dimarts, 25 de febrer de 2014

Lectura de la tesi de l'Ernest Bernat

L’Ernest Bernat va defensar la seva tesi doctoral amb la seva brillantor habitual (url). Aquí us poso informació sobre el contingut. Més endavant podreu descarregar-la al TDX.

Keywords: Brick masonry walls; Second-order effects; Buckling; Textile Reinforced Mortar; Strengthening; Numerical simulation, Analytical study.

  • Bernat, E.; Gil, L.; Roca, P.; Escrig, C. Experimental and analytical study of TRM strengthened brickwork walls under eccentric compressive loading. Construction and Building Materials 44, 35-47. 2013.
  • Bernat, E.; Gil, L.; Roca, P.; Sandoval, C. Experimental and numerical analysis of bending–buckling mixed failure of brickwork walls. Construction and Building Materials 43, 1-13. 2013.
  • Sandoval, C.; Roca, P.; Bernat, E.; Gil, L. Testing and numerical modelling of buckling failure of masonry walls. Construction and building materials, 25, 4394 - 4402. 2011.


A significant number of buildings are supported by load-bearing masonry walls. The preservation of these worldwide used structures is a sustainable alternative. However, there is little research about the structural response of these particular elements if compared with others materials like concrete or steels framed structures. Hence, a further study of the load-bearing masonry walls is necessary as a starting point for the preservation activities.

The load-bearing masonry walls are usually subjected to a vertical eccentric loading condition, which is related with their complex structural response. This response is characterised by the second-order bending effects due to the eccentricity of the load, the non-linear compressive response of the masonry and its almost negligible tensile strength. Thus, strengthening these walls, in order to increase their load- bearing capacity, is an interesting upgrading alternative to enhance their life-cycle.


The main aim of the thesis is to contribute to the understanding of the structural response of unreinforced and strengthened masonry walls loaded with eccentrically applied compressive loads. This aim will be achieved by completing the following partial objectives:
  • To gather information about the experimental response of load-bearing unreinforced and strengthened masonry walls under eccentrically applied compressive loads.
  • To compare current formulation used in the codes for calculating the load-bearing capacity of masonry walls.
  • To sumarize main numerical models developed for calculating the response of unreinforced and strengthened masonry load-bearing walls
  • To propose simplified analytical formulations to predict the response and the load-bearing capacity of unreinforced and TRM-strengthened masonry walls under eccentrically applied compressive loads. Comparing the results of these formulations with the experimental ones.
  • To perform an experimental campaign on full-scale unreinforced and TRM-strengthened walls
  • To develope and validate a numerical model for the analysis of unreinforced masonry walls and TRM-strengthened walls.
  • To compare the experimental and numerical results with those from the current standards.


An extensive experimental campaign has been carried out. It consisted of hundreds of characterisation tests to obtain the mechanical properties of the component materials which have been used to build twenty-nine full-scale walls. Twenty of these walls were unreinforced and the other nine were TRM (Textile Reinforced Mortar) strengthened. All of them have been tested under eccentric compressive loading conditions. The analysis of the strengthened walls included the influence of the strengthening mortar type on the load-bearing capacity. The effects using anchors or embedding different types of fibre grids have been also analysed.

A bidimensional (2D) simplified micro-model has been implemented to analyse these structural cases. This numerical tool has been validated using the data from the experimental campaign. Finally, analytical methodologies have been proposed to calculate the load-bearing capacity of unreinforced and TRM- strengthened brick masonry walls. Similarly, two current standards, Eurocode-6 and ACI-530 have been applied to the analysed cases and their results have been compared with the experimental ones.

Conclusions about the experimental campaign 

Regarding the material characterisation, it is concluded that the scattering of the mechanical properties of the masonry is significant and has to be taken into account in the calculation procedures or in the interpretation of the results. The larger scattering is observed for the Young’s modulus.
Regarding the tests on full-scale unreinforced walls it is concluded that the geometric parameters (geometric imperfections, eccentricity of the load and slenderness) are the ones that most influence on the load-bearing capacity and the structural response during the test.

By observing the failure patterns of the unreinforced walls it is concluded that the most likely failure mode is the mechanism formation after the opening of one or more mortar joints at a position near mid-height of the wall. In the case of the lesser slenderness walls or the case with centred load, crushing of the masonry is observed together with mechanism formation.

The initial experimental research about the performance of different TRM solutions concluded that the combination of carbon fibre grids and pozzolanic mortar did not fulfil the provider’s specifications. The observed response points out that the most probable cause was adherence problems between the mortar and the fibre because the other tested solutions (using different fibre grids and mortars) correctly reached the expected strength.

The tests on TRM-strengthened walls showed that different failure modes are possible: the joint opening together with the TRM tensile failure and the corresponding mechanism formation, the masonry crushing in compression which usually appears together with a tensile failure of the reinforcement and the shear-compressive masonry failure near the wall’s ends which is the most common failure mode observed. Thus, it is concluded that the performance of the TRM-strengthening system is enough as to change the failure mode of the walls from the mechanism formation typical of the unreinforced ones to the compressive/shear failure of masonry when strengthened.

From the results of the tests on full-scale walls it is concluded that the load-bearing capacity of the strengthened walls is less dependent on slenderness and eccentricity than for the unreinforced ones. In addition, using the TRM strengthening system tends to make more uniform the wall’s behaviour (in the sense of reducing the scattering) and to reduce the out-of-plane non-linear response. Finally, it is remarkable that the TRM is an effective strengthening method which can achieve more than 100% of load-bearing capacity increase.

By comparing the TRM-strengthened walls between them it is observed that it is possible to use two overlapped fibre grids embedded into a single mortar layer if the grid spacing is large enough for the mortar to penetrate. However, this solution provides just a slight increase of load-bearing capacity. Similarly, it was observed that using connectors makes no difference in the load-bearing capacity.
A significant conclusion regarding the use of the mortars distributed as part of the TRM is that the adherence of these mortars has proved to be enough to prevent the debonding failure for all analysed cases. Thus, using connectors for strengthening masonry walls is not necessary.

Regarding the structural response of the walls strengthened with different TRM solutions, it has to be highlighted that they all behave similarly up to loads close to the failure one. Thus, the strain on the strengthened face depends on the TRM system only for loads near the collapse. The experimental results show that the failure mode might be related with the measured strains at low loads (under 50% of the collapse load for each wall) but not with the TRM strengthening system. Thus, the failure mode detection might be possible.  

Conclusions about the numerical analysis 

The proposed model is a bidimensional, plain-strain simplified micromodel characterised by the use of contact elements to represent the tensile and shear response of the masonry and the TRM. This response, defined with a cohesive zone model, is linear up to the maximum strength and after that the joint opens or slides with a linear descending stress. The masonry-TRM contact is perfectly bonded for all cases. In compression, the masonry is set to be elastic-perfect plastic and modelled as a single material (without distinguishing between the brick and the mortar). Triangular objects are used to model the real hinges at the ends of the walls. The numerical model calculation has large deformation capabilities and the load is indirectly applied through an increasingly vertical displacement of the top of the wall. 

The prediction of the load-bearing capacity is very sensitive to the variation of the Young’s modulus of the masonry. In addition, the determination of this parameter shows large scattering which causes uncertainty in the value of this variable. Thus, the uncertainty of E might influence on the results of the numerical model.

Defining an inclined contact to make it possible the compressive-shear failure near the wall’s endings for the TRM-strengthened walls has proved to be an efficient solution to capture this failure pattern for the walls which failed in this way. Furthermore, it is concluded that considering the contact has no effects on the results when modelling walls which are not expected to fail in this way.
The proposed equation to calculate the first mode fracture energy, has brought suitable input data according with the accuracy of the obtained results for the particular analysed cases. Thus, it is considered that the equation might be an acceptable approach to calculate this required parameter although further research is needed.

The proposed model is better at predicting the load-bearing capacity of the most slender walls or the walls with the load applied with larger eccentricity for the unreinforced cases. On the contrary, it might be concluded that the model tends to underestimate the load-bearing capacity of the wall when the compressive response of the brickwork is the dominant process.

The tensile strength of the TRM’s mortar is an important parameter which has to be taken into account in order to obtain accurate results on the wall capacity. This is observed by comparing the theoretical simulated cases among them and analysing the influence of this variable.
The application of the model to theoretical cases proved that considering that the fibre grid is the only component that resists the tensile forces is not the best approximation to the problem because the strength and stiffness of the mortar has significant effect on the calculated response.

Conclusions about the analytical approach 

Two proposed analytical approaches aimed to calculate the load-bearing capacity of unreinforced and TRM-strengthened masonry walls have been used and compared with the Southwell Plot method. For the unreinforced walls the comparison with Eurocode-6 and ACI-530 was also performed. After carrying out all these calculations and comparison it has been obtained that there is not a unique methodology which works accurately for all the cases considered.  Therefore the application range of each of the proposed analytical approaches must be clearly indicated.

The proposed analytical method for unreinforced masonry walls (URMW) consisted on calculating the second order deflection which allows calculating the corresponding bending moment associated to the axial load. Then the maximum tensile and compressive stress due to the axial-bending combination is compared with the corresponding strengths. In contrast, the proposed analytical method for TRM- strengthened masonry walls is based on equilibrium and strain compatibility equations in the cross section to calculate the axial-bending limit combinations.

There is a general tendency of the codes (Eurocode-6 and ACI-530) to underestimate the load-bearing capacity of the tested unreinforced walls. ACI-530 achieves more accurate results than Eurocode-6 for the tested unreinforced masonry walls subject to eccentrically applied compressive load.

The analytical approach consisting of calculating the second order lateral deflections and obtaining the load-bearing capacity by imposing a cross section failure criterion used for the URMW is always applicable and shows accurate results for the most slender walls and the cases with large load eccentricity. Thus, it is concluded that this method is the most suitable one for cases with application range corresponding to slenderness over 12 and load eccentricity over 1/6 of the thickness, accordingly with the comparison with the experimental results. The proposed analytical approach for unreinforced walls is able to predict the failure mode of the cases within its application range.
However, this analytical method is not suitable for calculating the load-bearing capacity of the walls with lesser slenderness, which are not really affected by the second order deformations. It can be concluded that the method is extremely conservative for these cases and is out of its application range.

The Southwell Plot method is the most accurate one but this is not reliable because of its limited applicability. This method requires experimental data which is not always available or might not be consistent enough to be processed in order to predict the collapse load. So, the applicability range of Southwell Plot method is not defined and depends on the experimental results. In addition, this method could not be directly applied on walls with fixed-fixed configuration.


Bernat, E.; Gil, L.; Roca, P.; Escrig, C. Experimental and analytical study of TRM strengthened brickwork walls under eccentric compressive loading. Construction & building materials. 44, pp. 35 - 47. 07/2013.
Bernat, E.; Gil, L.; Roca, P.; Sandoval, C. Experimental and numerical analysis of bending-buckling mixed failure of brickwork walls. Construction & building materials. 43, pp. 1 - 13. 06/2013.

Sandoval, C.; Roca, P.; Bernat, E.; Gil, L. Testing and numerical modelling of buckling failure of masonry walls. Construction & building materials. 25 - 12, pp. 4394 - 4402. 12/2011.