Quantifying the probability of light damage to masonry structures

Abstract

To quantify damage to unreinforced masonry structures, sensitive to tensile stresses and thus to vibrations caused by induced earthquakes in the north of the Netherlands, a bottom-up or physical approach has been followed. First, the crack-based damage expected on these common structures, was defined on a continuous scale (Ψ) based on width, length and number of cracks, so that it could also be quantified. Then, the initiation of cracks was investigated on full-scale masonry walls, single-wythe and of fired-clay bricks, using high resolution Digital Image Correlation; at 0.1 mm in width, cracks become visible. Further, the propagation of cracks, as they widen and lengthen, was monitored during repeated and cyclic testing. At repeated, identical in-plane drift, cracks still propagate and damage increases, though the increase is minor.

The experiments on walls and spandrels, displaying horizontal, diagonal, and vertical cracks, were used to calibrate numerical, finite-element-method models. These reproduced the behaviour of the tests also in terms of crack patterns and propagation, besides stiffness, strength, and hysteresis. Then, the models were adapted to explore the effect of earthquake vibrations, also in combination with existing damage caused by settlement-like actions. In this manner, the effect of initial damage could be quantified. Several other parameters were varied, such as the material strength, the geometry of the masonry walls, the soil properties in a soil-structure interaction interface, the record, PGV, and repetition of the vibrations, and the intensity of initial damage.

Relationships between these parameters and damage were captured into a surrogate model, which was used in a MonteCarlo simulation to determine the probability of damage. The fragility curves reveal, for instance, that fired-clay brick walls with no visible pre-damage (Ψ0=0) have a 5% chance of visible damage (Ψ≥1) at a PGV of, for example, 10 mm/s, a probability that rose to 20% if the walls had undetectable pre-existing damage (Ψ0=0.5). The probability of exceeding aesthetic damage (Ψ≈2.5) at this PGV is less than 1%. A lower PGV is associated with a smaller probability of damage.

Furthermore, it was concluded that repeated events lead to an increase in damage of about 10% for five similar events. This increase is not noticeable. In a sequence of events, similar events accumulate little damage and increases appear when larger events are experienced by a masonry structure.