numerical model is a fixed crack orientation and the Shima bond-slip relation combined with truss elements using the full NR iteration scheme. The sensitivity analysis is followed by a quantitative analysis of 76 experimental cases to verify the accuracy of the obtained numerical model for a broad range of differently configured experimental cases. Analysis shows that dowel failure can get captured due to an excessive change in the dam-age-based shear retention factor using the obtained numerical model. However, decreasing sensitive load step sizes to very small ones results in flexural shear failure. Also, the quantitative simulations show that the numerical model simulations are largely accurate, with 62 simulated cases below a failure load percentage difference of 10 % compared to the experiment. The average percentage difference is 6 % between the simulations and the experiment.

Analysis shows that this research successfully obtains a numerical model that accurately simulates flexural shear failure for RC beams without stirrups. The information obtained from this research can be used to make modeling choices. In addition, some uncertainties for other modeling aspects are introduced for future research. These modeling aspects are the shear retention model, concrete elements compatibility with the reinforcements beam elements, and the global element size for beams deeper than 1200 mm.
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The use of precast Reinforced Concrete has been the norm for the construction of tunnel linings for decades. However, the use of Steel Fiber Reinforced Concrete is gaining popularity due to its beneficial mechanical properties, improved sustainability, improved durability, and lowered costs compared to traditional Reinforced Concrete (RC). The amount of reinforcing steel can be reduced significantly, lowering the costs and carbon footprint of a project making it an appealing alternative. One application of SFRC is found in tunnels making use of precasted concrete segments, typically built with a Tunnel Boring Machine (TBM). This type of tunnel is found in Amsterdam, namely the
Noord/Zuidlijn: a metro line linking the north and south of the city. This project is used as a reference to perform a feasibility study on the use of SFRC and investigate its benefits.

The research involves a structural analysis of an SFRC design considering the loads and boundary conditions of the original Noord/Zuidlijn. The loads occur at different phases in the realization of the tunnel: transient, construction, and service phase. These loads can lead to various failure mechanisms, with the primary concern being tensile splitting of the concrete. Each phase is defined by a dominant component that governs its behaviour. During the transient stage, involving demoulding, stacking, and handling of the segments, the bending stresses inside the segment need to be checked. During the construction stage, the ring joints of the segments presents a weakness and need to be checked for
spalling and/or splitting of the concrete. During the service stage, the longitudinal joint needs to be checked for splitting of the concrete and the global cross sectional stresses of the lining need to be examined.

Numerical models are created to assess SFRC’s performance in the governing parts of the tunnel during the three phases, with the addition of identical RC models as a basis for comparison. The general bending and shear stresses, as well as localised splitting and spalling stresses, are investigated in both the Serviceability Limit State and Ultimate Limit State. The structural behaviour of SFRC corresponded with the characteristics found in literature, with a higher initial cracking load than RC and a more stable crack propagation due to its residual tensile strength. The peak strength of SFRC is found to be lower, but still passes all the checks. The results show that an SFRC design with the
minimum fiber content of 30 kg/m3 is sufficient for the transient and construction phases, but 40 kg/m3 is needed for the service phase. The benefits of implementing SFRC in the Noord/Zuidlijn can be quantified in a steel reduction of 60%, which would mean a decrease in steel consumption of 3050
tons. The CO2 emissions would decrease with 5500 tons, equivalent to the amount absorbed by 220.000 trees over the course of one year.

The concluding results can be used as guidance when opting for SFRC in a new bored tunnel project. The performed design checks show a governing load situation in both the construction phase and the service phase. The sufficiency of SFRC for the ring joint check during construction is governed by the
splitting force between the loading shoes of the TBM. The magnitude of this splitting force depends on the size of the TBM, the characteristics of the soil, and the depth of the tunnel. A large diameter tunnel, high-friction soil, or deep tunnel will decrease the likelihood of a design with solely fibers. The same unfavorable conditions cause large internal bending moments which could pose problems for the longitudinal joint and global cross section check. A small diameter tunnel and a tunnel constructed in stiffer soil will increase the feasibility of a design making use of solely fibers ... Read more

Throughout the years, incremental iterative approaches have been shown to be excellent tools in describing the complex behaviour of structures under a wide range of circumstances. However, robustness issues arise for quasi-brittle structures due to the potential lost of convergence during the development of abrupt fracture mechanisms. In order to overcome these robustness issues, the framework of sequentially linear analysis (SLA) has been proposed: an event-by-event strategy in which a sequence of scaled linear analyses with decreasing secant stiffness is performed, representing local damage increments. The current SLA-framework is based on a fixed crack approach, potentially causing the development of severe spurious stresses and inaccuracies due to the misalignment of the crack with the principal stress directions. To this end, Hendriks and Rots proposed a model consisting of several parallel fractions or layers, from now on called the sublayer model. Each of the layers is elastic-perfectly brittle, but has different properties, chosen such to represent the overall constitutive softening behaviour as accurate as possible. The layers fail independent of each other and have their own specific crack direction. The main idea is to mimick a rotating crack by a superposition of sublayers with a fixed crack direction. The main goal of this thesis is to further elaborate, generalize and verify the sublayer model for quasi-brittle materials and capture the influence of rotating cracks on the structural response within the framework of existing regular sequentially linear analysis. In this thesis, the frameworks of regular SLA and the sublayer model were connected by a general transition from any saw-tooth law to sublayer material properties. An externalized procedure was created to automatically generate an input file for DIANA FEA and thereby facilitate verification of the sublayer model. Furthermore, the 2-dimensional framework of the sublayer model has been extended towards 3-dimensional structures to broaden the range of application. On top of that, concepts were proposed to improve the sublayer model: the tapered ripple band, reducing the required number of sublayers to reach a specific state by adding more saw-teeth near the end of the softening curve, and an improved algorithm, making use of the fact that the order of brittle fracture of the sublayers is known in advance, such that only those integration points that can actually become critical are monitored, thereby reducing computational efforts significantly. In this thesis, the sublayer model is proved to mimick a rotating crack within the framework of existing regular sequentially linear analysis based on a set of structural case studies (notched beam, shear notched beam, DEN-beam, full scale facade and full scale concrete dam). Compared to regular SLA, effects of stress locking are reduced, less wide localization bands are found and a more realistic collapse pattern is observed, thereby making the sublayer model more interesting for application in engineering practice. Furthermore, it has been shown that for the 3-dimensional framework of the sublayer model the same conclusions as for 2D can be made. In the authors opinion, the contributions of this thesis are a step towards a robust generally applicable computational method to simulate the complex structural behaviour of quasibrittle materials. ... Read more

The unreinforced masonry construction of Dutch terraced houses in Groningen is prone to lateral earthquake loading. To analyse the capacity of these houses, the faculty of Civil Engineering at the TU Delft started a test campaign. In this thesis, the experimental results served as benchmarks to validate a relatively new numerical method: Sequentially Linear Analysis (SLA). This method is developed to overcome numerical instability, which is a problem for regular non-linear finite element analyses (NLFEA). The objective is to investigate to what extent SLA is able to predict the behaviour of the two main components of a Dutch house, namely the shear wall and the out-of-plane loaded transversal wall, during a monotonic pushover test. Both pre-stressed components are modelled, using the (new) non-proportional loading algorithm and two modelling approaches were applied: the smeared crack approach and the discrete crack approach. Besides, two finite element types were used: the new implementation of the SLA code for shell elements is validated by modelling the shear wall with plane stress elements as well.
Results showed that SLA is able to predict the behaviour of pre-stressed masonry components using the non-proportional loading algorithm, except for the post-peak behaviour of the out-of-plane loaded transversal wall. As SLA is under development, the method still has difficulties to overcome. The defined stop criteria were helpful to temporarily deal with the identified problems, but further research needs to be done to actually solve the errors.
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