LABORATORY TESTS AND MECHANICAL MODELS
FOR THE VALIDATION OF FRP REINFORCEMENT OF MASONRY
STRUCTURES
Alessandro Baratta, Ileana Corbi and Ottavia Corbi
Dept. of Structural Engineering
University of Naples “Federico II”
Via Claudio 21, 80125 Napoli, Italy
ABSTRACT
In the present paper some problems about the refurbishment by FRP materials of masonry structures, e.g. the arch and the
panel, are treated by comparing theoretical and analytical data. On one side, a computational procedure is developed by
considering the NRT (non-resisting-tension) model for structural analysis of masonry structures; on the other side, a masonry
arch and some panels, subjected to vertical and horizontal loads, are tested before and after the application of the C-FRP
reinforcement, working in uni-axial stress state.
Moreover, both the numerical results and the recorded data relevant to the two cases are taken in comparison. One can note
that, especially in the case of FRP reinforcement, theoretical and experimental results for the considered masonry structures
are shown to be in good agreement, also emphasizing the effectiveness of the adopted reinforcement.
Introduction
Advanced technologies and the identification of innovative materials, such as composites, able to respond in a satisfactory
way to needs rarely met by the adoption of traditional materials and methodologies, are acquiring more and more interest for
protection of historical buildings.
Fiber Reinforced Polymers (FRPs) are a type of composites characterized by a polymeric matrix reinforced with continuous
fibers (see e.g. [12], [13]), which exhibit desirable features, such as high mechanical properties, lightweight, high resistance to
chemical agents and corrosion, increased fatigue resistance, reliability and durability, low thickness, adaptability and easy
applicability to complex structural shapes, low invasiveness on the construction. A wide range of amorphous and crystalline
materials can be used as the fiber in FRP materials. In the construction industry the most common fiber used are: glass fiber,
carbon fiber or aramid fiber. Carbon, glass and aramid fibers can be used separately or in conjunction as a hybrid to increase
the stiffness of a structural member or the area within a structure or some the other mechanical characteristics of the FRP
fibers (e.g. density, elastic modulus, tensile strength, ultimate elongation, etc). The embedded fiber matrix (polyester,
urethane, vinilester or epoxy) is responsible not only for keeping the fibers together but also to protect them against
environmental and localized effects. In order to help the application of the FRP reinforcements which are directly laminated on
the structure, some fire retardants are usually incorporated in the resin itself or as an applied gel-coat. Fillers and pigments are
also used in resins for a variety of purposes, the former principally to improve mechanical properties and the latter for
appearance and protective action. In the field of structural rehabilitation the most commonly adopted forms of FRP are strips
and tissues; strips, which are given by parallel continuous fibers, exhibit a mono-directional behavior, and are then strongly
non-isotropic; tissues, which are obtained by the plait of two series of parallel fibers, are characterized by reduced mechanical
characteristics of the final product, but are reduced in their anisotropy as well.
On the other side, the NRT (non-resisting-tension) model for structural analysis of masonry structures [10], [11] proves to be
an effective tool for analyzing the behavior of original structures as well as the effectiveness of reinforcements, also with
respect to seismic thrust. In particular, the present paper represents a part of a more extended research about a procedure for
solving two-dimensional equilibrium problems, which are representative of the behavior of masonry walls loaded by in-plane
forces. The elaboration of the mechanical model of a structure, e.g. a masonry panel, requires first of all that the
characteristics of the masonry texture are formally and qualitatively defined because they strongly condition the behavior and
the resistance of the structure. In the case of a structure composed by a regular distribution of masonry square blocks, it can
be modeled by assuming that the material has not the capacity to transmit any tensile stress along the joints’ direction, but that
a low and significant tensile resistance can arise by means of a suitable relative stagger between the blocks. So the panel can
be associated to an homogeneous bi-dimensional continuum by considering a very low tensile resistance due to the combined
action of the friction and of the stagger of the bricks, in absence of the breaking of the single block. On the other hand, in order
to study a masonry having an irregular texture, the Not Resisting Tension (NRT) model can be assumed as reliable, exhibiting
a simple linear elastic behavior under compression stress states and no resistance in tension, and, thus, resulting in an overall
fragile non-linear behavior. If the loading capacity of NRT structures can be investigated by means of the tools of the Limit
Analysis (L.A.) theory, on the other hand, the study of the intermediate crack situation can not be performed by L.A.techniques, whilst the elastic analysis of the masonry tissue under the assumptions of perfect integrity of the structure and of
purely compressive stresses can lead to significant results. In conclusion, some optimization (stress or strain) procedures,
deriving from the implementation of the basic variational methods extended to NRT models, can be developed (for the
extended procedure see e.g. [1], [2], [3], [4], [5], [7], [8], [9]).
In order to test the developed computational procedure some laboratory tests concerning the masonry structures, as the arch
and the panel, designed to be similar as the theoretical models are made. After loading up to near the collapse threshold,
some C-FRP provisions are applied on the masonry structures which are tested again. The recorded data in comparison with
the theoretical results show to be in good agreement, also emphasizing the effectiveness of the adopted reinforcement.
Numerical/experimental results of a masonry arch
In order to evaluate the benefits induced on a traditional masonry portal arch by the application of continuous carbon fiber
strips, experimental tests have been developed at the Laboratory of Materials and Structural Testing of the University of
Naples “Federico II”. The geometry of the portal arch is symmetrical (Fig.1.a) and the masonry is characterized by unit weight
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γ =12300 N/m and Young modulus E=5.5 GPa.
The structure is subject to its constant own weight and to a lumped horizontal force F, applied on the top right side of the right
abutment in the rightward direction in the increasing phase (Fig. 1.a and b), which is able to potentially produce collapse of the
structure according to a mechanism that is typical of earthquake failures of arch-portals, and it is intended to represent a
pseudo-seismic action, able to yield a measure of the structure attitude to sustain earthquake shaking.
(a)
(b)
(c)
Figure 1. Monitoring and loading equipment for the tested masonry arch (a) and (b), and
deformed configuration at collapse condition for the non-reinforced model as deducted from calculus codes (c).
In the first loading cycle, the structure firstly becomes isostatic by formation of three hinges: one at the keystone on the
extrados and two at the reins on the intrados. The increase of the horizontal force turns the structure into a collapse
mechanism by the further activation of a hinge at the bottom of the right side of the right pile [6]. Therefore the critical condition
is related to the activation of a collapse mechanism, characterized by one additional hinge at the bottom of the right pile on the
extrados. The collapse condition is reached at F∼80 N; the low failure value of the force shows that, due to the chosen elliptical
shape of the arch, the funicular line compatible with the applied loads and admissible (i.e. interior to the arch profile) is already
very close to the upper and lower bounds of the arch profile at the rest condition (Fig. 1.c).
After reaching the collapse condition and completing the unloading process, the portal arch is prepared for laboratory tests on
FRP reinforcements (Fig. 2.a), which are finalized to the evaluation of the benefits induced on the model response by the
application of carbon fiber strips. The adopted reinforcement, produced by FTS, is a BETONTEX system GV330 U-HT, made
by 12 K carbon fiber, jointed by an ultra light net of thermo-welded glass. The mechanical characteristics of the employed
carbon fibers are: tensile limit stress σfrp= 4.89 GPa, elastic modulus in traction Efrp=244 GPa, limit elongation εfrp=2%. The
FRP strip is characterized by thickness of 0.177 mm and depth of 100 mm. The FRP reinforcement is directly laminated on the
masonry, at the same time with the impregnation of the fibers by means of a special bi-component epoxy resin.
The collapse is reached at F∼800 N with an increase in the loading capacity of the portal arch of approximately 10 times with
respect to the unconsolidated case. The funicular line is now free to exceed the lower contour of the portal arch cross section
(Fig. 2.b).
(a)
(b)
Figure 2. Sketches of the deformed configuration at collapse condition for: (a) the extrados reinforced arch,
and (b) the reinforced model as deducted from calculus codes.
At first, one can observe that, in both the reinforced and non-reinforced cases, the representation of the collapse condition
deriving from the theoretical settlement of the problem leads to a situation relevant to the opening of fractures and subsequent
collapse mechanism activations which perfectly agrees with the real situation monitored during experiments: this is clear from
Figures 1.c and 2.b, showing the deformed configurations for the two cases obtained by the codes which have been produced
for numerically implementing the problems, whence one can deduct the hinges distribution.
The calculus code, implementing the above reported theoretic, is demonstrated to be able to capture the behavior of the portal
arch following the whole loading path up to collapse; Fig. 2.b) depicts the collapse mechanism of the structure, clearly due to
the formation of four hinges: one at the keystone on the extrados, two at the reins on the intrados, one at the bottom of the
right pile on the extrados.
Figure 3 depict the numerical/experimental comparison relevant to the right pile top displacement u(mm) versus the varying
load F(N) for the non-reinforced arch (Fig. 3.a) and reinforced with an extrados FRP strip (Fig. 3.b), showing a perfect
agreement of the data and, moreover, a pretty consistent increase in the model loading capacity when adopting the FRP
reinforcement. In particular, both numerical and experimental data agree in assessing the increment of the loading capacity of
the masonry arch due to the extrados FRP reinforcement at approximately ten times the original value.
u (mm)
10
Experimental
results
8
8
6
6
4
4
2
F (N)
0
0
20
Experimental
results
Trend line
Trend line
2
u (mm)
10
40
60
(a)
80
100
F (N)
0
0
200
400
600
(b)
800
1000
Figure 3. Absolute displacement u(mm) of the right abutment versus the horizontal force F(N):
a) non-reinforced and b) reinforced masonry arch.
Numerical/experimental results of a masonry panel
Some masonry panels have been realized at the Laboratory of Materials and Structural Testing of the University of Naples
“Federico II”, which are symmetrical, with a central hole covered by a steel architrave, and having upper part characterized by
a concrete fascia lightly reinforced by steel. The panel geometry is shown in Figure 4.a.
Two cases are presented relevant to a panel made with only tufa bricks and with tufa bricks jointed by a pozzuolana mortar in
order to confer a light additional resistance to the masonry.
In the first case, the panel is made of tufa bricks (type “yellow tufa of Naples”, Italy) not jointed to each other, in order not to
3
confer any additional resistance to the masonry; the masonry itself is characterized by unit weight γ =10300 N/m and Young
modulus E=5.5 GPa. In correspondence of the concrete fascia on the top of the panel a varying force has been applied, and
some loading/unloading cycles have been made. The induced displacements at some selected points (points 1, 2, 3 and 4 in
Figure 4.a) of the panel are recorded by a monitoring equipment consisting of: 4 transducers, placed at different locations of
the panel in order to record the absolute displacements, and 15 strain-gauges, arranged in 3 blocks of 5 strain-gauges, each
block is devoted to record the related strain situation (Fig. 4.b). In details two transducers are located horizontally at two
different heights on the panel right side (transducers 1 and 2), and two in correspondence of the opening, one in horizontal
position at the top of the left side of the hole (transducer 3) and the other one under the architrave, which is devoted
exclusively to control the panel deflection (transducer 4).
After the ultimate load carrying capacity has been attained, some FRP strips has been directly laminated on the masonry (Fig.
4.c), at the same time with the impregnation of the fibers by means of a special bi-component epoxy resin, and some
loading/unloading cycles have been made again. The adopted reinforcement, produced by FTS, is a BETONTEX system
GV330 U-HT, made of 12 K carbon fiber, jointed by an ultra light net of thermo-welded glass. The mechanical characteristics
of the employed carbon fibers are: tensile limit stress σfrp= 4.89 GPa, elastic modulus in traction Efrp=244 GPa, limit elongation
εfrp=2%. The FRP strip is characterized by thickness of 0.177 mm and depth of 200 mm.
A sample of the displacements s(mm) versus the varying force F(N) read by the transducer 1 during the loading/unloading
cycles in the non-reinforced case and in the reinforced case with some horizontally applied C-FRP strips is shown in Figure 5.a
and b.
In the second case, the panel is made of tufa bricks jointed by a pozzuolana mortar in order to confer a light additional
resistance to the masonry. The masonry is made with the same type of tufa bricks used in the building of the first panel, and a
varying force has been applied in the middle left part of the panel, rather than on the top, in way to mitigate the proneness of
the panel to sliding of bricks with respect to each other. The induced displacements at the selected points 1, 2, 3 and 4 have
been recorded during some loading/unloading cycles on the alone masonry panel and after the application of the C-FRP
reinforcement. Two applications of the FRP strips have been made: in the first case the C-FRP strips have been laminated
along the vertical direction on the panel (Fig. 4.d) in order to contrast the principal tensile stresses; in the second case other
horizontal strips have been superimposed on the last intervention (Fig. 4.e).
2,3 m
0,124 m
1
0,200 m
4
1,322 m
2,23 m
2
3
0,382 m
0,775 m
0,750 m
Transducer
( )
(a)
(b)
Strain-gauge
(c)
(d)
(e)
Figure 4. (a) Panel geometry; (b) monitoring/loading equipment for the tests applied on the masonry panel;
(c) C-FRP shear reinforcement; (d) flexural FRP reinforcement; (e) combined FRP reinforcement.
A sample of the displacements read by the transducer 1 during the loading/unloading cycles in the non-reinforced case and in
the two reinforced cases is shown in Figure 5.c, d and e.
By the diagrams in Figure 5, which report the displacements s(mm) versus the varying force F(N) read by the transducer 1,
some considerations can been made. In first instance it is evident the effect of the mortar between the bricks in terms of global
resistance, so the panel with mortar collapses in correspondence of load value about 5000 N instead of 2500 N in case of the
panel without mortar.
Then, with reference to the panel’s reinforcement by means of the application of some C-FRP strips, both in the panel with
mortar that without mortar, the major effect of the C-FRP intervention is the reduction of the stress in the masonry. In general
lower displacements at the locations monitored by the transducers can be recorded in the consolidated case with comparison
to the unconsolidated case. Actually one can notice that, with reference to the same load intensity (e.g. in correspondence of
the load value 3000 N in Figure 5.c, d and e), lower displacements can be recorded in case of FRP insertions. Obviously the
effect results much more evident in the panel with mortar with respect to the panel without mortar, and is evident still more
when the intervention becomes more invasive (Fig. 4.b). Moreover, the increase of the overall stiffness of the panel results in a
higher loading capacity with respect to non-reinforced masonry wall. In particular the trend of each curve, shows that it is
closer to the x-axis (representing the load variable), thus indicating an increase in the stiffness which is also related to an
higher collapse value of the load.
a)
20
c yc le 2
Trd 1
c yc le 1
20
18
18
16
16
14
14
12
12
u(mm)
u(mm)
b)
Trd 1
c yc le 1
10
c yc le 2
10
8
8
6
6
4
4
2
2
0
0
0
1000
2000
0
3000
1000
c)
d)
Trd 1
40
c yc le 1
c yc le 2
2000
3000
F(N)
F(N)
35
e)
Trd 1
40
c yc le 3
c yc le 1
Trd 1
c yc le 1
60
c yc le 2
c yc le 2
c yc le 3
35
50
30
30
25
25
20
u(mm)
u(mm)
40
20
30
15
15
20
10
10
10
5
5
0
0
0
1000
2000 3000 4000 5000 6000 7000
F (N)
0
0
1000
2000
3000
4000
F(N)
5000
6000
7000
0
2000
4000
6000
8000
10000
12000
F(N)
Figure 5: Displacements recorded by on the masonry panel without mortar in the non-reinforced case (a) and with FRP strips (b), and on the
panel with mortar in the non-reinforced case (c), and in the cases with different application of the FRP strips (d) and (e).
In the final step the theoretical results are compared to the data recorded by the transducers site at the points 1, 2 and 3
during the laboratory tests. To this aim, as regards to the experimental data, one refers to the displacements recorded by the
transducer 1 during the first cycle of the test in the phase of the load; on the other hand, the theoretical data are those relevant
to the wall having the geometry and the mechanical parameters of the masonry panel with mortar built for the laboratory tests.
In the case of non-reinforced panel (Fig. 6.a) the comparison between the theoretical results (continuous lines) and the
experimental data (red dots) shows a general behavior lightly more stiff than the theoretical one. This effect is probably due to
the condition where in the first phase of the computational procedure the NRT material deforms in tension through the
activation of micro fractures; an effect that evidently does not exist in the real behavior of the masonry. In particular, the
experimental curve relevant to the transducer 1 (Fig. 6.a) shows a sudden rise with respect to the experimental data; this effect
is due to the relative local sliding of the bricks that, in the tests, superposes to the general behavior of the panel.
Transducer 1
Trans ducer 1
Experimental data
Experimental data
Theoretical results
Theoretical results
1
1
0,8
0,8
0,6
u(mm)
u(mm)
0,6
0,4
0,4
0,2
0,2
0
0
0
0
100
200
300
400
500
100
200
300
400
500
F(Kg)
F(Kg)
(a)
(b)
Figure 6. Absolute displacement u(mm) of the right abutment versus the horizontal force F(N):
a) non-reinforced and b) reinforced masonry panel.
As concerns the C-FRP reinforced panel (Fig. 6.b) one can notice that, for the data recorded by the transducer 1, but in
general for the all monitored locations, the theoretical curves (continuous lines) and the experimental data (red dots) show a
very good agreement. Such adherence of the results can be easily explained, since the FRP reinforcements have been
applied on a structure that has already experimented the collapse condition with an already defined fracture scenario.
Moreover this suggests that, in the case of a masonry building, the FRP reinforcement reduces exclusively the relative sliding
between the bricks without influencing the general characteristics of deformability and stiffness.
Conclusions
The paper focuses on the possibility of proposing a theoretical treatment for the reinforcement with FRP of masonry structures.
Actually the modern technology of materials offers a wide variety of possibilities for the refurbishment of existing structures:
new advanced materials are often preferable to traditional materials for their enhanced characteristics in terms of
effectiveness, reliability and flexibility, which always ensure high standard of performance. In details the FRP materials are
special composites currently attracting much attention for refurbishing and/or consolidating masonry structures with effective
and low invasive interventions.
To this aim, starting from the NRT model, a theoretical procedure is developed to solve the problem of structural analysis of
masonry bodies. Moreover, some laboratory tests developed for evaluating the effectiveness of alternative technologies, and
based on the adoption of innovative materials for repairing ancient constructions, are reported with reference to the portal arch
and to the masonry panel with a central hole.
The data recorded during the laboratory tests in both two cases, not reinforced and reinforced, compared to the theoretical
results, show a perfect agreement of the experimental/theoretical data and, moreover, a pretty consistent increase in the
model loading capacity when adopting the FRP reinforcement. In particular, for the portal arch both numerical and
experimental data agree in assessing at approximately ten times the original value the increment of the loading capacity of the
masonry structure due to the extrados FRP reinforcement. On the other hand, for the masonry panel the increase of the
overall stiffness of the structure is put to evidence and the reinforcement results in a higher loading capacity with respect to
non-reinforced case.
The differences of behavior of the masonry structure before and after the application of the refurbishment, and the comparison
between different applications of the reinforcement, confirm the idea that researchers and technicians should know very well
the stress distribution and the fracture scenario before proposing any intervention on a structure, in order to select the really
most appropriate typology of reinforcement and to correctly use innovative materials as the composites.
Acknowledgments
The present research has been developed thanks to the financial support by the Department of "Protezione Civile" of the
Italian Government, through the RELUIS Pool (Convention n. 540 signed 07/11/2005, Research Line n. 8).
References
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Baratta, A., “Statics and reliability of masonry structures”, in “Reliability Problems: General Principles and Applications in
Mechanics of Solids and Structures”, F.Casciati & J.B.Roberts Eds, CISM, Udine, Italy (1991).
Baratta, A., Corbi, I., “A theoretical and experimental stress distribution in reinforced no-tension walls”, in: P.B. Lourenço,
P.Roca, C. Modena, S. Agrawal (Eds) “Structural Analysis of Historical Constructions”, vol.2, pp. 1289-1296, New Delhi,
India (2006).
Baratta, A., Corbi, I., “On the Analysis of Regular Masonry Walls with Friction”, 7th International Masonry Conference, p.
41, Westminster, Uk (2006).
Baratta, A., Corbi, O., “The No Tension Model for the Analysis of Masonry-Like Structures Strengthened by Fiber
Reinforced Polymers”, Intern. Journal of Masonry International, British Masonry Society, 16(3), 89-98 (2003).
Baratta, A., Corbi, O., “On Variational Approaches in NRT Continua”, Intern. Journal of Solids and Structures, Elsevier
Science, 42, 5307-5321 (2005).
Baratta, A., Corbi, O., “Fibre Reinforced Composites in Civil Engineering. Experimental Validation of C-Fibre Masonry
Retrofit”, Intern. Journal of Masonry International, British Masonry Society, 18(3), 115-124 (2005).
Baratta, A., Corbi, O., “Relationships of L.A. Theorems for NRT Structures by Means of Duality“, Intern. Journal of
Theoretical and Applied Fracture Mechanics, Elsevier Science. 2005, 44, 261-274 (2005).
Baratta A., Toscano R., “Stati Tensionali in Pannelli di Materiale Non Reagente a Trazione”, Proc. 6th Nat. Conf. AIMETA,
Genova (1982)
Baratta, A., Voiello, G., “Modelli Matematici per l' Analisi delle Strutture Murarie”, J. Restauro, Vol. 87/88, Napoli (1987).
Heyman, J., “The stone skeleton”, Journal of Solids and Structures,2, 269-279 (1966).
Heyman, J., “The Safety of Masonry Arches”, J. Mechanic Sciences, 2, 363-384 (1969).
Schwegler, G., “'Masonry Construction Strengthened with Fiber Composites in Seismically Endangered Zones”, Proc.
10th Eur. Conf. Earthquake Engineering, Vienna (1994).
Traintafillou, T.C., “'Innovative Strengthening of Masonry Monuments with Composites”, Proc. 2nd Int. Conf. Advanced
Composite Materials in Bridges and Structures, Montréal (1996).
Ugural, A.C., “Stresses in plates and shells”, McGraw-Hill (1999).