# Probability of damage of masonry structures due to external ground vibrations

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## Abstract

The SBR richtlijn A states threshold values for the vibration speeds causing a 1% probability of failure of masonry structures. These threshold values are very useful for structural designers, because during the construction of new structures or the demolition of existing structures, it is important to know if these structural vibrations can lead to damage to surrounding structures. However, for vibration speeds that exceed those threshold values, it is difficult to calculate the probability of failure of those structures. During this thesis, a procedure is proposed as a guideline to calculate probabilities of failure for masonry façades for vibration speeds higher than these threshold values.

Many factors influence the probability of failure for masonry structures, like soil properties, masonry properties, initial damage, initial loads or the type and frequency of structural vibrations. Also, it is important to know what should be considered damage. All these factors are implemented in this procedure. The proposed procedure is set up using two different models: a structural model, where the loads and façade dimensions and properties are implemented, and a probabilistic model, where the structural results are implemented, as well as stochastic parameters for some properties. This model leads to a probability of failure.

For the structural model, the software package SCIA Engineer has been used in this project. The structural model ensures that after drafting the façade, implementing the masonry properties, and applying the initial loads and the vibration speed and frequency, the maximum tensile stress for this frequency can be calculated. The tensile stress is the property that will determine if the structure fails, since the tensile stress of masonry is generally low. This tensile stress should then be implemented in the probabilistic model, which also takes the dispersion of the tensile strength and Young’s Modulus into account. A Monte Carlo simulation is performed, which results in the probability of failure of the specific façade for a specific vibration speed and frequency.

This thesis’ main focus was the linear-elastic procedure, where no soil-structure interaction was involved. Since masonry does not behave linearly after the first cracks initiate, some assumptions have been made to enable the calculation to be executed in a linear-elastic way, e.g. that failure occurs if the tensile strength is exceeded over a length of 210 mm. Also, in reality, soil-structure interaction will occur and will produce different structural results and following this, different probabilities of failure. Therefore, this study is able to provide a satisfactory statement regarding the probability of failure for masonry structures, but is not able to substantiate this statement completely.

In this thesis, the proposed procedure has also been executed on three different masonry facades in the city of Delft. The procedure is described extensively using these facades to provide a clear example how the reader can implement this procedure in their own projects. Also, because of the execution of this procedure on these façades, comparisons could be made, so the difference in probabilities of failure between façades, but also between different kinds of soil and vibration frequencies could be investigated.

The results show that the proposed procedure gives an adequate approximation for the probability of failure for masonry structures loaded by construction induced vibrations. Also, the results have been compared to a nonlinear case. This comparison shows that the assumptions that had to be made to approach this problem in a linear-elastic way were sometimes too conservative, but some assumptions were also a little too bold. Also, it is demonstrated that soil-masonry stresses have quite some influence on the structural results and therefore on the probability of failure, but more research regarding this topic is necessary to form a substantiated statement regarding the stresses at the soil-masonry interface.

Summarized, for this thesis, an assessment has been computed to determine the probabilities of failure for masonry structures using linear-elastic calculations. By following this procedure, one will be able to gather a good approximation of the probability of failure. However more research has to be conducted to ensure the soundness of this procedure.