2014-Numerical Modelling of Infilled Clay Brick Masonry Under Blast Loading

8/17/2019 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


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




5/16

(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



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


6/16

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



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



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



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 -


9/16

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



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


10/16

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



Table 6. Peak deflection and rotation of brick masonry (340 mm) for

surface blast of 100 kg TNT at detonation distance of 20 m


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 1:6 location at interface

Masonry 1:4.5 location at interface



11/16







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


0.00 0.010.000

0.02 0.03 0.04

0.005

0.05

Time (sec)


0.010

0.06

0.015

0.07

0.020

0.08 0.09 0.10







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




12/16

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).



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





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


13/16

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).





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








0.00 0.01

0.02

0.000.02

0.04

0.03

0.06

0.04

0.08

0.05

Time (sec)


0.06 0.07 0.08 0.09 0.10


14/16

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.










0.00 0.01

0.05

0.000.02

0.10

0.03

0.15

0.04

0.20

0.05

Time (sec)


0.25

0.06 0.07 0.08 0.09 0.10





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


15/16

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.










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





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


16/16

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.

REFERENCESABAQUS (2011). User’s Manual, Version 6.11, ABAQUS Inc., DS-

Simulia, Providence, USA.

Baylot, J.T., Bullock, B., Slawson, T.R. and Woodson, S.C. (2005).

“Blast response of lightly attached concrete masonry unit walls”,

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pp. 1186–1193.

Chen, F.W. and Han, D.J. (1988). Plasticity for Structural

Engineers, Springer-Verlag, New York, USA.

Dennis, S.T., Baylot, J.T. and Woodson, S.C. (2002). “Response of

1/4-scale concrete masonry unit (CMU) walls to blast”, Journal

of Engineering Mechanics, ASCE, Vol. 128, No. 2, pp. 134–142.

Laursen, T.A. and Yang, B. (2005). “New developments in surface-

to-surface discretization strategies for analysis of interface

mechanics”, VIII International Conference on Computational

Plasticity, CIMNE, Barcelona, Span.

Li, Q.M. and Meng, H. (2002). “Pressure impulse diagram for blast

loads based on dimensional analysis and single-degree-of-

freedom model”, Journal of Engineering Mechanics, ASCE, Vol.

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Pandey, A.K. and Paul, D.K. (2009). “Damage evaluation of

reinforced concrete containment shell subjected to blast loading”,

Current Science, Vol. 97, No. 3, pp. 336–341.

Pandey, A.K. (2010). “Damage prediction of RC containment shellunder impact and blast loading”, Structural Engineering and

Mechanics, Vol. 36, No. 6, pp. 729–744.

TM5-1300 (1990). Structures to Resist the Effects of Accidental

Explosions, US Army Manual, Washington, D.C., USA.

Varma, R.K., Tomar, C.P.S. and Parkash, S. (1997). “Damage to

brick masonry panel walls under high explosive detonations”,

Pressure Vessels and Piping Division, Vol. 351, pp. 207–216.

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International Journal of Impact Engineering, Vol. 37, No. 11,

pp. 1150–159.

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


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