DAMAGE EVALUATION MODEL FOR STRUCTURALELEMENTS OF BLOCK CONCRETE BUILDINGSJose Adolfo Ramos Huezo*
MEE09192

Supervisor:Tomohisa MUKAI**ABSTRACTThis study proposes a simplified methodology to estimate the damage level and reduction factor whichshows the residual seismic capacity of reinforced concrete block elements from the maximum
response calculated by methods such as pushover analysis, dynamic analysis and others. Themethodology is based on simplified models to estimate the maximum residual crack width from theresidual deformation related to flexural, shear and rotational components. The models are geometrical
relations calibrated by using test data. The calculated crack width is used later to estimate the residual
seismic capacity of the structural element. For this purpose, the necessary concept to evaluate therelations between the maximum residual crack width and the residual seismic capacity of structuralelements is introduced in this study. This concept is necessary at the reconstruction stage after anearthquake and can be applied to assess the necessity of repairs and seismic retrofit for the damaged
elements.
Keywords: Damage level, Residual crack width, Residual seismic capacity, Concrete block masonry.

1. INTRODUCTIONEl Salvador is often affected by earthquakes due to its location on the border of two tectonic plates, theCocos plate and Caribbean plate. The subduction process in the Pacific coast produces destructive
earthquakes with magnitude higher than 7.0, which commonly bring a big damage along the country.
Due to this reason and the seismic capacity of most Salvadorian structures, high damage
concentrations are commonly observed in the affected area when an earthquake occurs.
In this country, the damage evaluation of structures has gained importance in recent years
due to the lessons that past earthquakes have given. Following the experiences of the 1986 San
Salvador and 2001 earthquakes, a guideline to quickly assess the global damage of buildings wasdeveloped (quick inspection guideline). Although a method for quick inspection has been already
implemented, there is not a methodology to evaluate the damage state of structures either before orafter an earthquake. This is an important issue to be addressed because the damage level evaluation isnecessary to plan reconstruction strategies for the local authorities of the affected area. Pre-earthquake
damage evaluation is used to study and evaluate the damage level of structural components byperforming numerical analysis. This type of evaluation is strongly recommended to indirectly analyze
repair costs, seismic capacity reductions and other aspects related to the damage levels of structuralelements.

2. STRUCTURAL TESTThe studied specimens are concrete block walls which were built in accordance with the requirementsof the Salvadorian Housing Code published in 1997 (Wall-A) and 2004 (Wall-B), respectively. The
geometry and the vertical and horizontal reinforcement are presented in Figure 1. Additionally, the____________________________________________*Simeon Canas University, El Salvador
Building Research Institute, Japan**1

geometry and the reinforcement of the upper and foundation RC beam is also presented in Figure 1.
The nominal width of both walls is 10cm and the width of the mortar joint between blocks is 1cm.
Wall-A

Wall-B
Upper and foundation
beamFigure 1. Geometry and arrangements of steel reinforcement for Wall-A and Wall-B (unit: cm)
The load application
dispositive is composed by ahydraulic jack, which is able toprovide a cyclical load applied
parallel to the plane of the wall.
The use of vertical loads in thetested walls is not considered
because each tested specimen
represents the wall of a
Salvadorian one story housewith a flexible roof system.
Figure 2 shows the loading
setup.
Figure 2. Loading setup (unit: cm)
3. METHODOLOGY OF DAMAGE EVALUATION MODEL
A simplified methodology to obtain the maximum residual crack width of a reinforced concrete blockwall from numerical analyses is proposed. Hence, it is possible to relate the calculated crack widthwith the damage level and reduction of the seismic capacity of the damaged structural element.
The first step is to obtain the maximum response of the structural element under earthquake
which can be estimated by methods such as pushover and dynamic analysis, for instance. Then, theresidual displacement related to the maximum response is estimated by using the unloading stiffness.
In order to specify the dominant crack type, the next step is to decompose the residual
deformation in to flexural, shear and rotational components. The amount of each deformation
component is calculated by using the measured deformations of tested specimens.
Once each deformation component is obtained, the maximum residual crack width related
to each component is estimated. For this purpose crack models based on geometrical relations which
are calibrated by using test data are proposed.
Finally, the calculated maximum crack width can be associated with a damage level andthe residual seismic capacity represented by the reduction factor η. Figure 3 shows a scheme of theprocedure and required analysis in the proposed damage evaluation model.

ANALYSIS RESULTANALYSIS

Maximum response of the structure
1 - Stiffness degradation function
Residual displacement
2 - Separation of displacement components
3 - Damage models
4.1 - Residual crack width – ηReduction factor η

4.2 - Residual crack width – Damage level

Damage level and Reparability

Figure 3. Procedure to evaluate the residual seismic capacity of block concrete wall

LoadThe reduction of the seismic capacity due toMaximum response
damage can be related to the residual hysteretic energythat the structure can dissipate during a new earthquake.
In this sense, from the load-deformation curve obtainedby the test of structural elements, the residual seismic
capacity ( ) is calculated as the difference between theoriginal seismic capacity (=+) and thedissipated energy ( ). Figure 4 shows a scheme of thisconcept. (Maeda, 2009)
Residual
Conveniently, the reduction of the seismic
deformation ( )capacity is represented as a reduction factorof theDeformation
initial seismic capacity. This can be defined as theFigure 4. Determination of the residual
ration between the residual energy capacity and theseismic capacity (Maeda, 2009)
original energy capacity ( = / ).
In order to consider the reduction of the seismic capacity in the proposed model,
relationship between a reduction factor and the residual crack width is investigated.

4. RESULTS AND DISCUSSION
4.1 Calculation of the residual displacement from the maximum response of a structure
43Ky/Kr

The unloading stiffness is necessary to determine,from a given maximum response, the displacement
at unloading state (residual displacement).
In order to propose an unloading
stiffness function for concrete block walls, theunloading stiffness of the tested models wascalculated. Figure 5 shows the ratio between theyielding stiffness
and the unloading stiffness
for both specimens. A trend line of the results
could be drawn in Figure 5 and represented by Eq.1.

2Wall-B

1

Wall-A

0
0.0

2.5

5.0

7.5

10.0

Ductility factor

12.5

Figure 5. Ratio Unloading stiffness to yielding
stiffness

= 0.81.

(1)

Using Eq.1 it is possible to estimate the residual displacement as a function of themaximum response which is represented by the maximum displacement
and lateral applied load
as follows:
=−

0.81.

.

(2)

4.2 Separation of deformation components
The amount of flexural δf, shear δs androtational δr deformation component for
Wall-A and Wall-B are presented inTable 1 and Table 2, respectively. The
tables show the average values
corresponding to the tendency presented
by each deformation component. These
values are considered from the first crackstate to the yielding state (0.12% and0.15% for Model A and B, respectively)
and from the yielding drift angle to theultimate state.

Table 1. Percentage of deformation components (Wall-A)
Drift angle (%)
δf/δt
δs/δt
δr/δt
0.68
0.26
0.05
0.04 to 0.18
0.55
0.24
0.20
0.18 to 0.4
Table 2. Percentage of deformation components (Wall-B)
Drift angle (%)
δf/δt
δs/δt
δr/δt
0.74
0.11
0.15
0.04 to 0.15
0.52
0.36
0.12
0.15 to 1.11

4.3 Models for crack evaluation of block concrete elements
The proposed models are developed to be applied in similar boundary and loading conditions to thatused in the tested block concrete walls. For instance, as for the testing procedure, axial loads tosimulate the weight of upper stories were not applied and the boundary condition of the top of thewalls was unfixed (cantilever beam).
As for the model of flexural cracks, the cracking pattern shown in Figure 6 produces a
flexural drift angle represented by Eq.3. The value x can be calculated as 52cm for displacement
smaller than the yielding point and 21cm for larger displacements by section analysis.
=∑(3)

From the instrumental data, the variationof the longitude
andis represented by ∆and ∆ , respectively (see Figure 6). Assuming∆ ≈ 0 and ∆ ≅ ∑the following equation
can be written:∆=(4)is the ratio between the sum of
flexural crack width ∑and the maximum crackwidth. This factor is used to relate theFigure 6. Flexural crack modelgeometrical models and the instrumental data. Finally, Eq.5 is obtained from the system presented inFigure 6.
=.( − ).ℎ(5)In the same way, a model for the maximum crack width due to the rocking effect ispresented by Eq.6=.( − )ℎ(6)As for the shear cracks, the proposedmodel is based on the assumption that thehorizontal shear deformation is produced by thesum of the horizontal component of the shear crackwidths ∑(. cos ( )) (see Figure 7). The
maximum shear crack width is estimated by Eq.7,
whereis a calibration factor calculated as= ∑(. cos ( )) /=.
. .

()Figure 7. Shear crack model(7)4.4 Residual seismic capacity-maximum residual crack width relationship

Table 3. Damage level and η for Wall-A and Wall-B
Damage level
Crack width (mm)
ηI
W<0.4
0.9
II0.4<W<3.00.5
III
3.0<W<6.00.2
IV>6.001

Reduction Factor ηFigure 8 shows the relation between the reduction
factor and the maximum residual crack width of thetested walls. Additionally the maximum residual crack
width which defines each damage level is presented.
From this figure the following table is obtained:

Wall A

0.8

Damage
Level

0.6

III

0.4

DamageLevel

0.2

IIWall B

IV00246Maximum residual crack width (mm)Figure 8. η-residual crack width

4.5 Residual seismic capacity and damage level state from a given maximum response
Max residual crack width(mm)106Measured
crack widths
Estimatedcrack width

4Damage Level III
η=0.2

8Damage Level IVη=0.0

Damage Level II
η=0.5

20

0.0

0.5

1.0
1.5
Max drift angle (%)

Figure 9. Calculated residual crack width

2.0

As a result of the procedure proposed inFigure 3, Figure 9 is presented. Thisgraph shows the calculated maximum
residual crack width for Wall-A. From
this figure, an acceptable agreement
between the measured and thecalculated residual crack width can beobserved. Additionally, the damagelevel and reduction factor presented intable 3 are shown in this figure. Bymeans of these results, it is possible tojudge the damage level and the residualseismic capacity of a block concrete wall from a given maximum response.
Considering that the fact that flexural crack was the widest in Wall-A, the estimation of themaximum crack widths was applied for the flexural deformation only. As a result of the calculation, acalibration factor= 2.51 was used. It is worth mentioning that in a normal calculation, the shear
and rotational cracks should be also calculated in order to select the maximum results of them(max ( w , w , w)).
It is important to mention that the applicability of the results is restricted to walls withsimilar geometrical properties, reinforcement and failure mode of the specimens used in this study.
The importance of new experiments with variation in the characteristics of the specimens will benecessary to obtain widely applicable results.

5. CONCLUSIONS
Concretely, the relationships between the damage level and the residual seismic capacity for structuralelements in block concrete houses are shown by using test data. Using this relationships and maximum
response displacement of block concrete structure obtained by dynamic analysis, the procedure toevaluate the damage level of structural elements could be shown.
As for the investigation to estimate above relationships, the residual seismic capacity ofmasonry wall was calculated by using the residual crack width of structural elements. Secondly, thedamage levels of this element were defined considering the damage state (serviceability, reparability,safety).
As for the investigation to propose above procedure, the whole calculation flow was shownin Figure 4. In order to complete this procedure, the method to estimate the residual displacement andthe crack model to estimate crack width for the block concrete wall were proposed.

6. RECOMMENDATION
It is necessary to perform new structural tests to make the future guideline for damage evaluation ofstructural elements widely applicable.
It is strongly recommended that we should investigate the relation between the damagelevel of structural elements and buildings and define the residual seismic performance of building.

AKNOWLEDGEMENT
I want to express my heartiest gratitude to my advisor and supervisor Dr. Tomohisa MUKAI for his
valuable advice, comment and encouragement during this study.

REFERENCES
H. Choi, Y. Nakano, N. Takahashi, 2007.
EQTAP, 2002, IISEE/BRI.
M. Maeda, 2009, D. E. Kang, 2009.
M. Maeda, Nakano, 2004, 13th World Conference on Earthquake Engineering Vancouver, B.C., Canada.
Ministry of Public Works,1997, Special Code for Design and Construction Houses.
Ministry of Public Works,2004, Special Code for Design and Construction Houses.
TAISHIN Project, 2008, JICA Cooperation Project in El Salvador.

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