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J. Civil Eng. Architect. Res. Vol. 2, No. 12, 2015, pp. 1181-1191 Received: May 27, 2015; Published: December 25, 2015
Journal of Civil Engineering
and Architecture Research
Assessment and Alternative Design Solutions for Strengthening of RC Structure—A Case Study
Tanya Chardakova and Marina Traykova
Department of RC Structures, University of Architecture, Civil Engineering and Geodesy, Sofia, Bulgaria
Corresponding author: Tanya Chardakova ([email protected])
Abstract: The rehabilitation and strengthening of an existing reinforced concrete structure of a technical room, part of a fountain in a public garden are presented. The lack of maintenance during long years of use and the unfavorable climatic conditions have led to many damages in the structural elements. The paper addresses a study for two alternative design solutions for strengthening—with reinforced concrete and with fiber reinforced polymer (FRP). The case presented some interesting design challenges that are discussed in the paper: the geometry of the structure, the concept of the design, the technical limitations and requirements of the stakeholder, etc. The site investigation and the general conclusions for the actual state of the structure are presented in the paper first. Then numerical assessment of the structure is done, using the results of the site investigation. Finite element analysis is used for this purpose. A detailed analysis of the two design solutions is presented. Due to technical requirements of the stakeholder, some redistribution of bending moments is allowed after the strengthening. Both design solutions are based on this fact. Original design procedure for the design of the strengthening with reinforced concrete, taking into account the initial loading of the structure before the strengthening is presented. The reasons for the final choice of design solution are discussed. Finally, some general conclusions and recommendations in such cases are given. Key words: RC Structures, rehabilitation, strengthening, FRP, shotcrete, moment redistribution, initial loading.
Nomenclature:
As,e Existing reinforcement (mm2) As,r Strengthening reinforcement (mm2) Asw Transverse reinforcement (mm2) Mp1 Bending moment from initial loading p1 (kN.m)
Mp2 Bending moment from loading, applied after strengthening (kN.m)
MEd Design bending moment (kN.m) Msy Yielding bending moment (kN.m) VEd Design shear force (kN) VRd,e Shear force resistance of the existing element (kN) VRd,r Added shear force resistance after the strengthening (kN)b Width of the section (mm) de Design height of the existing section (mm) dr Design height of the strengthened section (mm)
fcd Design compressive cylinder strength of the concrete (MPa)
fyd,e Design yield stress of the existing steel reinforcement (MPa)
fyd,r Design yield stress of the strengthening steel reinforcement (MPa)
x Height of the compression zone (mm) z Moment arm of the inner forces (mm)
εce,p1Maximal strain of the existing concrete under initial loading (dimensionless)
εce,p2Maximal strain of the existing concrete under loading, applied after the strengthening (dimensionless)
εse,p1Strain of the existing reinforcement steel under initial loading (dimensionless)
εse,p2Strain of the existing reinforcement steel under loading, applied after the strengthening (dimensionless)
εsr Strain of the strengthening reinforcement steel (dimensionless)
σce,p1Maximal stress of the existing concrete under initial loading (MPa)
σce,p2Maximal stress of the existing concrete under loading, applied after the strengthening (MPa)
σse,p1Stress of the existing reinforcement steel under initial loading (MPa)
σse,p2Stress of the existing reinforcement steel under loading, applied after the strengthening (MPa)
σsr Stress of the strengthening reinforcement steel (MPa) θ Angle between the crack and beam axis
1. Introduction
The National Palace of Culture in Sofia, Bulgaria, is
an emblematic building in the center of the city. The
Assessment and Alternative Design Solutions for Strengthening of RC Structure—A Case Study
1182
building and the garden in front of the Palace are
executed in the 80s of the 20th century. The fountain
and the water cascade are the “heart” of the whole
complex and a very attractive place for rest and walk.
During a very long period of time the unfavorable
climatic conditions and the lack of maintenance have
led to serious damages and to the decreasing of the
bearing capacity of the main structural elements. In
the same time, many inappropriate interventions are
executed. All these circumstances determined the
actual state of the structure.
The existing structure is executed from cast in situ
reinforced concrete and consists of slabs, beams and
columns. The structure forms a cascade, each level
being a beam slab and the bottom of the fountain—a
flat slab. For the shifting of the levels beams are
designed, so each level is encircled by series of beams
(Figs.1 and 2). During the major part of the year the
structure is under water.
Fig. 1 View of the fountain.
Fig. 2 Partial section of the structure.
The assessment of the actual state of the structure is
performed in two steps: Site investigation and
numerical assessment. Based on the results, two
alternative design solutions for rehabilitation and
strengthening are developed.
Based on a real case study, the paper deals with the
design process of the strengthening of existing
structures. Many factors: technical, financial,
architectural, specific requirements etc., can play a
decisive role for the final solution. The correct
engineering approach sometimes needs a complex
analysis of the structure: site investigation with
detailed description of the actual state of the structure,
numerical assessment for identification of the
problematic details, design of the appropriate
strengthening. It’s possible to choose a variant
different from the traditional approaches or to propose
alternative solutions. Finally the retrofit solution
should focus mainly on developing safe, simple and
cost effective technique which satisfies the
requirements of the acting standards.
2. Site Investigation
The site investigation is focused on the
determination of the grade of the concrete and the
diameter and the type of the reinforcement steel. A
visual inspection of the structural elements is done.
According to the results of the instrumental
assessment the following results for the materials are
found:
The grade of the concrete is C40/50 for the slabs
and the beams at level -0.15, +0.65 and +1.05 and
C45/55 for the slab and the beams at level +0.25 (the
grade notification is in accordance with BDS EN 1992
[1]);
The grade of the concrete for the columns is
C28/35;
The diameter of the reinforcement is: for the
slabs 14 mm, for the beams 16 mm and for the
columns 18 mm.
The following conclusions after the site
investigation are made:
Assessment and Alternative Design Solutions for Strengthening of RC Structure—A Case Study
1183
Serious cracks (Fig. 3);
Very high level of carbonization of the concrete
(Fig. 4);
Loss of concrete cover;
Corrosion of the reinforcement;
Serious damages in the insulation on the top side
of the slab.
3. Numerical Assessment
The existing structure is assessed for gravity loads
only, as it is underground and its surrounding thick
walls act as a stiff box, so seismic action is not an
issue. A static analysis of the existing structure is
performed, as follows:
Fig. 3 Wide cracks at the bottom side of the slab.
Fig. 4 Effects of carbonization.
the slabs at level +1.05, +0.65 and +0.25
are solved separately as simply supported one-way
slabs;
the slab at level -0.15 is solved by finite element
analysis; the model is partial of the slab itself, the
surrounding beams and the relevant supports (modeled
as simple)—the columns under this slab and the wall
on axis 8 (Fig. 5); the latter is necessary due to the
lack of direct support of beams 28 and 29 (numbers of
the beams in accordance with Fig. 6);
the beams are solved by finite element analysis of
a model of the whole structure (Fig. 7), as the load
path is not quite clear, due to the fact, that beams 28
and 29 are not supported directly; again, the columns
and the walls are modeled as simple supports;
the axial forces in the columns are obtained by
the finite element model of the beams; incidental and
second order eccentricity are calculated in accordance
with [1].
The numerical assessment of the capacity of the
existing structural elements is based on the site
investigation results. The capacity is compared to the
design effects, obtained by the static analysis. The
following conclusions are made, based on this
comparison and the actual state of the structure:
Fig. 5 Finite element model of the slab at level -0.15.
Assessment and Alternative Design Solutions for Strengthening of RC Structure—A Case Study
1184
Fig. 6 Numbering of the beams.
Fig. 7 Finite element model of the beams.
the calculated capacity of the slabs for bending
and shear is adequate and the deflections are within
acceptable limits, so design of their strengthening is
not needed; however, due to their poor actual state,
rehabilitation is necessary and minimal strengthening
is recommended;
the capacity of some of the beams for bending in
the mid span, bending over the support and/or shear is
not adequate; for these beams strengthening shall be
designed; for the other beams rehabilitation is
necessary and minimal strengthening is recommended;
the capacity of all the columns for axial force
with and without bending is quite adequate, indeed by
a large margin; their actual state is very good, too -
much better than the state of the slabs and beams;
therefore, no strengthening is needed and only
rehabilitation is recommended.
4. Alternative Design Solutions for the Strengthening of the Structure
Two alternative design solutions for strengthening
are presented: by reinforced concrete and by fiber
reinforced polymer (FRP). Regardless of the choice of
strengthening solution, rehabilitation of the structure is
required, including:
filling of cracks with low viscosity epoxy resin;
treatment of the exposed reinforcement by
corrosion inhibitor;
removal of loose concrete until the substrate is
solid;
cleaning of the concrete and reinforcement steel
until free of dust, rust, grease, oils, etc; additional
roughening of the concrete surface if needed;
treatment of the deteriorated concrete surfaces by
thixotropic low-shrinkage fiber reinforced cement
mortar after proper preparation of the substrate.
4.1 Concept of the Design
There is a thick, high-strength stucco, fountain
equipment and decorations at the upper side of the
slabs, as well as boards at the upper side of the beams.
The stakeholder requires these to be left intact.
Therefore, the strengthening at the upper side of the
structure would be technically challenging. The
concept of the design is based on that fact. Regardless
of the choice of strengthening solution, all
interventions are to be at the bottom side of the
structure. As the clear height of the technical room
under the fountain is limited, significant increase of
Assessment and Alternative Design Solutions for Strengthening of RC Structure—A Case Study
1185
the height of the elements is not appropriate. Thus, the
concept of the design is to add strengthening tensile
reinforcement—either steel rods with subsequent
shotcreting, or FRP.
This approach is very suitable for increasing the
capacity for bending in the mid span of the beams.
Concerning the capacity for bending over the supports,
however, this would not be of much help. One
possible solution is to allow the forming of plastic
hinges in the beams near the supports, and to
redistribute the moments from these sections towards
the mid span (Fig. 8). This approach is very common
for the reinforced concrete structures, and recent
studies show that it is applicable for continuous RC
beams strengthened with FRP, too [2-4].
Thus, the design moment in the mid span is
determined by Eq. (1):
, , 2I J
i pl i elM MМ M
(1)
where the notifications are according to Fig. 8.
To increase the capacity of the beams for shear,
transverse reinforcement should be added. Given the
cross-section of the beams and the fact that
interventions are only to be undertaken from the side
of the technical room, the shear additional transverse
reinforcement is L-shaped, anchored at the bottom
side of the beam.
4.2 Strengthening with Reinforced Concrete
The following assumptions are adopted for the
design of the strengthening:
Bernoulli's hypothesis is valid;
tension stresses in the concrete are neglected;
the deformation of the reinforcing rods is equal to
the deformation of the adjacent concrete;
slipping between strengthening and existing
material is neglected;
the stress-strain relationship of the materials is
according to Fig. 9;
the superposition principal is adopted to account
for the initial loading of the structure, along the lines
of FRP strengthening [5, 6] (Fig. 10).
Fig. 8 Redistribution of the moments in the beams.
Fig. 9 Stress-strain relationship of the a) concrete; b) reinforcement steel.
,, ,
, ,
,,
3
. ..
2
.
.
c eyd e s e
c e yd ee
c ec e cd
c
x bf A
xd x
f
(3)
First the stress and strain state of the sections under
initial loading is determined in accordance with
Chardakova et al. [7]. For this purpose the yielding
moment of the section is calculated by Eq. (2), which
is a moment equilibrium equation in accordance with
Fig. 11:
Assessment and Alternative Design Solutions for Strengthening of RC Structure—A Case Study
1186
, ,. .3sy yd e s e exM f A d
(2)
where x is determined using the equations of the
physics and the geometry (Eq. 3).
The stress and strain of the concrete and the
reinforcement are determined by the same system of
equations. It is verified that the maximal concrete
strain is lower than εc3 (εc3 according to Fig. 9a). If this
is not so, the obtained results are not valid and
recalculation is needed [7].
As the moment from the initial loading (just before
strengthening) Mp1 is lower than the yielding moment,
the stress and strain state of the section under initial
loading (Fig. 12) can now be determined:
1, 1 ,
1, 1 ,
1, 1 ,
, 1, 1 ,
3
.
.
.
.
pse p yd e
sy
pse p yd e
sy
pce p ce sy
sy
ce pce p cd e
c
MMM
fMMM
f
(4)
For the design of the strengthening it is assumed
that both the existing and the new materials are fully
used, i.e. their stress and strain are:
,
, 2 , , 1
, 2 3 , 1
, 2 , 1
sr yd r
se p yd e se p
ce p cu ce p
ce p cd ce p
ff
f
(5)
Here the design compressive strength of the new
concrete is not relevant, as the strengthening is in
tension zone. Nevertheless, it is the common practice
to recommend the grade of the new concrete to be at
least one above the grade of the existing concrete, due
to contact slip issues. In this case however this is not
possible, as the grade of some the slabs is as high as
C45/55, and the grade of the shotcrete is limited by the
specifics of the technique (water-cement ration,
chemical additives, etc.). Thus the highest locally
available grade of shotcrete is recommended and the
new-old concrete connection is verified.
The design height of the strengthened section dr is
predetermined by technical requirements.
The stress and strain state of the section under
loading after strengthening is shown at Fig. 13 [7].
The parameters α and β, defined at Fig. 13 are
calculated:
3 3
3 , 1
2 1
3. 1
cu c
cu ce p
(6)
Relative compression zone height ξ, relative arm of
the couple of the inner force ζ, and relative moment
mEd are calculated:
2 , 2 ,
2, 2
1 .
. ..
0,5. 1 . . .
r
p se p s e r eEd
r ce p
xd
M A d dm
b d
(7)
Then the required strengthening reinforcement is
calculated by Eq. (8):
2 , 2 ,,
. . . .
. .p se p s e e r
s rr yd
M A d dA
d f
(8)
The required transverse reinforcement is calculated
by Eq. (9):
, , ,. . .ctgswRd r Rd e ywd r
r
AV V z fs
(9)
It turns out that minimal transverse reinforcement is
sufficient for the strengthening of the beams.
The connection between the new and old concrete is
calculated in accordance with BDS EN 1992 [1]. The
stress in the contact surface is calculated for the most
unfavorable conditions possible:
, ,,
.0,5. .s r yd r
Ed surface cdsurface
A fv f
A (10)
Assessment and Alternative Design Solutions for Strengthening of RC Structure—A Case Study
1187
The contribution of the cohesion is neglected for the
calculation of the required dowel reinforcement, as the
intervention technique is shotcreting:
,,
,
.
.Ed surface surface
s dowelsyd dowels
v bA
f (11)
where μ is the friction coefficient.
Detail of the strengthening of one of the beams is
given at Fig. 14.
4.3 Strengthening with FRP
The design of the strengthening with FRP is in
accordance with CNR-DT 200 [6]. For the
strengthening for bending, FRP plates (laminates) are
suitable, and for shear-FRP strips. Only one layer of
FRP plates is used, as higher number of layers will
decrease the capacity of the beam for moment
redistribution [2, 3]. For the same reason special
consideration is given to the strengthening
configuration [4].
First, the ultimate design strength for intermediate
debonding is calculated:
,2 .fdd cr fddf k f (12)
where kcr can be taken equal to 3 and ffdd is the ultimate
design strength for laminate/sheet end debonding (this
failure mode can be avoided by proper anchoring).
Fig. 10 Superposition principal.
Fig. 11 Stress and strain state of the section under yielding moment.
Fig. 12 Stress and strain state of the section under initial loading.
Assessment and Alternative Design Solutions for Strengthening of RC Structure—A Case Study
1188
Fig. 13 Stress and strain state of the section under loading, applied after strengthening.
Fig. 14 Detail of the RC strengthening of the beam.
Assessment and Alternative Design Solutions for Strengthening of RC Structure—A Case Study
1189
The corresponding design strain is:
,2fddfdd
f
fE
(13)
where Ef is the elasticity modulus of the FRP.
Then the maximal tension strain of the FRP is:
max . ;fkfd a fdd
f
(14)
where εfk is the limit strain of the FRP, ηa is the
environmental conversion factor, and γf is partial
safety factor.
Again for the design of the strengthening for
bending, the initial loading is accounted for. The
design process is iterative: the quantity of the selected
FRP material is chosen, then the bending capacity is
calculated. For this purpose it is first assumed that the
FRP system reaches its limit strain before the concrete
(the assumption is checked in the end and if it is not
correct the moment is recalculated for crushing of the
concrete failure mode). Then the height of the
compressive zone is determined using the force
equilibrium equation. After that the bending capacity
can easily be calculated using the moment equilibrium
equation.
The strengthening for shear is somewhat unusual, as
it is not the typical U-wrapping, but L-wrapping, due to
the shape of the beam. However, given that proper
anchoring is ensured, the same approach as for
U-wrapping, proposed in CNR-DT 200 [6], can be used.
Again the design process is iterative: the quantity of the
selected FRP material is chosen, then the FRP
contribution to the share capacity is calculated:
, .0,9. . . .ctgfed fRd f f
Rd f
f wV d t
p
(15)
where γRd is partial factor, ffed is effective FRP design
strength, tf, wf and pf are the strip thickness, the strip
width and the axial distance between the strips.
Detail of the strengthening of one of the beams is
given at Fig. 15.
Fig. 15 Detail of the FRP strengthening of the beam.
4.4 Comparison of the Alternative Design Solutions and Final Decision for the Strengthening
The two alternatives are compared, so the
stakeholder can take informed decision for the best
solutions, given their priorities:
the capacity for bending of the elements after
strengthening is almost equal for the two alternatives;
the capacity for shear of the beams is higher even
with minimal strengthening with reinforced concrete
than that with FRP, because of the increase of the
cross-section dimensions;
the capacity for shear of the slabs is significantly
increased with reinforced concrete, but remains
practically the same as prior the strengthening with
FRP;
the stiffness of the elements, especially the slabs,
is significantly increased with reinforced concrete, but
remains practically the same as prior the strengthening
with FRP;
Assessment and Alternative Design Solutions for Strengthening of RC Structure—A Case Study
1190
the FRP strengthening technique is much quicker
and requires less wet processes;
the cost of the initial investment is much higher
for the FRP strengthening;
the FRP technique is much more sustainable,
because of the high effectiveness of the material.
Based on this information, given in detail, the
stakeholder made the decision that the strengthening
with reinforced concrete is undertaken. The main
reason for this decision was the cost of the FRP
interventions.
5. Conclusions
In this paper the site investigation, numerical
assessment and two alternative design solutions for the
strengthening of the structure of a fountain in Sofia,
Bulgaria is described. The case study is specific in
several ways: the concept of the design, the geometry
of the structure, the technical limitations, etc.
Based on this specific case study, the following
general conclusions can be made:
When there are technical limitations for the
strengthening, the redistribution of the bending
moments is a possible solution. However, the
redistributed moment should not be more than 30% of
the elastic moment, or else large rotation in the plastic
hinge can be expected.
When the load path or the static scheme of the
existing structure is not clear, full finite element model
of the structure may be the best solution for the
assessment.
The final decision whether or not a structural
elements should be strengthened should be made not
only based on the results from the numerical
assessment, but also based on the actual state of the
structure. In this case the numerical assessment shows
that many of the elements do not need to be
strengthened, but the site investigation proves
otherwise: the wide cracks suggest that these elements
have not responded well to the past and present loads
and actions.
The value of the initial loading of the existing
structure that is to be strengthened is crucial for the
effectiveness of the interventions. Therefore, it should
be clarified prior the design and taken into account in
the calculations.
The accompanying activities like the replacement
of insulation may proof to be as important as the
strengthening itself. In this case all the structural
problems were effects from the poor maintenance and
leaking. Without the execution of proper
waterproofing, all the undertaken interventions would
be just a temporary solution of the structural problems
and in a few years the state of the structure would be
as bad as it was before the strengthening.
In order to be able to use the remaining capacity
of the existing structure, rehabilitation should be
undertaken before any strengthening interventions.
Without this step, the adequacy of the design solution
is questionable.
The choice of strengthening materials is
dependent on the characteristics of the existing
materials. Sometimes, however, technical limitations
are the leading factor when choosing strengthening
materials. In such cases verification of the new-old
material connection is mandatory.
The decision-making for the most suitable
strengthening technique should be made on the basis
of certain technical, socio-economical and
architectural criteria that are predetermined. Weight
factors should be assigned to each criteria, depending
on the priorities of the decision-maker.
References [1] BDS EN 1992-1-1:2005/NA:2015 Design of reinforced
concrete structures, General rules and rules for buildings, Bulgarian Institute of Standardization, 2015. (in Bulgarian)
[2] A. Maghsoudi, H. Bengar, Moment redistribution and ductility of RHSC continuous beams strengthened with CFRP, Turkish J. Eng. Env. Sci. 33 (2009) 45-59.
[3] H. Akbarzadeh, A. Maghsoudi, Experimental and analytical investigation of reinforced high strength concrete continuous beams strengthened with fiber reinforced polymer, Materials & Design 31 (2010) 1130-1147.
Assessment and Alternative Design Solutions for Strengthening of RC Structure—A Case Study
1191
[4] M. Aiello, L. Valente, A. Rizzo, Moment redistribution in continuous reinforced concrete beams strengthened with carbon-fiber-reinforced polymer laminates, Mechanics of Composite Materials 43 (2007) 453-466.
[5] ACI 440.2R-08 Guide for the design and construction of externally bonded FRP systems for strengthening concrete structures, American Concrete Institute, 2008.
[6] CNR-DT 200/2004: Guide for the design and
construction of externally bonded FRP systems for strengthening existing structures-materials, RC and PC structures, masonry structures, National Research Council, Rome, 2004.
[7] T. Chardakova, K. Vazgechev, M. Traykova, Strengthening of structural elements from monolithic RC beam-column structures, New Campaign, Sofia, 2015. (in Bulgarian)