J.G. Rots

A plane stress softening plasticity model for orthotropic materials

A plane stress model has been developed for quasi-brittle orthotropic materials. The theory of plasticity, which is adopted to describe the inelastic behaviour, utilizes modern algorithmic concepts, including an implicit Euler backward return mapping scheme, a local Newton-Raphson method and a consistent tangential stiffness matrix. The model is capable of predicting independent responses along the material axes. It features a tensile fracture energy and a compressive fracture energy, which are different for each material axis. A comparison between calculated and experimental results in masonry shear walls shows that a successful implementation has been achieved.

Smeared and discrete representations of localized fracture

The possibilities of smeared and discrete crack concepts for simulating localized fracture in softening materials are investigated. First, comparisons are made between fixed, multi-directional and rotating smeared cracks, whereby the crack orientation is kept constant, updated in a stepwise manner or updated continuously, respectively. Next, the smeared approaches are compared to analyses on systems of predefined potential discrete cracks. Results indicate that (1) fixed smeared cracks may produce overstiff behavior while rotating smeared cracks do not, (2) smeared cracks may give rise to stress-locking while discrete cracks do not. Examples are shown for concrete and masonry.

Analysis of concrete fracture in direct tension

Abstract The direct tension test on concrete specimens is analysed using finite elements. The analysis shows that the behaviour after peak load is strongly non-homogeneous and involves asymmetric crack propagation. These observations, which are supported by experimental evidence, have consequences for deriving “stress-strain” relations from direct tension tests, since they demonstrate that the observed softening behaviour is partially a structural effect. Attention is furthermore drawn to the possibility of snap-back behaviour in strain-softening concrete and to consequences thereof for numerical and experimental investigations.

The role of crack rate dependence in the long-term behaviour of cementitious materials

Evidence has been presented for the necessity to consider the crack rate dependence as an important source of time dependence next to bulk creep in a porous, cementitious material. Only by including this contribution to the cracking resistance, the observed times to failure and the crack mouth opening displacements in three-point bending creep tests of concrete beams can be computed with reasonable accuracy.

Numerical Analysis of Tunnelling Effects on Masonry Buildings: The Influence of Tunnel Location on Damage Assessment

The architectural heritage is subjected to various risk factors like the lack of maintenance, the material decay and the external solicitations. Nowadays, due to the ever-increasing demand for urban space, a relevant cause of structural damage that the historical buildings experience is the ground settlement due to excavation works. In the city of Amsterdam, for example, the construction of the new North-South metro line will involve an area characterized by the presence of many ancient masonry buildings. A fundamental phase of the design of this kind of projects is the assessment of the risk of subsidence which can affect the existing structures. The actual method to perform this assessment provides for a preliminary screening of the buildings located in the area surrounding the excavation, in order to evaluate which structures are at risk of settlement induced damage. It is based on the simplification of the building as a linear elastic beam and the assumption of the absence of interaction between the soil and the structure. An improved classification system should take into account the main parameters which influence the structural response, like the nonlinear behaviour of the building and the role played by the foundation in the soil-structure interaction. In this paper, the effect on the damage mechanism of the excavation advance and the location of the tunnel with respect to the building is evaluated. Numerical analyses are performed in order to understand the effect of different settlement profiles of the ground. A coupled model of the structure and the soil is evaluated, taking into account a damage model for the masonry building and the nonlinear behaviour of the soil-structure interaction. This paper demonstrates the importance of 3D modelling; neglecting the tunnel advance can lead to an underestimation of the damage.

Damage Functions for the Vulnerability Assessment of Masonry Buildings Subjected to Tunneling

This paper describes a new framework for the assessment of potential damage caused by tunneling-induced settlement to surface masonry buildings. Finite element models in two and three dimensions, validated through comparison with experimental results and field observations, are used to investigate the main factors governing the structural response to settlement. Parametric analyses are performed on the effect of geometrical and structural features, like the building dimensions, the nonlinear behavior of masonry, and soil-structure interactions. These results are used to create a framework of an overall damage model that correlates the analyzed parameters with the risk of the building being damaged by a given level of settlement. The proposed vulnerability framework has the potential to be developed as a decision and management tool for the evaluation of the risk associated with underground excavations in urban areas.

Form-finding of shell structures generated from physical models

Vector form intrinsic finite element is a recently developed and promising numerical method for the analysis of complicated structural behavior. Taking the cable-link element as example, the framework of the vector form intrinsic finite element is explained first. Based on this, a constant strain triangle element is introduced, and relevant required equations are deduced. Subsequently, the vector form intrinsic finite element is successfully applied to carry out form-finding of shells generated from physical models, such as hanging models, tension models, and pneumatic models. In addition, the resulting geometries are analyzed with finite element method, thus demonstrating that a dominant membrane stress distribution arises when the shell is subjected to gravitational loading.

Investigation of the Shear-Sliding Behavior of Masonry Through Shove Test: Experimental and Numerical Studies

To assess the shear properties of masonry for existing buildings, the shove test method proposed by ASTM C1531 can be carried out, in which the load required to slide a single brick with respect to the surrounding masonry is measured. To control the vertical stress-state on the tested brick, two flat-jacks can be inserted in mortar bed joints in close proximity of it, thus prescribing a predefined level of compression. Although this test seems straightforward, uncertainties have not been resolved yet regarding the actual vertical compressive stress present on the tested brick and the effect of dilatancy. To gain a better insight into the shear-sliding behavior of masonry during the shove test, both experimental tests and numerical simulations were considered in the current research. To analyze these aspects and to precisely define a testing protocol, the experimental tests were performed in a controlled laboratory environment on a single wythe calcium silicate brick masonry wall. In parallel, numerical analyses were carried out using a simplified micro-modeling strategy, in which every brick was modelled, and the mortar joints were considered as zero-thickness interfaces. A composite interface model was used, including a tension cut-off, a Coulomb friction domain and a compressive cap. For the analyzed case study, the numerical results allowed to gain a better understanding of the aspects influencing the shear-sliding behavior of masonry during the shove test.

From Brick to Element: Investigating the Mechanical Properties of Calcium Silicate Masonry

Since the 1980s in the Netherlands, the demand for accelerating the construction process and subsequently reducing the construction costs has led to the replacement of traditional brick masonry with larger masonry units assembled with a thin mortar layer. Accordingly, different masonry unit sizes ranging from traditional bricks (210 × 70 × 100-mm) to larger elements (900 × 650 × 100-mm) have been produced by the calcium silicate industry and widely used for the construction of unreinforced masonry (URM) buildings. To properly assess the performances of URM buildings, numerical and analytical methods require a complete description of the mechanical behavior of masonry at material level. Despite the widespread application of both calcium silicate brick and element masonry, a refined characterization of the mechanical properties of masonry has not received much attention. As a result, an experimental study was conducted at Delft University of Technology for the material characterization of calcium silicate brick and element masonry, with a view to assessments for induced seismicity in Groningen. By using well-designed testing set-ups, the compression, shear and bending properties of calcium silicate specimens were measured, with an aim to understand the strength, stiffness as well as softening post-peak behavior in compression and in shear of both masonry types. This paper provides insight into the nonlinear behavior of the calcium silicate brick and calcium silicate element masonry as a support to the development and validation of numerical and analytical models for the seismic assessment of URM structures.

Form-control of shell structures generated from hanging models with target heights

Shell structures generated from hanging models have structurally efficient forms. Form-control of these shells, which aims to obtain structural forms with single- and multiple target heights due to some architectural requirements, is discussed in this article. First, the vector form intrinsic finite element method is applied to generate the equilibrium form of hanging membranes and thus shell structures. Subsequently, the form-control problem is discussed, which aims to generate a structural form subject to given target height constrains. By introducing the Local Linearization Method to adjust Young’s modulus of the initial structural model, a form-control strategy to generate the equilibrium structural form with a single target height is proposed. By introducing the Inverse Iteration Method to adjust the geometry of the initial model, a form-control strategy to generate the equilibrium structural form with several target heights is proposed. Moreover, to verify the effectiveness of the vector form intrinsic finite element method and form-control strategies, structural analyses and shell behavior assessment of these shells are conducted. These strategies are effective and efficient, which can help architects or engineers to determine structurally efficient geometries in the design process much more easily.