Πειραματική και αριθμητική διερεύνηση της συμπεριφοράς τμημάτων λιθοδομής που υποβάλλονται σε εργαστηριακές φορτίσεις που προσομοιώνουν την εντός επιπέδου ένταση υπό κατακόρυφα φορτία και σεισμικές δράσεις
Authors: Κωτούλας Λάμπρος 
Published: November 2022

The general objective of the present research is on the one hand to clarify the behavior of load-bearing masonry specimens and more specifically of three leaf masonry with joints of sufficient thickness made of traditional mortars and on the other hand to create sophisticated models that will accurately predict their response. The study is divided into two main domains. The first concerns all the required experimental tests carried out in the laboratory of strength of materials and constructions (E.P.A.Y.K.) of the Aristotle University of Thessaloniki and the second the creation of reliable and complex numerical models, which will be able to predict quite precisely the behavior of that kind of masonry walls and generally the behaviour of such structures. In the present work, three-leaf masonry wallets are made of four different traditional mortars with average joint bed and head thickness range from 20.00 mm to 40.00 mm. Through simple laboratory tests to the materials (mortar, stone) an attempt is made to compose complex inelastic statutory laws in order to fill the ABAQUS requisite input data (elastoplastic characteristics of stones, mortar and the interface of the joints) of the fully detailed micromodels. Through the response of the micromodels, follows the calibration of a simpler computational model (macromodels), which will allow inelastic analyzes of larger structures and not only structural elements (lower computational cost). As mentioned above the computational program used for the numerical analyzes of this thesis is Simulia ABAQUS. The whole work is divided into eight chapters: The first chapter is purely introductory. Initially, limited historical data are given on the evolution of masonry buildings over time, while the strategies of simulating are briefly presented as well. In the second chapter, through detailed bibliographic research, masonry mechanical properties are described and analyzed, especially through experimental sequences. Parallel, the efforts made in recent decades by the researchers in order to create numerical models, which can realistically predict the behavior of such a predominantly anisotropic and multiphase material, are being recorded. Furthermore, the literature review contains in detail the new trend and the ways of restoration (intervention mortars, grouts) and reinforcement (carbon fabrics, SRG, tassel, TRM, etc.) of structural systems made of masonry. The third chapter provides an extensive analysis of the consisting materials of a masonry wall. Firstly, a large number of prismatic specimens of the four different mortars, with dimensions according to EN1015-11 (160 mm – 40 mm – 40 mm) are manufactured, so as to calculate Young’s modulus, the compressive and flexural strength of each mortar in specific time intervals (28 days, 3 months, 6 months, 12 months). The importance of the evolution of the strength of mortars lies in two main aspects. On the one hand to clarify the way that the mechanical characteristics changes over time and on the other hand to find the mechanical characteristic at the specific age as the walls of the following chapters subjected to vertical compression (chapter 5) and diagonal tension (chapter 7) tests. Then follows the same procedure for the natural stones used for the construction of the walls, the core of the three-leaf masonry (mortar and stone crushing) as well as the restoration grouts. Regarding that the most vulnerable point of a masonry is the joint between the mortar and the units, special attention was paid to this part as well. For this reason, simple specimens consisting of two stones and an intermediate semi thick layer of joint were made and subjected to bending test, in order to obtain the flexural strength of the interface. The second set of experimental tests concerns reinforcing materials. As the main characteristics of the CFRP and the glass grid are already provided by SIKA materials, more attention was given to the TRM (Textile Reinforced Mortar) reinforcement system and its detachment from the surface of the stone masonry. A single layer of fiberglass was placed in cement mortar matrix. Then, square specimens (265 mm x 265 mm x 25 mm) were tested in diagonal tension and rectangular specimens (240 mm x 160 mm x 30 mm) in four-point bending. Finally, using a mechanical jack, the debonding of the TRM from the tone masonry surface was calculated. The second part of the chapter concerns a detailed numerical investigation. In order to establish correct and realistic stress – strain curves of all individual materials and the properties of interfaces, simulations were made for each one of the above cases. In this way, elastoplastic laws of materials were calibrated and adopted in the more complex simulations of the next chapters. In the fourth chapter two more crucial parameters for the final calibration of the micromodel are investigated. The initial shear strength / cohesion between the stones and the mortar joint and the sliding friction coefficient. Five triplet specimens were built up, one for the M1, M3, M4 mortar and two for the M2 mortar. By applying relatively high vertical compressive stress (0.15 MPa), to ensure the pure horizontal movement of the middle of the three stones, the above parameters were quantified for all specimens. Adopting the exact geometry of the experimental set up, numerical models were created using the methodology of the simplified micromodel. The stones with elastic characteristics and the joint interface were essentially simulated. The mortar was completely ignored in this phase. Thus, both the elastic and inelastic characteristics of the interface (except for its tensile strength) were calibrated and in combination with the results of Chapter 1 (conversion of the flexural strength of the interface to purely tension) all the parameters required for the full definition of the interface were clarified. The first part of the fifth chapter presents the response of the walls in term of axial stresses – vertical / horizontal strain diagrams, as well as their mode of failure under vertical compression load. The wall dimensions are: 600 mm x 500 mm x 830 mm (LxWxH) and were made in the laboratory of experimental strength of materials and structures (A.U.T.H.) by the same materials as those examined in chapter 1. In the second part an attempt is made to simulate them with the method of the micromodel. For each specimen, one either of the north or the south side was selected (orientation of the specimen in the laboratory – dimensions: 600 mm x 500 mm) and the exact geometry of the stones and the joints (horizontal and vertical) were simulated in full detail. Because of the fact that a detailed 3D simulation of all faces requires huge computational cost, it was chosen to give depth to the face that was simulated, equal to the width of the physical specimen, ie 500 mm. In addition, an adhesive surface was defined between each stone and joint with the properties derived from the fourth chapter. Good convergence between analytical and experimental results, leads to the next step which is the calibration of a new masonry model considering that the specimen is no longer composed by separate building materials with distinct mechanical properties, but as a single homogenized material applied to all the model (macromodel method). Concrete Damage Plasticity (CDP) was used for this purpose. Using as compressive strength the response of the micromodel described above, a very good convergence was observed between the latter model and the experimental recordings. The necessity of the experimental tests becomes clearer, when a comparison between them and macromodel simulations whose mechanical characteristics (compressive strength, tensile strength and modulus of elasticity) were derived either from empirical formulas or regulations (blind test) was made. In both cases the results proved to be rather misleading. The sixth chapter deals with the response of masonry specimens under diagonal tension loads. The natural specimens consist of the materials studied and presented in the first chapters. Their dimensions differ relatively from the walls of the fifth chapter only in length, which now amounts to 650 mm. As before, for each wall either the south or the north side was simulated and the same technique was used to build the three-dimensional micromodel. At this point, it should be underlined that a crucial and important parameter for the simulations is to copy as far as possible the experimental setup. In this way the accuracy of the adopted boundary conditions is achieved. Based on the value of the tensile strength obtained from the micromodel, the macromodel was calibrated only in relation to this parameter, completing though the calibration of the macromodel. By adopting values of the regulations and performing blind tests again, this kind of test proves even more the need for experimental measurements and that their absence can lead to completely wrong conclusions as concerns the stone wall strength and generally its response. The seventh chapter deals with the response of the already cracked walls of the fifth chapter, after their reinforcement with strips of carbon fiber and without the previous repair of the existing damages. Initially, their surface is smoothed by applying a cement-based coating and then they are placed in height, using resin, four strips of carbon fiber, each 120 mm wide. The average distance between the strips is 80 mm, while covering the entire length of the west side in each specimen with a second layer. The experimental results are compared with those from the simulation of the micromodel and the macromodel with the results proving the correctness with which the numerical analyzes were set up. The eighth chapter concerns the reinforcement of pre-cracked specimens under diagonally tension loads. The reinforcement schemes under consideration are as follows: 1.Placing half section of a tuft parallel to the continuous horizontal joints in five layers per height or in three layers per height and two diagonal crosses. In the first case belong the specimens C2M4-OLD and C4M2-OLD of the sixth chapter, while in the second the walls C1M1-OLD and C3M3-OLD. Each time it is used the half section of the tuft, ie 14 mm2. The gluing was carried out with epoxy resin, while special attention was paid to the points where the tuft changed direction (wall corners). This was followed by the simulation with the method of the micromodel. As the laboratory sequence of the specimens did not contribute to a total drop in the strength of the virgin specimen (20% maximum drop in all specimens), only the main crack pattern was taken into account in the simulation, just as recorded in the failure mode of Chapter 6, 2.Installation of TRM on the south and north side. The TRM did not wrap the specimens as in the previous case, but was placed on two opposite sides. The specimens of the previous case (1) were used after the tuft was completely removed and only their horizontal and vertical joints were partially restored with the use of cement-based mortar. In order to take into account the great damage that the specimens have undergone, the simulations considered a small fracture of the flexural and shear strength of the interface, which does not exceed 20% of the maximum values derived from the chapters one and four. The same assumption is made for all computational models from now on, 3.After the removal of the TRM and without any repair, the walls were coated and three strips of CFRP per height were set parallel to the layers of the horizontal joints. Each strip has a width of 120 mm and a single layer (thickness 0.129 mm) is placed at a time, with the appropriate second layer overturn, anchoring on the west side. Numerical analyzes of the micromodel and the calibrated macromodel of the pre-test specimen of case (1) followed, but also adopting low strength, as mentioned in the previous case, 4.Laying four CFRP strips in height parallel to the layers of horizontal joints. These specimens are the reinforced specimens already examined in the seventh chapter (dimensions 600 mm x 500 mm x 830 mm) under vertical compression loads, having been damaged by the two previous experimental tests. The simulation of the specimens using both the methods of micromodel and macromodel are governed by the same principles mentioned and analyzed above, 5.In the specimens that have undergone two tests of strong compression, seven strips of carbon fabric are placed, covering practically the entire perimeter of their surface. These walls are subjected to a diagonal tensile test and then a numerical simulation is attempted to predict their behavior using the micromodel and macromodel methods. In ninth chapter, the statutory laws that resulted from the calibration of all the parameters of the numerical macromodel are applied in shear walls. For that purpose, five natural walls are examined, which have been constructed in the laboratory of experimental strength of the materials and constructions of AUTH in an earlier period, however, using the same composition as the traditional mortars examined in Chapter 3 and natural stones of the same origin. All these shear walls have the same dimensions which are 1500 mm in length, 1400 mm in height and 500 mm in thickness. The prementioned shear walls are subjected to recycling horizontal loading under continuous compressive pressure. Using only the simplified simulation method (macromodel) an effort to predict the shear behavior of the experimental specimens both in terms of equivalent shear strength and in the form of failure is being made by the author. The tenth and final chapter includes all the significant conclusions that derive from all the previous work and the whole methodology which was followed, which can be summarized to the following: 1.Extensive experimental study to quantify the basic mechanical characteristics of materials, 2.Extensive experimental study to determine the mechanical behavior at mortar – stone interfaces in very simple specimens (triplets in bending or shear with axial tension), 3.Experimental study on walletes in specific tests of axial compression or diagonal tension, 4.Through all the above, certification of the suitability of statutory laws related to the numerical simulations of micromodels, 5.Use of numerical micromodels to properly calibrate simplified macromodels that can be used to simulate the behavior of prototype structural elements under complex stresses, resulting from a combination of vertical loads and seismic – type horizontal actions. The certification of the reliability of the macromodels with this step-by-step evolutionary process, which at each step is based on experimental measurements, is also a guarantee for the realism of the numerical simulations of the behavior of the prototype structural elements and, by extension, of the prototype structures. For this reason, extended laboratory sequences took place in order to check the fidelity of the computational tools. In this way, highly reliable numerical models can be created that will be able to predict accurately the behavior of such a complex, inhomogeneous building material and the corresponding masonry structural elements constructed in this way. This is the central goal of this work.