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Numerical Modelling of Masonry Panel
Subjected to Surface Blast Loading
Saba Shamim1
Ph.D. Scholar, Department of Civil engineering
Aligarh Muslim University (A.M.U.), Aligarh, Uttar Pradesh (India)
Shakeel Ahmad2 Professor, Department of Civil engineering
Aligarh Muslim University (A.M.U.), Aligarh, Uttar Pradesh (India)
Rehan A. Khan3 Professor, Department of Civil engineering
Aligarh Muslim University (A.M.U.), Aligarh, Uttar Pradesh (India)
Abstract- Site investigation of blast phenomenon is not always possible due to various restrictions concerning life and
environmental well-being. Nevertheless, computational technology has made it possible to simulate blast scenario and its
effect on structures. However, such software’s are based on numerical theories defining several parameters. The
effectiveness of numerical model depends on proper computation of these parameters. The present study aims at
calibrating the numerical model of masonry infill panel based on dilation angle. For the purpose, actual experimental
blast test data for masonry wall were taken from literature. Further, parametric studies have been carried out
investigating the effect of scaled distance and weight of charge on the calibrated wall. It was found that both scaled
distance and weight of charge greatly influence the peak displacement and end rotation response of the wall panel.
Moreover, dilation angle proved to be an influential parameter for generating precised numerical model of masonry.
Keywords- Masonry, Blast Load, Finite Element Modelling, Dilation Angle, Weight of Charge, Scaled Distance
I. Introduction
Masonry is one of the oldest and most commonly used building materials which is not only durable and easy to
apply but also provides acoustic insulation and fire protection along with aesthetic appearance to the structure at a
very low cost. But, brick masonry materials offer relatively small resistance against blast loading, unlike most of the
building materials [15]. Investigation on behaviour of masonry against the action of blast loading has been given due
consideration over last decade due to increase in Terrorist bombing attacks. However, experimental study of blast is
not always possible due various constraints risking the life and environmental well-being. Besides, there are several
computational methods and software that can effectively simulate the blast effects on structure for example;
ABAQUS, SAP2000, LS-DYNA, ANSYS etc. But, numerical simulation of structure as well as blast requires a
deep insight about the subject.
P.W. Sielicki and T. Lodygowski [12] investigated the response of masonry wall subjected to close-in explosion.
The explosive loading was presented by a rapid pressure wave which propagates through the ambient air. Based on
the experimental data a novel numerical approach using VUMAT subroutine in ABAQUS was suggested for
modelling the brittle behaviour of two-phase masonry subjected to blast. This complex experiment was numerically
modelled by mixing the newly developed material response described by equations of the state for the air and
explosive respectively. Finally, the numerical studies were compared with the experimental results, consequentially
developing the pressure-impulse curves and masonry failure. S.H. Alsayed et al. [17] tested a half-scale externally
strengthened infill masonry walls using GFRP sheets against the blast loads due to C-4 explosive. The response of
strengthened walls was compared with un-strengthened infill masonry walls. The field test results of un-
strengthened as well as the strengthened walls were simulated using ANSYS-AUTODYN. The blast pressures
recorded during the experiments were also validated with numerical results of analysis. The numerical models were
then used for studying the effect of various parameters such as scaled distance and FRP end anchorage. X. Yuan et
al. [21] analyzed the blast properties of the masonry infill walls with the finite element program LS-DYNA by the
way of distinctive consideration of the bricks and mortar material in contrast to the experimental data. The
Journal of Xi'an University of Architecture & Technology
Volume XII, Issue VII, 2020
ISSN No : 1006-7930
Page No: 846
numerical results have a good agreement with experimental data. The reliability and efficiency of this method in
predicting the dynamic responses of masonry walls to blast loads was proven. X. Wei and M.G. Stewart [20] carried
out numerical simulations to estimate the response and damage of unreinforced brick masonry walls subjected to
explosive blast loading based on the transient dynamic finite element program LS-DYNA. A new model for strain
rate effects of bricks and mortar was included in the numerical analysis. The results obtained from the numerical
models were compared with field test data and good agreement was found. Parametric studies were conducted to
evaluate the effect of material strength, boundary conditions, and thickness of the wall on the blast response of
unreinforced brick masonry walls. It was found that boundary conditions and wall thickness significantly affect the
blast response, while the effect of material strength was relatively small.
Masonry wall when subjected to blast undergo tensile flexural failure. However, shearing of bed joints is an
accompanied response during any lateral load. . The shearing of bed joints in masonry is technically known as
dilatational behavior which is a well known phenomenon and has already been studied by various researchers
[example; 2, 9-11, 16]. During the dilation process the shearing along bed joints also causes upward translation,
resulting in global volume increase of masonry model and this effect is usually considered while describing the
inelastic behaviour of masonry. Hence, for defining a non-linear numerical model angle of dilation is an important
parameter. Therefore, such a phenomenon needs to be correctly incorporated during the computational modelling.
The present study aims at calibrating the numerical model of masonry panel enclosed in RC frame based on angle of
dilation (Ψ) of masonry using Finite Element (FE) tool in ABAQUS/Explicit software [1]. An experimental wall test
data of masonry infill RC frame wall subjected to blast were taken from the literature for the purpose of validation.
Later, parametric studies were carried out on the calibrated wall model to investigate the effect of scaled distance
and weight of charge.
II. Numerical Modelling
2.1 Modelling of masonry panel-
The material properties for defining the elastic behaviour of masonry are modulus of Elasticity (E), Poisson’s ratio
and density whose values were taken as; 3000MPa, 0.2 and 2100kg/m3 respectively [4]. However, the non-linear
behaviour of masonry was modelled using elastic-plastic strain hardening theory wherein; Mohr Coulomb (MC)
yield and failure criterion was considered. The elastic-plastic model for masonry uses the classical plasticity theory
which comprises of strain rate decomposition into elastic and inelastic strain rates, elasticity; yield; flow; and
hardening [3]. The Mohr Coulomb Plasticity (MCP) program in ABAQUS considers both Mohr-Coulomb (MC)
criteria as well as non-associated plastic flow of cohesive frictional materials.
The Mohr-Coulomb (MC) yield and failure surface is defined as (1),
𝐹 = 𝑞𝑅𝑐 − 𝑝 𝑡𝑎𝑛∅ − 𝑐 = 0 (1)
where, c and Ø are material cohesion and internal friction angle. p and q are first and second stress invariants. Rc is
the measure of Mohr-Coulomb deviatoric stress defined by (2),
RC (∅,θ)= 1
3𝑐𝑜𝑠(𝜃 +
𝜋
3)𝑡𝑎𝑛∅ +
1
√3𝑐𝑜𝑠∅𝑠𝑖𝑛 (𝜃 +
𝜋
3) (2)
The yield function in meridional and deviatoric planes is shown in Figure 1; the shape of which is controlled by
varying the material internal friction angle (Ø).
The non-associated flow potential function is defined as (3),
𝐺𝑃 = √(𝛼𝑐𝑡𝑎𝑛𝛹)2 + (𝑞𝑅𝑚𝑝)2 − 𝑝𝑡𝑎𝑛Ø (3)
where, c are the initial cohesion yield stress at zero plastic strain, taken as equal to 0.7115MPa [7] and α is the flow
potential eccentricity in the meridional plane respectively (Figure 2). Ψ is the dilation angle measured in the p-Rmp
plane. The shape of deviatoric failure surface is governed by a factor ‘e’ (4) which depends on the angle of friction
(Ø).
𝑒 = 3−𝑠𝑖𝑛∅
3+𝑠𝑖𝑛∅ (4)
Journal of Xi'an University of Architecture & Technology
Volume XII, Issue VII, 2020
ISSN No : 1006-7930
Page No: 847
Figure 1. Mohr-Coulomb yield surface in meridional and deviatoric planes
Figure 2. Non-associated flow potential in meridional and deviatoric planes
Therefore, MCP model consists of three basic parameters namely; dilation angle, frictional angle and cohesive yield
stress at zero plastic strain. The accuracy of numerical model depends on the effective evaluation of these
parameters. M. Godio et al. [11] illustrated a noteworthy effect of the dilatancy of the joints on strength of masonry
by comparing the strength of the masonry for dilatant joints (associative case, Ψ=Ø) and non-dilatant joints (non-
associative case, Ψ=0). S. Burnett et al. [16] included the effect of varying dilatancy in modelling the masonry wall
subjected to out of plane impact loading and found that cracks width increases with decrease in dilation angle.
During the shear failure of masonry, it is usually observed that initial shear displacement us parallel to the joint is
accompanied by displacement normal to the joint ut (Figure 3). The ratio ut/us is defined as the coefficient of
dilatancy (tan Ψ). Typically measured value of coefficient of dilatancy (tanΨ) lies in the range 0.1 to 0.7 depending
on the roughness of the unit surface [9]. In other word, the value of dilation angle for masonry may vary between
Ψ= 6° to 50°. For cohesive frictional materials (like masonry) the dilation angle (Ψ) is always taken smaller than the
internal friction angle in analytical modelling. The value of internal friction angle of masonry was taken as 54.9° [7].
Thus, in present study, the numerical model was calibrated based on values of Ψ (6° to 50°), for achieving the most
précised model; simulating the experimental results.
Figure 3. Simple dilatant friction model, showing initial ‘saw tooth’ type sliding
Journal of Xi'an University of Architecture & Technology
Volume XII, Issue VII, 2020
ISSN No : 1006-7930
Page No: 848
2.2 Modelling of RC frame-
For defining the elastic behaviour the values of density, modulus of Elasticity and Poisson’s ratio were taken as
2400kg/m3, 22000MPa and 0.15 respectively for concrete whereas; 8050kg/m3, 200000MPa and 0.3 for steel
respectively [4].
Inelastic behaviour of concrete was modelled using Concrete Damaged Plasticity (CDP) program which includes
basic parameters defined as; dilation angle (Ψ), flow potential eccentricity (e), initial biaxial/uniaxial compressive
stress ratio (fb0/fc0), shape of failure surface (Kc) and viscosity (μ). For concrete dilation angle (Ψ) is equal to the
internal friction angle which may take values between 36° to 40° [5]. Herein, Ψ=38° was taken for the numerical
simulation. However, other parameters were given default input values (i.e., e=0.1, fb0/fc0=1.16, Kc=0.667 and μ=0)
as recommended by ABAQUS. In addition to these basic parameters stress-strain relationships were also identified
based on the compressive and tensile strength of concrete taken as respectively. Non-linear behaviour of steel
reinforcement was modelled using elasto-plastic strain hardening model wherein, values of yield stress, ultimate
stress and plastic strain at ultimate stress were taken as 415MPa, 712MPa and 0.072 respectively. Further, to account
for the effect of high strain loading (blast); Dynamic Increase Factor (DIF) equal to 1.12, 1.19 and 1.17 were
adopted for masonry [22], concrete [18] and steel [18] respectively.
2.3 Modelling of interface
The interface between the masonry and RC frame was modelled using Penalty method which is based on Coulomb
Friction model of slip-stick interface behaviour. The coulomb friction model states that the contact pair can carry
shear stresses (τ) up to a certain limit (τmax) across the interface, also known as sticking state (i.e., τ < τmax = µ Pc + c)
thereafter, they will lose the shear strength and start sliding at the interface relative to each other. Here, µ and c are
contact coefficient of friction and contact cohesion at the contact interface respectively. The approximate value of
coefficient of dry friction as obtained by the laboratory experimental study can range from 0.5 to 0.9 for different
mortar types of the masonry wall and RC frame and; for any value of μ within this range numerical results do not
reflect any noteworthy change in results [4]. In present case, μ=0.8 was taken for modelling the interface. In the
constraint, steel reinforcement was considered to be embedded with steel assigned as embedded region and concrete
as host region.
III. Computation of Surface Blast Parameters
In a phenomenon of blasting the shock waves almost instantaneously amplify the pressure to the peak incident
pressure. These shock waves move radially from the point of burst with a diminishing shock wave velocity U, which
is in excess of the sonic velocity of the medium. During expansion, the blast wave decays in strength as the distance
of the shock waves increases from ground zero. The wave front impinges on the structures located within the path
and then the complete structure is engulfed by the shock pressure as the wave expands in air.
Surface blast also called hemispherical burst loading, occurs when the centre of detonation is on the ground and the
waves reflect instantaneously. Due to nearness of explosive to the ground, there is an immediate interaction between
the ground and the blast wave thereby resulting in an amplified effect. The generated pressure would be
approximately twice that produced by the same charge under free air burst conditions. Total pressure acting on the
structure due to surface blast has three components; incident over-pressure, reflected overpressure and drag pressure
of the accompanying blast wind.
Bureau of Indian Standard (BIS) discusses about the development of idealized surface blast Pressure time (P-t)
history. In Indian code [8] various blast parameters from ground burst of 1Tonne TNT explosive corresponding to a
range of stand-off distances are been specified. Using the cube root scaling law given in equation (5) and (6), these
blast parameters were determined from the code for a required weight of charge (in kg TNT) at specific standoff
distance and blast (P-t) profiles were generated as required in Section 5.1 and 5.2 (Figure 11 and Figure 13).
Scaled distance, 𝑥 = 𝐴𝑐𝑡𝑢𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝑊1/3 (5)
Scaled time, 𝑡0 =𝐴𝑐𝑡𝑢𝑎𝑙 𝑡𝑖𝑚𝑒
𝑊1/3 (6)
where, W = yield of explosion in equivalent weight of the reference explosive measured in Tonnes.
Journal of Xi'an University of Architecture & Technology
Volume XII, Issue VII, 2020
ISSN No : 1006-7930
Page No: 849
IV. Validation Study
R.K. Varma et al. [14] carried out experimental trials on several full-scale cantilever masonry infill panels enclosed
in RC frames under the action of blast. This experimental wall model was developed in ABAQUS/Explicit [1] using
Finite element (FE) macro modelling approach and; three tests which were conducted using Trinitrotoluene (TNT)
explosive on 230mm thick wall were chosen for the purpose of validation (Table - 1).
Table - 1 Details of experimental Blast trails considered in present study
Identification
Wall
thickness
(mm)
Weight of
charge, (kg
TNT)
Standoff
distance, R (m) Blast (P-t) profile
Test 1 230 21.5 4.0
Test 2 230 50.6 5.5
Test 3 230 51.4 5.5
The infill masonry (3000mm x 3000mm x 230mm) and RC frame (230mm x 235 mm) were modelled using Cubic
elements (C3D8R; 3-Dimensional, 8-Nodes with Reduced Hour-Glass) whereas, steel reinforcement was modelled
using Truss elements (T3D2; 3-Dimentional, 2-Nodes). The numerical model was discretised using 100mm mesh
size after performing a Mesh convergence test for 50mm, 75mm, 100mm and 150mm sizes of the mesh. The reason
for using coarser mesh is just to reduce the running time of the model. A total of 3490 elements were generated
having 5358 nodes (Figure 4). Also, the wall was restrained in three global directions at the base whereas, remained
free at the top (cantilever wall).
0
1.3
0 1.73
Pre
ssu
re (
MP
a)
Time (ms)
0
1.84
0 2.1
Press
ure (
MP
a)
Time (ms)
0
2.01
0 1.92
Press
ure (
MP
a)
Time (ms)
Journal of Xi'an University of Architecture & Technology
Volume XII, Issue VII, 2020
ISSN No : 1006-7930
Page No: 850
Figure 4: Mesh model of the wall under study
The response of experimental wall subjected to blast in terms of displacement was found to be highest in the mid-
section of masonry infill panel while; the RC frame remained in undamaged state. The peak displacement observed
in the masonry panel during experimental trail of Test 1 was about 127.5mm whereas, during Test 2 and Test 3 the
masonry panel collapsed completely and hence the displacements were reported to be greater than the thickness of
wall (>230mm).
The numerical model of wall considered for present work was calibrated, considering several values of angle of
dilation (Ψ) between 6° to 50° (see section 2.1) at an interval of 3° to get the best numerical model simulating the
experimental results of Test1, Test2 and Test 3. The scatter plot shown in Figure 5 indicates peak displacement
values corresponding to each dilation angle obtained during the present numerical simulation. Also, displacement-
time variation of numerical model for Ψ=6°, Ψ=10˚, Ψ=15˚, Ψ=25˚ and Ψ=35˚ are shown in Figure 6, Figure 7 and
Figure 8 as sample for wall Test 1, Test 2 and Test 3 respectively. Thus, a decrease in peak displacement value was
observed for each increment in the dilation angle. Also, the rate of decrease is quite distinguishable which can
greatly influence the precision of numerical model.
For Ψ=18°, the numerical peak displacement for Test 1 was equal to 126.1mm(very close to experimental
displacement ~127.5mm) whereas, for Test 2 and Test 3 were equal to 223.8mm, 227.3mm (both dissatisfying the
experimental displacement i.e., >230mm) respectively. However, for Ψ=15° the numerical peak displacements were
found as 129.7mm (~127.5mm), 230.7mm (>230mm) and 232.5mm (>230mm) respectively which are to a great
extent satisfying the experimental results. Moreover, while considering a slight increase in Ψ>15°, the peak
displacement of Test 1 were found to be overvalued compared to the experimental value. Therefore, on the basis of
calibration; at Ψ=15°, numerical model was found to be most remarkably validating the experimental blast trails.
Journal of Xi'an University of Architecture & Technology
Volume XII, Issue VII, 2020
ISSN No : 1006-7930
Page No: 851
Figure 5. Comparison of peak displacement at mid section of masonry panel
Figure 6. Numerically obtained Displacement-time variation while simulating Test 1 corresponding to several dilation angles (Ψ) in present study
Figure 7. Numerically obtained Displacement-time variation while simulating Test 2 corresponding to several dilation angles (Ψ) in present study
50
100
150
200
250
5 8 11 14 17 20 23 26 29 32 35 38 41 44 47 50
Pea
k D
isp
lacem
en
t (m
m)
Dilation angle (Ψ°)
Total Collapse Limit
Test 1 (Experimental)
Test 1 (Presesnt Study)
Test 2 (Present Studyl)
Test 3 (Present study)
0
40
80
120
160
0.00 0.02 0.04 0.06 0.08 0.10
Dis
pla
cem
en
t (m
m)
Time (sec)
Test 1- Present StudyΨ=6°
Ψ=9°
Ψ=15°
Ψ=24°
Ψ=36°
0
50
100
150
200
250
0.00 0.02 0.04 0.06 0.08 0.10
Dis
pla
cem
en
t (m
m)
Time (sec)
Test 2- Present StudyΨ=6°
Ψ=9°
Ψ=15°
Ψ=24°
Ψ=36°
Deflection >230mm
Journal of Xi'an University of Architecture & Technology
Volume XII, Issue VII, 2020
ISSN No : 1006-7930
Page No: 852
Figure 8. Numerically obtained Displacement-time variation while simulating Test 3 corresponding to several dilation angles (Ψ) in present study
V. Parametric study
Within the scope of this parametric study variation of weight of charge and scaled distance have been investigated.
Also, for the purpose of parametric study the top of the calibrated wall has been restrained in the z-direction as
shown in Figure 9, considering the fact that in actual there will be a slab having high in-plane stiffness.
The responses of wall have been investigated in terms of peak displacement (δ) and corresponding end rotation (Ʊ).
Based on the value of Ʊ, PDC-TR 06-08 Rev 1 [13] recommends four levels of expected damage that may occur in
masonry wall subjected to blast defined as; superficial damage (Ʊ <1.5°), moderate damage (1.5°≤Ʊ <4°), heavy
damage (4°≤Ʊ <8°) and hazardous damage (Ʊ≥8°). Therefore, the damage state of wall has also been determined.
Figure 9: FE model of wall showing support condition
5.1 Effect of weight of charge (W)
Weight of explosive is generally expressed in terms of TNT (Trinitrotoluene). The first step in quantifying the
explosive wave from a source other than the TNT, is to convert the charge mass into an equivalent mass of the TNT
[6]. Therefore, TNT equivalent weight of charge W1=25kg, W2=50kg, W3=75kg and W4=100kg was considered
for constant standoff distance 20m. The blast (P-t) curve for W1, W2, W3 and W4 are shown in Figure 10 wherein;
the area under the (P-t) profile denotes the impulse (I). The unit for impulse, pressure and time are Kilo-Pascal
(kPa), Mega-Pascal (MPa) and milliseconds (ms) respectively. The dynamic performance of masonry in terms of
displacement at the mid section of masonry panel is shown in Figure 11. Also, the values peak displacement (δ) and
end rotation (Ʊ) along with the damage assessment is indicated in Table - 2.
0
50
100
150
200
250
0.00 0.02 0.04 0.06 0.08 0.10
Dis
pla
cem
en
t (m
m)
Time (sec)
Test 3- Present StudyΨ=6°
Ψ=9°
Ψ=15°
Ψ=24°
Ψ=36°
Journal of Xi'an University of Architecture & Technology
Volume XII, Issue VII, 2020
ISSN No : 1006-7930
Page No: 853
Figure 10. Blast (P-t) profile for (a) W1= 25kg (b) W2= 50kg (c) W3= 75kg (d) W4= 100kg generated using Indian code
Figure 11. Variation of Displacement with time for different weight of charge (W) corresponding to a constant standoff distance 20m
Table - 2 Comparison of peak values and corresponding damage state between various weight of charge (W)
W (kg TNT) δ (mm) Ʊ (°) Damage assessment
W1 =25 28.2 1.08° Moderate damage
W2 =50 76.0 2.91° Moderate damage
W3 =75 151.8 5.82° Heavy damage
W4 =100 229.6 >8° Hazardous failure
0
0.171
0 8.55
Press
ure (
MP
a)
Time (ms)
(a)
0
0.267
0 7.35
Press
ure (
MP
a)
Time (ms)
(b)
I= 0.981kPa-sec
0
0.251
0 9.46
Press
ure (
MP
a)
Time (ms)
(c)
I= 1.187kPa-sec
0
0.289
0 9.54P
ress
ure (
MP
a)
Time (ms)
(d)
I= 1.379kPa-sec
0.0
100.0
200.0
300.0
0.000 0.020 0.040 0.060 0.080 0.100
Dis
pla
cem
en
t (m
m)
Time (sec)
W1= 25kg
W2= 50kg
W3= 75kg
W4= 100kg
I= 0.731kPa-sec
Journal of Xi'an University of Architecture & Technology
Volume XII, Issue VII, 2020
ISSN No : 1006-7930
Page No: 854
5.2 Effect of scaled distance (Z)
Through the introduction of scaling laws the effect of distance and charge weight on the blast characteristics can be
taken into account simultaneously. Hopkinson-Cranz scaling law, also known as cube root scaling is one of the
most widely accepted laws which states that “Self-similar blast waves are produced at identical scaled distances
when two explosive charges of similar geometry and of the same type of explosive, but different sizes, are
detonated in the same atmosphere” [19]. Hopkinson-Cranz gave a dimensional scaled distance (𝑍 =𝑅
𝑊1/3) where, R
is the distance from the detonation source to the point of interest or target (in metre/m) and W is weight of explosive
or charge weight (in kilogram/kg). Scaling actually provide a correlation of parameters between a particular
explosion and a standard charge of the same substance.
The effect of Z on numerical wall was studied for different values indicated as; Z1=2.2m/kg1/3, Z2=4.3m/kg1/3,
Z3=6.5 m/kg1/3 and Z4=8.6 m/kg1/3. The blast (P-t) curves obtained from IS code corresponding to each considered
scaled distance is shown in Figure 12 (where, Impulse (I) = area under the curve). The results of the analysis
showed that mid section of the masonry panel was most vulnerable whereas, the RC frame was found to be
negligibly affected against blast loading. The comparison of peak values of displacement (δ) and their
corresponding end rotations (Ʊ) are listed in Table - 3, along with the identification of damage in wall for each Z1,
Z2, Z3 and Z4. Also, the variation of displacement with respect to time at mid section of the masonry panel for
various scaled distances is shown in Figure 13.
Figure 12. Blast (P-t) profile for (a) Z1=2.2m/kg1/3 (b) Z2=4.3m/kg1/3 (c) Z3=6.5m/kg1/3 (d) Z4=8.6m/kg1/3 generated using Indian code
0
1.28
0 4.55
Press
ure (
MP
a)
Time (ms)
(a)
I= 2.912kPa-sec
0
0.289
0 9.54
Press
ure (
MP
a)
Time (ms)
(b)
I= 1.379kPa-sec
0
0.181
0 13.15
Press
ure (
MP
a)
Time (ms)
(c)
I= 1.190kPa-sec
0
0.151
0 14.94
Press
ure (
MP
a)
Time (ms)
(d)
I= 1.128kPa-sec
Journal of Xi'an University of Architecture & Technology
Volume XII, Issue VII, 2020
ISSN No : 1006-7930
Page No: 855
Figure 13. Variation of displacement with time for different scaled distances (Z)
Table - 3 Comparison of peak values and corresponding damage state between various scaled distances
Z (m/kg1/3) δ (mm) Ʊ (°) Damage assessment
Z1 =2.2 >230 >8° Hazardous
failure/Total collapse
Z2 =4.3 229.6 >8° Hazardous failure
Z3 =6.5 72.5 2.77° Moderate damage
Z4 =8.6 54.7 2.09° Moderate damage
VI. Conclusions
Masonry infill RC framed wall which has been previously tested in field against blast load was modelled in
ABAQUS/Explicit using Mohr Coulomb plasticity (MCP) approach. The surface blast (P-t) profile was developed in
accordance with the Indian code for each blast scenario.
Based on the dilation angle of masonry, the wall was first calibrated for achieving a good agreement between the
numerical (present study) and experimental results. The effect of dilation angle was found to be quite significant on
the numerical model as; the peak displacement in masonry panel was found to be decreasing with respect to
increasing angle of dilation; that too at a distinguishable rate. Therefore, it can be concluded that precision of
numerical model to a great extent depends on proper selection of dilation angle. Hence, dilation angle should
perhaps be considered an important parameter in numerical modelling.
Moreover, parametric studies were performed on the calibrated model to investigate the effect of weight of charge
and scaled distance. The mid-section of the masonry panel was found to be most susceptible whereas, the RC frame
was found to be least affected during the dynamic analysis. Also, it was observed that peak displacement and
consecutive end rotation increases with increasing weight of charge (at constant standoff distance, 20m) and,
decreases with increasing scaled distance (Z). Besides, the damage states of wall were also identified based on the
observed end rotations. Therefore, the results of parametric study conclude that both weight of charge and scaled
distance are momentous parameters influencing the damage state of wall.
REFERENCES
[1] ABAQUS 6.14. User Documentation, Dessault Systems, 2014
[2] A. Spada, G. Giambanco and P. Rizzo, “Damage and plasticity at the interfaces in composite materials and
structures”, Comput Methods Appl Mech Eng, 1998, 198(49-52), 3884- 3901
[3] A.K. Ghosh, A.M. Arnde and J. Colville, “Finite Element Modeling of Unreinforced Masonry”, 10th IB2 Mac,
Calgary, Canada, July 5-6, 1994
0.0
100.0
200.0
300.0
0.000 0.020 0.040 0.060 0.080 0.100
Dis
pla
cem
en
t (m
m)
Time (sec)
Z1= 2.2m/kg^1/3
Z2= 4.3m/kg^1/3
Z3= 6.5 m/kg^1/3
Z4= 8.6m/kg^1/3
Journal of Xi'an University of Architecture & Technology
Volume XII, Issue VII, 2020
ISSN No : 1006-7930
Page No: 856
[4] A.K. Pandey and R.S. Bisht, “Numerical Modelling of Infilled Clay Brick Masonry under Blast Loading”,
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[14] R.K.Varma, C.P.S. Tomar, S. Parkash and V.S. Sethi, “Damage to brick masonry panel walls under high
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[16] S. Burnetta, M. Gilberta, T. Molyneauxb, G. Beattiec and B. Hobbs, “The Performance of Unreinforced
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[17] S.H. Alsayed, H.M. Elsanadedy, Z.M. Al-Zaheri, Y.A. Salloum and H. Abbas, “Blast response of GFRP-
strengthened infill masonry walls”, Construction and Building Materials, 2016, 115, 438–451.
[18] Unified facilities criteria: UFC 3-340-02 (2008), “Structures to resist the effects of accidental”, Department of
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[19] W.E. Baker, P.A. Cox, P.S. Westine, J.J. Kulesz and R.A. Strehlow, “Explosive Hazards and evaluation”,
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[20] X. Wei and M.G. Stewart, “Model Validation and Parametric Study on the Blast Response of Unreinforced
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[21] X. Yuan, L. Chen, J. Wu and J. Tang, “Numerical simulation of Masonry Walls Subjected to Blast Loads”,
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International Journal of Impact Engineering, 2017, 104, 107-126
Journal of Xi'an University of Architecture & Technology
Volume XII, Issue VII, 2020
ISSN No : 1006-7930
Page No: 857
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