A probabilistic model to evaluate structural masonry

Research in the Reyntjens Laboratory on ancient masonry deals with different aspects of restoration and renovation of masonry structures. First of all an extensive database is being built up which describes, explains and helps to diagnose the damage at historical masonry structures (expert system for the evaluation of ancient brick masonry).

A nondestructive technique, based on electrical resistivity measurements, is being developed to evaluate the extent of deterioration at the inside of massive masonry elements (geo-electrical resistivity measurements, K. Vendrickx). The resistivity method enables to make an image of the internal geometrical and physical situation of the masonry. Eventually, it can be used to compare the situation before and after a consolidation or strengthening treatment. Concerning consolidation and strengthening, the Reyntjens Laboratory focuses on grouting with mineral and polymer grouts, or combinations of both. Extensive research is being done on grout development, where chemical and physical compatibility, stability, mixing procedure and time-evolution of strength and stiffness are studied (Eleni Toumbakari).

Characterization of the masonry with respect to permeability for the specific grouts and their flow and distribution inside the masonry element will help to design the grouting process (mathematical model for the flow of cement grouts in masonry, Filip Van Rickstal). At the end it should be possible to have an on-line control of the grouting process: nondestructive measurements show the distribution of the grout in the masonry, and if the grout flow deviates from the required one, the grout and grouting parameters will be changed interactively to correct the flow.
However, consolidation and strengthening of ancient masonry are always an expensive procedure. Therefor it is of utmost importance to decide whether or not the masonry has to be strengthened or consolidated. Such a decision must be based on safety or risk considerations.

Recent developments in the rational use of masonry have improved the research into its failure mechanisms and its material properties. Based on the growing interest in the reliability of masonry structures, this research aims to develop a probability based model to evaluate the reliability of existing unreinforced masonry structures. The way this research project is built, corresponds with the international code ISO 2394 : "General principles on reliability for Structures".

The central theme is to calculate the reliability index b or the probability of failure p_f of a structural element as defined in modern codes dealing with the design of masonry. For this, available probabilistic methods such as FORM/SORM (First Order Reliability Method/Second Order Reliability Method) are used. By means of a reliability assessment, the impact of a restoration can be evaluated. Moreover, it enables one to decide whether or not a restoration with strengthening or consolidation will be necessary. Thus, it supports the decision process.

But, before being able to evaluate the reliability, knowledge must be gathered about the possible failure criteria g_i(x₁, x₂, ..., x_n) and its parameters. Because design codes mostly contain the failure criteria implicitly, research is executed into the possible failure criteria and their mutual dependency. The parameters x₁, x₂, ..., x_n have to be defined, their probability distribution has to be selected and optimal estimation of the distribution parameters is required.

The knowledge of the failure modes and failure mechanisms of masonry lead to failure criteria for which the great amount of material properties is difficult to gather from experiments. Research is focussed on obtaining the material properties from cores taken from the masonry structure and on the triaxial behavior of the masonry. Therefore, a specially designed triaxial cell with larger dimensions is installed at the Reyntjens Laboratory. Beyond gathering data for the material properties, the research program also aims to optimize the procedure of testing cores to obtain the required information. A total of 20 representative walls is already made in the laboratory for the test program.

Secondly, finite element calculations will be used to calculate the stresses in the masonry structure. On the moment, linear-elastic models are used. Afterwards these models will be evaluated with more complex models that give a better simulation of the real structural behavior of masonry as established from test results.
At last, information needs to be provided on the model uncertainty, related from the executed simplifications in the analysis (FORM instead of SORM, linear-elastic analysis instead of nonlinear, ...). Verification by means of test results and more precious modeling will provide an accurate value for the model uncertainty.

System reliability of an existing structure is important as system failure is normally the worst consequence of structural failure. Therefore, quantifying the global probability of failure is important. Calculating the global probability of failure of a complete building is however, at least for the moment, a problem too complicated to handle and, consequently, the structural reliability method will be extended to calculating the global probability of failure of structural elements. These calculations require the joining of the reliability analysis (FORM) and the finite element analysis (local/global probability of failure).

Copyright 1996, Katholieke Universiteit Leuven
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URL: http://www.bwk.kuleuven.ac.be/bwk/materials/ls02.htm