A reliability analysis requires the knowledge of the limit state functions, which distinguishes the safe domain from the failure domain. Because design codes mostly contain the failure criteria implicitly, research is executed into the possible failure criteria and their mutual dependency.
The research results until now, has pointed out useful failure criteria to judge the local probability of failure for masonry shear walls. Further research is dealing with the translation of the failure modes for an out of plumb standing wall into limit state functions. These are used to obtain a global probability of failure for that structural element.
Failure criteria for masonry shear walls
Using the compressive strength of masonry as a threshold for a compression failure criterion is an approximation that is believed to be too narrow, to model the failure of a masonry structure. Structural masonry, and in particular historical masonry that has been primarily designed to withstand vertical loads, most often fails due to tensile or shear stresses.To evaluate the different failure modes in structural masonry, shear walls are an interesting subject. Tests on shear panels in the laboratory, show that three types of failure modes are activated, which mainly describe the real failure process.
These failure modes can be modeled as in figure 1. For the shear strength of the masonry, a Coulomb criterion is commonly accepted. Test results show that better correspondence is obtained when adding a tensile threshold and a compression cap, which leads to the failure envelope drawn in figure 1. To simplify calculations, the parabolic compression cap is linearised. This has a negligible influence on the results.
The three failure modes are represented by following criteria (limit state functions):
| - (mode I) shear failure of bed joints: | gL1 : c + msy - tyz= 0, |
| - (mode II) compression strength of masonry: | gL2 : f'm - sy - tyz = 0, |
| - (mode III) tensile strength of the masonry: | gL3 : sy - ft = 0. |
Failure criteria for an out of plumb standing wall
To calculate the global probability of failure of an out of plumb standing wall, research was focused on its failure modes and corresponding failure criteria. These had to be kept simple in order not to be obliged to elaborate the joining of the finite element model and the reliability algorithm. On the moment, such an integrated algorithm is not yet available.Three different limit state functions were used, built to evaluate the remaining stability of the out of plumb standing wall (figure 2):
- - controlling the overall stability:
- g(e0,e1,e2,G1,G2)=G1.(e0-e1)+G2.(e0-e2) = 0,
- - controlling whether the vertical loads are still applied in the mid-third of the cross-section:
- g(e,d)=e-(d/3),
- - controlling whether the threshold compressive strength is not exceeded using a NTM-element (Non Tension Material):
- - g(smax ,f'm) = smax - f'm.
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