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.

**Publications**

- 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.

**Motivation**

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.

**Objectives**

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.

**Results**

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.

**Publications**
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.