A Hyperbolic model for Degradation in Tension mode-I Fracture of Masonry

Abstract

The growing need to understand the behaviour of un-reinforced masonry URM), subjected to
repeated light man-made earthquakes caused by the extraction of gas in the north-eastern part
of The Netherlands has resulted in intense research to determine the exact process of crack
initiation and propagation. The historical masonry buildings and Dutch terraced houses in
Groningen are prone to light damages which become severe upon repeated lateral earthquake
loading. Although there are material models that describe the behavior of modern brick
masonry, they do not accurately represent the mechanical properties of 19th century clay brick
masonry. This led to a large-scale research into the mechanical behavior of un-reinforced
masonry and an orthotropic continuum macro-model called the Engineering Masonry Model
(EMM) was proposed. The existing tension constitutive model in EMM assumes a secant
unloading-reloading branch which does not consider the strength degradation of URM under
repeated loading. Since tension mode-I fracture results in cracking of URM, it is important
to study the effects of repeated loading on the propagation of the crack and its effects on the
capacity of the structure.
This thesis presents a degradation model to represent the strength deterioration of URM
observed during repeated loading. The constitutive model formulated in this thesis is based on
hyperbolic functions along with a secant slope for the unloading-reloading branch. To justify
the model assumptions, a single linear 4-node element is analysed with the new model and the
effect of varying different components of the constitutive equations is established. The window
bank spandrel sample modeled as a 4-point bending test is analysed using the new model for 10,
30 and 100 repetitions. It is shown that the hyperbolic model can predict accurately the stress
reduction within each repetition displacement set and also represent the crack width widening
and crack propagation accurately when compared to the experimental results. The new model
is tested on a wall with a window opening sample and the results closely matched that of the
experiment. Finally, recommendations are provided for further development of the hyperbolic
model and calibration of the material properties.