2014-numerical modelling of infilled clay brick masonry under blast loading
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1. INTRODUCTIONClay brick masonry is widely used as a filler wall in
framed construction as well as load bearing wall in
residential buildings in India. It is a weak linkin framed construction as masonry infill walls may not
be able to resist the lateral forces because of low
flexural strength. Unreinforced masonry walls can
present a significant safety hazard to building
occupants in a blast event. It is desirable to study the
behaviour of unreinforced masonry walls under blast
loading which will help in designing the masonry to
prevent the catastrophic failure and reduce the debris
velocity which may otherwise pose a serious safety
hazard.
Advances in Structural Engineering Vol. 17 No. 4 2014 591
Numerical Modelling of Infilled Clay Brick Masonry
Under Blast Loading
A.K. Pandey1,* and R.S. Bisht21Structural Engineering Group, CSIR-Central Building Research Institute, Roorkee, India
2BPPP Group, CSIR- Central Building Research Institute, Roorkee, India
Abstract: Numerical modeling and simulation of clay brick masonry infilled in a
reinforced concrete frame (RC frame) subjected to blast loading has been presented in
this paper. The pressure loading generated in blast shock has been applied on the
masonry and the reinforced concrete frame and time history analysis has been madeusing ABAQUS finite element software package. The slip and separation at the joints
of RC frame and masonry occurring during blast loading due to large difference in
their stiffness has been modeled using contact algorithm. The study of the infilled
brick masonry has been carried out with elasto-plastic strain hardening model using
Mohr-Coulomb yield and failure criterion and contact algorithm for modeling contact
behaviour at the interface of masonry wall and RC frame. The non-linearity in RC
beam/column has been modelled using concrete damaged plasticity model. The
parameters for non-linear finite element modeling of masonry have been
experimentally determined. In order to gain confidence in the analysis, the proposed
constitutive models have been validated with available experimental results on infilled
masonry walls. The parametric study has been made for surface blast of 100 kg TNT
at a detonation distance 20, 30 and 40 m for 340 mm and 235 mm thick masonry walls
with three grades of mortar infilled in a RC frame. The effect of variation of contact
friction between mortar and RC elements on the behaviour of masonry walls has alsobeen studied.
Key words: masonry, blast shock, contact algorithm, flexural bond strength, scaled distance.
Simplified equivalent single degree of freedom
(TM5-1300 1990; Li et al. 2002) models are used to
predict the behaviour of structural elements under blast
loading, however in such an analysis the effect of localized damage, variation of material parameters and
real boundary conditions e.g. slip and separation with
the RC elements may not be possibly accounted. Studies
(Pandey et al. 2009; Pandey 2010) are reported for
modeling of reinforced concrete structures under blast
loading using non-linear constitutive material models.
Some studies (Dennis et al. 2002; Baylot et al. 2005;
Wei et al. 2010) under blast loading are reported for
modeling the behavior of infilled brick/block masonry
with brick/block and mortar modeled separately without
*Corresponding author. Email address: [email protected]; Fax: +91-1332-272272; Tel: +91-1332-283293.
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friction between mortar and RC elements on the
behaviour of masonry walls has also been investigated.
2. EXPERIMENTAL TESTS FORCONSTITUTIVE MODELING OF BRICKMASONRY
Several studies have been reported on compressivebehaviour of clay brick masonry and attempts also have
been made to develop constitutive modelling of clay
brick masonry under uniaxial compression. The
behaviour is not fully understood as there is wide
variation in the compressive strength of bricks
(compressive strength of bricks varies 4–120 MPa)
being used in different countries. In north India, the
compressive strength of clay bricks varies from
10–20 MPa. The stress-strain behaviour of clay brick
masonry has been obtained from experiments. Under
blast loading, lateral force is exerted on the masonry and
behaviour in flexure is more important and bond
strength plays an important role as bond between brick
and mortar is very low. The masonry constituents e.g.
brick and mortar has very little tensile capacity. For
nonlinear material modelling under blast loading the
tensile and flexural strength is also an important
parameter. Splitting tensile strength of bricks, mortar
and flexural strength of brick masonry has been
obtained by experiments for modelling the behaviour.
The strength properties of constituents of masonry are
shown in Table 1.
3. METHODOLOGY FOR NUMERICALMODELLING OF INFILLED MASONRY
The non-linear finite element analysis of masonry wall
infilled in the RC frame has been made using ABAQUS
finite element software. Eight noded iso-parametric
brick element has been used for modelling the brick
masonry and concrete in RC frame and 3D truss element
for modelling the reinforcing bar. The material non-
linearity of masonry has been modelled using elasto-
592 Advances in Structural Engineering Vol. 17 No. 4 2014
Numerical Modelling of Infilled Clay Brick Masonry Under Blast Loading
modeling for the interface. This also requires huge
computational effort as brick and mortar is separately
modeled however the accuracy is not good as the
interface is not modeled. It is reported that boundary
conditions (changing pinned or fixed) have a marked
influence on the response, however in a framed
construction, the masonry is partially infilled as there iscontact between the reinforced concrete beam/column
and masonry. Further during blast loading lateral
pressure is applied and because of lower stiffness of
masonry compared to RC beam and columns, there will
be possibility of separation at the joints as masonry will
deform more compared to RC beam/column. Thus for
realistic modelling the behaviour at interface, hinged or
fixed boundary conditions may not be appropriate.
Therefore in this study, contact algorithm has been used
to model the boundary conditions for the infilled
masonry and friction has been varied to study the
behaviour the masonry under blast loading. The non-
linear material modelling of infilled brick masonry has
been made with elasto-plastic strain hardening models
using Mohr-Coulomb yield and failure criterion. The
behaviour of RC beam/column has been studied using
concrete damaged plasticity model.
In this study precise determination of blast shock
parameters (peak static over-pressure, positive phase
duration, reflection coefficient, dynamic pressure, etc.)
for a given blast charge and detonation distance has
been obtained using a computer program. The pressure
loading generated in blast shock has been applied on themasonry infilled in a reinforced concrete frame and time
history analysis has been made. Parameters for
mathematical modeling of masonry have been
experimentally determined. The proposed constitutive
models have been validated with available experimental
results on infilled masonry walls. The parametric study
has been made for surface blast of 100 kg TNT at a
detonation distance 20, 30 & 40 m for masonry with
three grades of mortar. The effect of variation of contact
Table 1. Strength properties of constituents of masonry
Splitting Flexural Compressive strengthUnit tensile strength (MPa) bond strength (MPa) MPa
Brick 0.91 - 13.46
Mortar (Cement and sand)
0.21 6.78
1:6 0.79 - 13.86
1:4.5 1.15 - 24.80
1:3 -
Brick Masonry
1:6 - 0.17 3.05
1:4.5 - 0.21 3.581:3 - 0.28 4.59
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plastic strain hardening theory with Mohr-Coulomb
yield and failure criterion.
The material non-linearity of concrete is modelled
using elasto-plastic damaged plasticity model and non-
linearity in reinforcing bar is modelled using elasto-plastic
strain hardening model. The methodology is presented as
flowchart as shown in Figure 1. As shown in Figure 1,
contact constraint is applied as boundary condition. The
blast force is applied as pressure loading varying with
respect to time and non-linear dynamic equation of motion
Advances in Structural Engineering Vol. 17 No. 4 2014 593
A.K. Pandey and R.S. Bisht
Yes
No
No
Analysis of proposed finite element model for infilled clay brick masonry(using implicit method of integration)
Stiffness formulation for brick masonryfinite element model
Discretization of Brick Masonry(Eight-noded brick element)
Desired outputs (dynamic response of infilled clay brick masonry)
End
Calculate output parameters (displacements, velocities, accelerations, stress, strain,forces/reactions)
• Apply boundary conditions
• Apply contact constraints
• Apply dynamic blast loading
• Apply contact algorithm and constraints
Stiffness formulation for RC framefinite element model
Discretization of concrete beam and columnand reinforcement (8 noded brick element and
3D truss element
• brick masonry• RC frame
(i) Physical model parameters for brick masonry and RC frame (size and shape)
(ii) Non-linear material model input parameters:
(iii) Parameters for interface control model between masonry and RC frame
Combined stiffness formulation for infilled clay brick masonry
Update
balanced nodal
forces and go
for next
iteration and
reduce time
step if required
Check for yielding of various (masonry, concrete, steel) element at gauss pointsand calculate resistive nodal forces and check for convergence, check for slip
using contact conditions
If convergence
If it is required toupdate the stiffness
matrices
Update Mathematical model
Nexttime step
Start
Figure 1. Flow chart of proposed finite element analysis for infilled brick masonry under blast loading
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has been solved using implicit method of integration.
Contact algorithm has been used to simulate contact
interface of the infilled masonry wall by imposing contact
constraints resulting in slip which requires small time step
and as shown in Figure 1, time step size is modified.
Contact modelling leads to real boundary simulation
between the RC frame and masonry wall.
3.1. Proposed Non-Linear Material Modelling of Brick Masonry
The non-linear constitutive material modelling of clay
brick masonry wall has been made using Mohr-
Coulomb criterion with non-associated plastic flow of
cohesive-frictional material which incorporates both the
internal friction and dilatational effects. Nonlinear
material behaviour is based on the phenomenon of
macroscopic plastic yielding mainly due to frictional
sliding between material particles. The nonlinear
material plasticity is characterized not only by the use of Mohr-Coulomb yield criterion but also by the plastic
flow rule. The plastic flow is mainly due to the rate of
plastic strain increment vector d ε. pij
and material flow at
yield is governed by the gradient of the plastic potential
flow. It is called associated plasticity, if the angle of
dilation ψ is equal to the angle of internal friction φ . It
means that the plastic flow develops along the normal to
the yield surface. In general, however, the material
plastic flow is non-associated in nature i.e., the vector of
plastic strain rate is not normal to the yield surface and
therefore, the dilation angle is not equal to the internalfriction. The dilation angle is always taken smaller than
the internal friction angle in numerical modelling,
particularly for cohesive frictional materials.
Generalized form of Mohr-Coulomb criterion is
expressed in terms of three stress invariants. The first
invariant as expressed in terms of equivalent pressure
stress, written as
Second invariant is expressed in the form of Von-
mises equivalent stress, written as
where, σ 1, σ 2, σ 3 and are the principal values of Cauchy
stress tensor σ ij , and sij is the stress deviator tensor,
defined as,
q s sij ij =
= −( ) + −( ) + −(
3
2
1
21 2
2
2 3
2
3 1σ σ σ σ σ σ )){ }2
p ii= −1
3σ
Third invariant is expressed as, where,
, and S 1, S 2, and S 3 are the
principal values of deviatoric stress tensor S ij . Thus,
from the above expressed three stress invariants, the
mohr-coulomb yield surface is defined as,
(1)
where, φ (Θ, f n) and c(ε – p, Θ, f n) are the internal friction
angle and material cohesion parameters respectively.
These are the functions of temperature,Θ, other
predefined variables, f n(n = 1, 2, ...) and ε – p
is equivalentplastic strain expressed as:
and its rate associated with the plastic
work expression rate . The
Mohr-Coulomb deviatoric stress measure, Rmc(θ ,φ ),
used in above Eqn 1 is defined as
where, θ deviatoric polar angle is written in the
form, . The yield function in meridional
and deviatoric planes is shown in Figure 2, and the
shape of yield surface is also controlled by varying the
internal friction angle of material, φ .
Flow rule associated with the yield criterion states
that the material flow is possible as the material is in a
state of yield i.e., after yielding the plastic deformation
begin normal to the yield or plastic potential surface.
The total strain increment tensor is expressed as the
superposition of elastic and plastic components of strain
increment tensors
(2)
Following, the stress-strain relations of plastic flow
relate to the plastic strain increment, d ε pij , as
mentioned in above Eqn 2 is for non-associated
plasticity written as
d d d ij ij e
ij pε ε ε = +
cos 3
3
θ ( ) =
r
q
Rmc( , ) cos tan
cos
sinφ θ θ π
φ
φ
θ π
= +
+
( ) +
1
3 3
1
3 33
& & &W c p p
ij ij p
= =ε σ ε
ε ε ε p ij p
ij p
=
2
3
F R q p cmc= − − =tanφ 0
J s s s s s sij jk ki3 1 2 3
1
3= =
r J
=
3
2
3
1
3
s pij ij ij = +σ δ
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Numerical Modelling of Infilled Clay Brick Masonry Under Blast Loading
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(3)
where, g is expressed as
Therefore, the non-associated plastic potential flow
G p is defined as
(4)
where, c0 is the initial cohesion yield stress at zero
plastic strain, α is the flow potential eccentricity in the
meridional plane, Ψ (Θ , f n) dilation angle measured in
the p-Rmwq plane. Where, Rmw is the deviatoric elliptical
G c R q p p mw= ( ) + −α ψ ψ 02 2
tan ( ) tan
gc
G
ij
p
ij
=
∂
∂
1σ
σ
d d
g
G
ij p
p
p
ij ε
ε
σ =
∂
∂ function as used in Eqn 4, and as shown in
above Figure 3 is the out of roundedness parameter and
it depends on the frictional angle of material, φ .
3.2. Material Model for RC Beam/Column The reinforced concrete beam column has been
modelled using 8-noded isoparametric solid element
with embedded reinforcement modelled using 3-D truss
element. The nonlinearity in concrete has been
modelled using concrete damaged plasticity model and
nonlinearity in reinforcing steel using elasto-palstic
model. The concrete damaged plasticity model
available in ABAQUS has the capability for the
analysis of concrete structures under dynamic loading.
It has the capability of modelling the ductile and brittle
behaviour of concrete under high and low confining
pressures.
e =−
+
3
3
sin
sin
φ
φ
Advances in Structural Engineering Vol. 17 No. 4 2014 595
A.K. Pandey and R.S. Bisht
R mc q
p
c
ϕ
= 0
4π π
3=
2
3=θ
θ
θ
Figure 2. Mohr-Coulomb yield surface in meridional and deviatoric planes
Figure 3. Non-associated flow potential in meridional and deviatoric planes
π 4
3=θ
π 2
3=θ
= 0θ φ 3 − sin
φ 3 + sine =
R mw q
c
p
ψ
αc 0
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3.3. Contact Formulation of Infilled Masonry Wall
Contact nonlinear effect is included in this study which
allows separation between the masonry wall and stiffer
RC frame while changing various contact interaction
properties e.g., tangential and normal constraints
between the contact pairs. The contact model is basedon surface-to-surface discretizaton with finite sliding
algorithm, interface interaction by hard contact and
coulomb friction using penalty method for enforcement
of normal and tangential contact constraints
respectively.
3.3.1. Contact properties and constraintsPenalty method used to enforce contact constraints for
interface friction modelling is based on coulomb friction
model of slip-stick interface behaviour. The coulomb
friction model relates the maximum shear τ max stress to
the normal contact pressure Pc at the contact interface in
which the contact pair can carry shear stresses up to a
certain limit or τ max across their interface. It is also
known as sticking state (i.e., τ < τ max = µ Pc + c),
thereafter they will start sliding at the interface relative
to each other. Where µ and c are contact coefficient of
friction and contact cohesion at the contact interface
respectively.
The hard contact using penalty constraint
enforcement to the normal interaction relationship is
used to model normal contact behaviour. It is found that
the contact convergence rate can be improved bypenalty method to enforce contact constraints to
tangential as well as normal behaviours, since it permits
and/or minimizes some penetration of the slave surface
into the master surface. Therefore, we used penalty
method for enforcement of tangential as well as normal
contact constraints. The basic coulomb friction model
used only the coefficient of friction as an input
parameter to enforce contact constraint to the tangential
contact behaviour. The coefficient of dry friction is
obtained by the laboratory experimental study and its
approximate value can range from 0.5 to 0.9, for
different mortar types of the masonry wall and RC
frame.
3.3.2. Contact discretization and algorithmSurface-to-surface contact formulation between
masonry wall and stiffer RC frame is performed by
surface-to-surface discretization with finite sliding
algorithm. In this formulation, the slave surface is
chosen as masonry wall with fine-mesh while master
surface is chosen as stiffer RC frame with coarse-mesh.
This avoids any excessive penetration of the master
surface into the slave surface and increases contact
convergence rate. However, it is found that the surface-
to-surface discretization results more stable contact and
better convergence behaviour as contact conditions are
imposed in an integral sense over a finite region (finite
elements) of the slave surface instead of at a particular
slave node as reported in Laursen et al. (2005). Finite
sliding tracking approach for contact algorithm isconsidered for large plastic deformations between the
contact pair. Although, it is a general computational
expensive algorithm, but small sliding algorithm does
not allow for large frictional sliding between the contact
surfaces. Hence, surface-to-surface discretization with
finite sliding algorithm which supports large plastic
deformations with more frictional sliding efficiently is
well suited and applied to this contact problem under
blast event. This is found to be more appropriate than
any other contact formulation such as node-to-surface
discretization with small sliding contact.
4. VALIDATION OF PROPOSEDMETHODOLOGY
The proposed methodology has been validated by
comparing the deflection response of masonry walls
obtained using the proposed methodology with
experimental values earlier obtained in blast loading
trials by Varma et al. (1997). The size of the wall (inside
dimension) as shown in Figure 4 is 3000 mm in length,
3000 mm in height and 345 mm in thickness. The wall
is enclosed in a reinforced concrete frame with cross
sectional area 350 × 345 mm. The frame and wall asshown in Figure 5 have been modelled using 8 nodded
iso-parametric brick elements, and 5000 elements of
masonry and 1500 elements of RC frame have been
used for desired level of accuracy in numerical model
for the response of the masonry wall. The bottom of the
RC frame has been restrained in the three directions and
596 Advances in Structural Engineering Vol. 17 No. 4 2014
Numerical Modelling of Infilled Clay Brick Masonry Under Blast Loading
Figure 4. View of blast load trials on masonry encased in RC
frame (Varma et al. 1997)
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based on experimental study an appropriate interfacial
dry coefficient frictional µ ≈ 0.80 (approximate
experimental variations 0.50 to 0.9 for different mortar
grades) value is used at interface between masonry wall
and RC frame. The material properties for 1:6 masonry
walls used in blast loading trials are given in Table 2(a).
Concrete is modelled as elasto-plastic considering strain
hardening and softening using concrete damaged
plasticity model available in ABAQUS. The material
properties for concrete and steel are given in Table 2(b).
The comparison of values of peak deflection obtained
from the numerical analysis for thirteen cases are
presented in Table 3. As seen from the Table 3,theoretical and experimental deflections are
comparable, and more close as compared to Wei et al.
(2010) in most of the cases. However in one case, there
is wide difference in experimental and theoretical
values, the reason for this difference may be due
erroneous functioning of the sensor during the
experiment. Numerically this wide difference in this
case has also been observed by Wei et al. (2010). Table 3
also shows predicted numerical results in some cases are
close to or greater than the thickness of the masonry
wall. Varma et al. (1997) classified this as Level A
damage, which meant total collapse of infilled brick
masonry as well as permanent bending of RCC
column/beam.
5. COMPUTATION OF BLAST PRESSUREAND OTHER BLAST LOAD PARAMETERS
Explosives detonated in air produce shock waves, which
is composed of high intensity of shock front and
impinges on structure lying on its path. Immediately
Advances in Structural Engineering Vol. 17 No. 4 2014 597
A.K. Pandey and R.S. Bisht
Figure 5. Finite Element Model of brick masonry with fine mesh
and RC frame with coarse mesh used in interface contact analysis
Brick masonry
RC frame
Table 2(a). Material properties of brick masonry
Initial yieldstrength (MPa) /
Type of brick Modulus of compressive Plastic strain at Tensilemasonry elasticity (MPa) Poisson’s ratio strength (MPa) peak stress strength (MPa)
1:6 2000 0.20 0.92/3.05 0.0020 0.18
1:4.5 3000 0.20 1.07/3.58 0.0018 0.21
1:3 5000 0.20 1.38/4.59 0.0015 0.27
Table 2(b). Properties of concrete and steel used for modelling RC beam/column
Properties Concrete Steel
Grade M-15 Fe-415
Peak stress/yield strength (MPa) 20.0 415.0
Modulus of Elasticity (MPa) 22000 200000
Poisson’s ratio 0.15 -
Cracking strain 0.00012 -
Percentage steel in beam/column - 4.1
Yield stress (MPa) and Plastic strain 8.0 0.0000 415.0 0.000
12.8 0.00016 415.0 0.007
16.8 0.00036 721.0 0.072
18.2 0.00049
20.0 0.00099
18.5 0.00140
16.2 0.00200
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with the impingement of shock wave there will be
reflection, which will clear in a time t c (depends upon
the size of the structure) and the structure is subjected to
over-pressure and dynamic pressure of the blast wind.
Total blast pressure on the structure is composed of
three parts, incident over-pressure, reflected
overpressure and drag pressure of the accompanyingblast wind.
The Indian Standard requires that a building may be
designed for a bare charge of 100kg at distance of 40 m
for residential building, 30 m for community buildings
and 20 m for buildings housing services. Calculations for
blast pressures and positive phase duration and reflected
pressure have been made using developed software for
blast of 100 kg at a detonation distance of 20, 30 and 40
m. The above mentioned parameters as obtained from
the developed software are given in Table 4.
6. PARAMETRIC STUDIESInfilled clay brick masonry with three grades of mortar
(1:3, 1:4.5, 1:6) have been analysed for the pressure
time history obtained for surface blast of 100 kg TNT at
a detonation distance of 20, 30 and 40 m. Salient
features of the blast wave are given in Table 4. The
material properties of the brick masonry are given inTable 2(a). The analysis has been made for wall made
of 1.5 brick with thickness equal to 340 mm and one
brick wall of thickness equal to 235 mm for three grades
of mortar. These two thickness walls are used as outer
walls in the Indian construction industry. The walls are
infilled in a reinforced concrete frame with square cross
section of size equal to wall thickness. Concrete in RC
frame is idealised as elasto-plastic strain hardening
material using concrete damaged plasticity model and
the properties are given in Table 2(b). The bottom of the
598 Advances in Structural Engineering Vol. 17 No. 4 2014
Numerical Modelling of Infilled Clay Brick Masonry Under Blast Loading
Table 3. Numerical results compared with observed test results
Experimental Numerical Numericalresults of results of results of
Positive peak peak peakScaled Peak phase deflection deflection deflection
Wall Weight of Stand-off distance blast duration (mm) by (mm) in (mm) bythickness charge distance Z pressure X 10-3 Varma et al. present Weiet
S. No. (mm) (kg) (m) (m/kg1/3) (MPa) (second) 1997* study al . 2010 **
1. 345 22.4 5.5 1.95 0.94 2.37 47.0 48.6 46.3
2. 345 22.4 7.0 2.48 0.90 2.30 40.0 37.2 26.2
3. 345 43.2 4.5 1.28 2.85 1.56 103.8 112.7 94.6
4. 345 23.4 4.0 1.40 2.50 1.30 117.0 76.1 68.8
5. 345 23.3 6.0 2.10 0.76 3.15 25.5 43.5 36.2
6. 345 26.6 4.0 1.33 4.56 0.98 120.0 131.1 -
8. 345 11.7 5.0 2.20 0.478 3.35 18.0 24.5 -
9. 345 50.6 3.75 1.01 5.194 1.18 C >300 >345
10. 235 21.5 4.0 1.44 1.30 1.73 127.5 109.5 101.7
11. 235 50.6 5.5 1.49 1.84 2.10 C >230 >230
12. 235 51.4 5.5 1.48 2.01 1.92 C >230 >230
13. 235 50.8 5.5 1.49 1.84 2.10 C >230 >230
*experimental values obtained in blast loading trials by Varma et al. (1997), C = Collapse
**observed numerical results (Wei et al. 2010) of peak deflection at centre for masonry with 2.5 (MPa) mortar strength
Table 4. Blast load parameters for surface blast 100 kg TNT
Detonation distance (d) for surfaceblast of 100 kg TNT
S.N. Blast load parameters d = 40 m d = 30 m d = 20 m
1. Positive face duration(to) – ms 20 18 14
2. Clearance time for reflection(tc) – ms 15 14 14
3. Peak static overpressure (Pso) – MPa 0.0193 0.0306 0.0620
4. Peak reflected over pressure (Pref ) – MPa 0.0658 0.1044 0.211
5. Peak dynamic over pressure (pdo) – MPa 0.0067 0.0105 0.020
6. Pressure after clearance of reflections effects (Ptc) – MPa 0.065 0.0910 -
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frame is restrained in all the three directions and top
restrained in only horizontal direction parallel to
direction of blast as in actual structure there will be a
slab which has a very high in plane stiffness.
6.1. Response of Masonry Wall (340 Mm
Thickness) for Variation in Grade of Mortar in Masonry The non-linear finite element analysis results of
masonry wall of 340 mm thickness subjected to blast
pressure of 100 kg TNT at a detonation distance of 30 m
are presented in Figure 6 and Table 5. The analysis has
been made for three cases by changing the material
parameters corresponding with the wall made with three
grades of cement sand mortar (1:6, 1:4.5 and 1:3). The
variation of deflection with time at central node of the
wall (1.5 m from top and bottom and sides) and at
interface with the RC frame (Figure 6) indicate that peak
deflection occurs at different timings because withchange in properties of the masonry, its period of
vibration changes. The peak values of deflection at a
central node and at interface are given in Table 5. It is
seen that the peak deflection in three cases of masonry
(1:6, 1:4.5 and 1:3) are 27.7, 22.8 and 17.5 mm
respectively. The peak deflection at interface of brick
masonry and frame in these three cases are 4.6, 3.5 and
2.6 mm respectively. The support rotations are less than
one degree. As per masonry damage criteria (TM-5-
1300 1990), masonry will be reuseable with retrofitting.
The masonry with three grades of mortar has beensubjected to a blast 100 kg TNT at a distance of 20 m.
As seen from the Table 4, there is substantial increase in
blast pressure in this case. Variation of deflection of
central node and interface with time is shown in Figure
7 and peak values of deflection, their timings of
occurrence and support rotation is shown in Table 6. As
seen from the Table 6, the peak values of deflection in
the three cases of masonry (1:6, 1:4.5 and 1:3) at central
node are 72.5, 62.5 and 49.4 mm respectively. The
deflection values at the interface are 14.9, 10.8 and 7.5
mm respectively. The rotation at interface is more than
one degree in all the three cases which indicate that the
masonry will become non-reuseable as per TM-5-1300
in all the three cases.
The deflection response of masonry with three grades
of mortar subjected to blast of 100 kg TNT at a distance
Advances in Structural Engineering Vol. 17 No. 4 2014 599
A.K. Pandey and R.S. Bisht
Table 5. Peak deflection and rotation of brick masonry (340 mm) for surface
blast of 100 kg TNT at detonation distance of 30 m
Grade of mortar Peak deflection (mm) Time of peak Rotation
S.N. in masonry At centre At interface deflection (Degrees)
1. 1:6 27.7 4.6 0.035 0.88
2. 1:4.5 22.8 3.5 0.031 0.74
3. 1:3 17.5 2.6 0.027 0.57
Figure 6. Variation of displacement with time of masonry wall (T = 340 mm) for blast of 100 kg TNT at a detonation distance of 30 m
0.100.090.080.070.060.05
Time (sec)
0.040.030.020.010.000.000
0.005
0.010
0.015
0.020
0.025
D i s p l a c e m e n t ( m )
Masonry 1:6, location at centreMasonry 1:4.5, location at centreMasonry 1:3, location at centreMasonry 1:6, location at centreMasonry 1:4.5, location at centreMasonry 1:3, location at centre
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of 40m is shown in Figure 8 and Table 7. Similar trend
in values of peak defection at central node and at
interface for the three grades of masonry has been
obtained except that the peak values of deflection are
much lower and the support rotations are less than one
degree.
6.2. Response of Masonry Wall (340 mm thickness) for Variation in Detonation Distance
The deflection response of 1:6 mortar masonry wall, for
blast of 100 kg TNT at detonation distance of 20, 30 and
40 m are shown in Figure 9 and Table 8. As seen from
the Figure 9 and Table 8, deflection response is very
sensitive with respect to distance of detonation. As a
detonation distance of 20, 30 and 40 m the peak
deflection is 72.5, 27.7 and 22.4 mm respectively. Thevelocity at central node of the masonry for three
detonation distances of 20, 30 and 40 m are 2.60, 1.55
and 1.1 m/sec respectively.
6.3. Response of Masonry Wall (340 mm thickness) for Variation in Interface Dry Coefficient of Friction
The response of 1:3 mortar brick masonry wall subjected
to blast of 100 Kg TNT at a distance of 30 m has been
studied by changing the coefficient of friction between
the contact surfaces. As seen from the Figure 10, the
variation of dynamic response of masonry wall is
decreasing with increasing the coefficient of friction. It
clearly indicates that the coefficient of friction at the
contact interface plays a vital role for obtaining an
appropriate dynamic response under blast loading. As
seen from Figure 10, there is more variation in wall
deflection at low values contact friction (30%)compared with (50% and above). Therefore, based on
600 Advances in Structural Engineering Vol. 17 No. 4 2014
Numerical Modelling of Infilled Clay Brick Masonry Under Blast Loading
Table 6. Peak deflection and rotation of brick masonry (340 mm) for
surface blast of 100 kg TNT at detonation distance of 20 m
Grade of mortar Peak deflection (mm) Time of peak Rotation
S.N. in masonry At center At interface deflection (Degrees)1. 1:6 72.5 14.9 0.048 2.20
2. 1:4.5 62.5 10.8 0.043 1.98
3. 1:3 49.4 7.5 0.039 1.60
Figure 7. Variation of displacement with time of masonry wall (T = 340mm) for blast of 100 kg TNT at a detonation distance of 20 m
0.00 0.01
0.01
0.000.02
0.02
0.03
0.03
0.04
0.04
0.05
Time (sec)
D i s p l a c e m e n t ( m ) 0.05
0.06
0.06
0.07
0.07
0.08 0.09 0.10
Masonry 1:6 location at centre
Masonry 1:4.5 location at centre
Masonry 1:3 location at centre
Masonry 1:6 location at interface
Masonry 1:4.5 location at interface
Masonry 1:3 location at interface
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A.K. Pandey and R.S. Bisht
Table 7. Peak deflection and rotation of brick masonry (340 mm) for
surface blast of 100 kg TNT at detonation distance of 40 m
Grade of mortar Peak deflection (mm) Time of peak Rotation
S.N. in masonry At centre At interface deflection (Degrees)
1. 1:6 22.4 3.5 0.040 0.75
2. 1:4.5 13.5 2.2 0.035 0.43
3. 1:3 8.9 1.3 0.030 0.29
Figure 8. Variation of displacement with time of masonry wall (T = 340 mm) for blast of 100 kg TNT at a detonation distance of 40 m
0.00 0.010.000
0.02 0.03 0.04
0.005
0.05
Time (sec)
D i s p l a c e m e n t ( m )
0.010
0.06
0.015
0.07
0.020
0.08 0.09 0.10
Masonry 1:4.5 location at centre
Masonry 1:6 location at centre
Masonry 1:3 location at centre
Masonry 1:4.5 location at interface
Masonry 1:6 location at interface
Masonry 1:3 location at interface
Figure 9. Variation of displacement with time for blast of 100 kg TNT at various detonation distances for 1:6 Masonry (T = 340 mm)
0.00 0.01
0.01
0.000.02
0.02
0.03
0.03
0.04
0.04
0.05
Time (sec)
D i s p l a c e m e n t ( m ) 0.05
0.06
0.06
0.07
0.07
0.08 0.09 0.10
Detonation distance = 20 m
Detonation distance = 30 m
Detonation distance = 40 m
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experimental study, an appropriate coefficient of
friction, µ ≈ 0.80 (experimental variations 0.50 to 0.90
for different mortar grades), at the interface has been
considered for infilled masonry wall boundary
conditions for all numerical models under blast event.
Also beyond an interface frictional limit of 0.5, the
variation in deflection response narrows down as seenfrom the Figure 10.
6.4. Response of Masonry Wall (235 mm thickness) for Variation in Grade of Mortar in Masonry
The masonry wall of 235 mm thickness infilled in RC
frame has been analyzed by changing the material
parameters for three grades of mortar for blast pressure
corresponding to detonation distance of 20, 30 & 40 m.
The variation of deflection with time at central node of
the wall (1.5 m from top and bottom and sides) and at
interface with the RC frame for blast of 100 kg TNT at 30
m detonation distance is shown in Figure 11. It is seen
from the Figure 11 that peak deflection occurs at different
timings because with change in properties of themasonry, its period of vibration changes. The peak values
of deflection at a central node and at interface are given
in Table 9. It is seen that the peak deflection in three cases
of masonry (1:6, 1:4.5 and 1:3) are 85.6, 74.0 and 65.9
mm respectively. The peak deflection at interface of brick
masonry and frame in these three cases are 21.4, 18.1 and
15.2 mm respectively. Masonry will become non-
reusable as per masonry damage criteria (TM-5-1300).
602 Advances in Structural Engineering Vol. 17 No. 4 2014
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Table 8. Peak deflection and rotation of 1:6 brick masonry (340 mm) for
surface blast of 100 kg TNT at various detonation distances
Velocity atDistance of Peak deflection (mm) Time of peak Rotation central node
S.N. detonation (m) At centre At interface deflection (Degrees) (m/sec)
1. 20 72.5 14.9 0.048 2.20 2.60
2. 30 27.7 4.6 0.035 0.88 1.55
3. 40 22.4 3.4 0.031 0.75 1.10
Figure 10. Variation of peak deflection (T = 340 mm) at centre with time for surface blast of 100 kg TNT at a detonation distance of 30 m
using different interface contact friction
Contact friction = 30% location at centre
Contact friction = 40% location at centre
Contact friction = 50% location at centre
Contact friction = 60% location at centre
Contact friction = 75% location at centre
0.00 0.01
0.01
0.000.02
0.02
0.03
0.03
0.04
0.04
0.05
Time (sec)
D i s p l a c e m e n t
( m )
0.05
0.06 0.07 0.08 0.09 0.10
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The results of nonlinear finite element analysis
masonry wall of 235 mm thickness with three grades of
mortar subjected to a blast 100 kg TNT at a distance of 20
m are presented here. Variation of deflection of central
node and interface with time is shown in Figure 12 and
peak values of deflection, their timings of occurrence
and support rotation is shown in Table 10. As seen from
the Table 10, the peak values of deflection in the three
cases of masonry mortar (1:6, 1:4.5 and 1:3) at central
node are 268.0, 222.7 and 202.5 mm respectively. The
deflection values at the interface are 47.2, 39.6 and 32.2
mm respectively. The rotation at interface is more than
six degrees in all the three cases which indicate that the
masonry will become non-reusable as per TM-5-1300 in
all the three cases further it is to be noted that in the case
of 1:6 masonry, displacement is more than the thickness
of the wall and near collapse situation has arisen as per
the experimental fact observed by Verma et al. (1997)
in their trial.
The deflection response of masonry with three grades
of mortar subjected to blast of 100 kg TNT at a distance
of 40 m is shown in Figure 13 and Table 11. Similar
trend in values of peak defection at central node and at
interface for the three grades of masonry has been
obtained except that the peak values of deflection are
much lower. The support rotations for three grades of
masonry (1:6, 1.45 and 1:3) are 1.86, 1.59 and 1.42
degrees respectively. In this case also masonry will
become non-reusable as per masonry damage criteria
(TM-5- 1300).
Advances in Structural Engineering Vol. 17 No. 4 2014 603
A.K. Pandey and R.S. Bisht
Table 9. Peak deflection and rotation of brick masonry (235 mm) for
surface blast of 100 kg TNT at detonation distance of 30 m
Grade of mortar Peak deflection (mm) Time of peak RotationS.N. in masonry At centre At interface deflection (Degrees)
1. 1:6 85.6 21.4 0.065 2.46
2. 1:4.5 74.0 18.1 0.059 2.13
3. 1:3 65.9 15.2 0.057 1.94
Figure 11. Variation of displacement with time of masonry wall (T = 235 mm) for blast of 100 kg TNT at a detonation distance of 30 m
Masonry 1:6 location at centre
Masonry 1:4.5 location at centre
Masonry 1:3 location at centre
Masonry 1:6 location at interface
Masonry 1:4.5 location at interface
Masonry 1:3 location at interface
0.00 0.01
0.02
0.000.02
0.04
0.03
0.06
0.04
0.08
0.05
Time (sec)
D i s p l a c e m e n t ( m )
0.06 0.07 0.08 0.09 0.10
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7. CONCLUSIONSA methodology for prediction of non-linear dynamic
response of brick masonry infilled in a RC frame
subjected to blast loading has been proposed. Elasto-
plastic strain hardening material model for brick
masonry, concrete damaged plasticity model for
modelling non-linearity in concrete and contact
algorithm for boundary conditions have been used using
ABAQUS finite element software. Following
conclusions have been drawn from the study.
1. The masonry infilled in a reinforced concrete
frame which has already been tested in blast
loading trials earlier has been modelled using
the proposed methodology. The experimental
and theoretical predictions are comparable in
most of the cases.
2. Parametric studies for masonry wall of 340 mm
thickness (1.5 brick thickness) indicate that for
blast of 100 kg TNT at detonation distance of
20 m, deflection at central node is 72.5, 62.5 and
59.4 mm for the three grades of the masonry and
resulting rotation at support is more than one
degree in all the three cases, which indicate that
the wall become non-reusable after the blast. For
the case of detonation distance of 40 m, the
deflection is comparatively much smaller the
deflection values for three grades of mortar are
22.4, 13.5 and 9.4 mm respectively. The support
rotations are close to 0.5 degrees, which indicate
reusable masonry. For the detonation distance of
30m, the deflection values are 27.7, 22.8 and 17.5
mm and support rotations are close to one degree.
604 Advances in Structural Engineering Vol. 17 No. 4 2014
Numerical Modelling of Infilled Clay Brick Masonry Under Blast Loading
Figure 12. Variation of displacement with time of masonry wall (T = 235 mm) for blast of 100 kg TNT at a detonation distance of 20 m
Masonry 1:6 location at centre
Masonry 1:4.5 location at centre
Masonry 1:3 location at centre
Masonry 1:6 location at interface
Masonry 1:4.5 location at interface
Masonry 1:3 location at interface
0.00 0.01
0.05
0.000.02
0.10
0.03
0.15
0.04
0.20
0.05
Time (sec)
D i s p l a c e m e n t ( m )
0.25
0.06 0.07 0.08 0.09 0.10
Table 10. Peak deflection and rotation of brick masonry (235 mm) for
surface blast of 100 kg TNT at detonation distance of 20 m
Grade of mortar Peak deflection (mm) Time of peak Rotation
S.N. in masonry At centre At interface deflection (Degrees)
1. 1:6 268.0 47.2 - 8.42
2. 1:4.5 222.7 39.6 0.095 6.99
3. 1:3 202.5 32.2 0.088 6.50
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3. The parametric studies for wall of 235 mm
thickness ( one brick thickness) indicate that for
blast of 100 kg TNT at a distance of 20 m , peak
deflection at central node are 268.0, 222.7 and
202.5 mm for three grades of masonry mortar
(1:6, 1:4.5 and 1:3) and support rotations are
more than 6 degrees, the masonry wall will
become non-reusable, it is to be noted that in the
case of 1:6 masonry, displacement is more than
the thickness of the wall and near collapse
situation has arisen. For the blast of 100 kg at a
distance of 30 & 40 m also the support rotations
are much larger than one degree and masonry
will become non-reusable as per masonry
damage criteria (TM-5-1300).
4. The velocity at central node for surface blast of
100 kg TNT charge at detonation distance of 20,
30 and 40m are 2.60, 1.55 and 1.1 m/s for 1:6
grade of masonry mortar respectively. For
masonry with other grades of mortar the velocity
values are very close to masonry with 1:6 grade
of mortar. At the central node in all the three
cases yielding has taken place and high values of
plastic deformation has taken place and debris
velocity from central node will travel a distance
of 1.40 m, 0.84 m and 0.55 m for three
detonation distances.
5. The dynamic response of masonry wall is
decreasing with increasing the coefficient of
friction at the contact interface of masonry and
RC frame. But, an appropriate interface contact
friction is very useful for blast response of
masonry walls while the interface contact
modelling because of more variation in wall
peak deflection response at low contact friction
values. It is also found that beyond an interface
frictional limit of 0.5, the variation in deflection
response narrows down.
Advances in Structural Engineering Vol. 17 No. 4 2014 605
A.K. Pandey and R.S. Bisht
Figure 13. Variation of displacement with time of masonry wall (T = 235 mm) for blast of 100 kg TNT at a detonation distance of 40 m
Masonry 1:6 location at centre
Masonry 1:4.5 location at centre
Masonry 1:3 location at centre
Masonry 1:6 location at interface
Masonry 1:4.5 location at interface
Masonry 1:3 location at interface
0.00 0.01
0.01
0.000.02
0.02
0.03
0.03
0.04
0.04
0.05
Time (sec)
D i s p l a c e m e n t ( m ) 0.05
0.06
0.06
0.07 0.08 0.09 0.10
Table 11. Peak deflection and rotation of brick masonry (235 mm) for
surface blast of 100 kg TNT at detonation distance of 40 m
Grade of mortar Peak deflection (mm) Time of peak Rotation
S.N. in masonry At centre At interface deflection (Degrees)
1. 1:6 65.7 16.8 0.063 1.862. 1:4.5 56.1 14.2 0.057 1.59
3. 1:3 49.3 12.1 0.055 1.42
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ACKNOWLEDGMENTSThe article forms part of Supra Institutional Project of
CSIR-Central Building Research Institute programme
and is being published with the permission of Director
CSIR-CBRI Roorkee.
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NOTATION
c cohesive strengthc0 initial cohesive strength at zero plastic
strain
F yield function
G p plastic potential function
Pc normal contact pressure
p, q, r stress invariants
Rmc mohr-coulomb deviatoric stress
measure
Rmw deviatoric elliptic function measure
S ij stress deviator tensor
S 1, S 2, and S 3 principal values of stress deviator
tensorW . p rate of plastic work
σ ij cauchy stress tensor
σ 1, σ 2, and σ 3 principal values of cauchy stress tensor
ε ij strain tensor
ε pij
plastic strain tensor
ε – p equivalent plastic strain
ε eij
elastic strain tensor
φ angle of internal friction
Ψ dilation angle in meridional plane
θ deviatoric polar angle
Θ temperatureµ coefficient of dry friction at contact
interface
τ equivalent shear stress at contact
interface
τ max limit of shear stress at contact interface
α potential flow eccentricity in
meridional plane
Numerical Modelling of Infilled Clay Brick Masonry Under Blast Loading