blast loading response of a special concrete slab reinforced …jestec.taylors.edu.my/vol 15 issue 6...

Journal of Engineering Science and Technology Vol. 15, No. 6 (2020) 3803 - 3819 © School of Engineering, Taylor’s University

3803

BLAST LOADING RESPONSE OF A SPECIAL CONCRETE SLAB REINFORCED WITH EMBEDDED CNC STEEL PLATE

ALAA M. AL-HABBOBI, SAAD J. AL-WAZNI*

Department of Civil Engineering, Faculty of Engineering, University of Kufa, P.O Box 21, Kufa, Najaf Governorate, Iraq

*Corresponding Author: [email protected]

Abstract

This study proposes replacing the ordinary reinforcing bars of the one-way concrete slab by embedded steel plate cutting using CNC method. The new proposed structural model is analysed under blast loading. This type of model is very important in special structures such as a military warehouse to increase withstanding of the structural slab when the explosion has occurred. Two concrete slab models were numerically tested, the first is with ordinary reinforcement and the other is with embedded CNC steel plate only. The ordinary RC slab model was adopted from literature to verify the procedure of analysis under blast loading in this research. A parametric study on this first model was implemented to investigate the effect of changing in material properties, blast load properties, reinforcement steel ratios and stiffness on the behaviour of dynamic response for the slab model. The second proposed model was simulated using embedded CNC steel plate with keeping an equivalent moment of inertia and area of ordinary reinforcement in the cross section of the slab. Also, two types of the opening shapes in the CNC plate, square and circular, and two sizes of openings, 37.4 mm and 155.7 mm, were investigated. The finite element analysis of the model was implemented using ABAQUS Explicit-software. The blast load was generated using the CONWEB model provided in ABAQUS software. The results extracted from the analysis of the proposed model are compared with those extracted from the original model. The maximum displacement in the mid-span of the slab is the reference parameter to perform the comparison. The results exhibit significant effect of the proposed model by reducing the maximum displacement in the slab model by reduction percentage of 12.1%.

Keywords: Blast load, Embedded CNC steel plate, Nonlinear dynamic analysis, RC slab.

3804 A. M. Al-Habbobi and S. J. Al-Wazni

Journal of Engineering Science and Technology December 2020, Vol. 15(6)

1. Introduction Serious damage can be appeared in the structures exposed to blast loads. In the near time, some studies were implemented to investigate the structural behaviour of the RC slab structure under blast loads. Meantime, this type of structure is important in the structural design for military buildings as well as some special civilian structures [1]. In Iraq, the researches in this field are very important and need more interest because the war against terrorist organizations is continuous.

Nowadays, the researchers have more attract for structural members of the buildings such as beam, slab and column to investigate the dynamic nonlinear behaviour. To get credible estimations, the structural members could be studied separately, particularly after the enhancement of the structural modelling software [2]. In previous studies, the experimental and numerical simulations of RC structures were applied under blast loads [1, 3]. The expansive of the experimental testing of the blast loading comes from the need of the specialized laboratory with all tools. Therefore, the numerical simulation of these structures under special loads using finite element software is available. The previous studies such as Yao et al (2016) studied the Anti-blast implementation and damage features of reinforced concrete slab subjected to 0.13 kg and 0.19 kg TNT charge weight experimentally and numerically [1]. The geometry of their selected slab model was 850 mm × 750 mm × 30 mm using 6 mm steel bar in one layer with changing reinforcement ratios of 0.44%, 2.42% and 3.76%. Their numerical analysis was conducted using LS-DYNA-software. They concluded that the displacement and the damage severity decrease with increasing the reinforcement ratio which has significant effect due to blast load [1].

Thiagarajan et al. [2] conducted experimental and numerical analysis of RC slab subjected to blast loading to study the sensitivity of mesh size and using high strength material [2]. They selected a slab model that has dimensions of 1652 mm × 857 mm × 101.6 mm with steel bar diameter of 9.5 mm which is spaced in 101.6 mm in the middle and 50,8 mm at the edges. They analysed their slab model using LS-DYNA-software by adopting concrete damage model. They concluded that the mesh sensitivity is decreased for high strength material and good estimation of a maximum displacement was simulated for used material model. Ranji and Esmaeli [3] analysed the one-way RC slab model using Fiber Reinforced Polymer (FRP) subjected to blast loading numerically using ABAQUS-software. They carried out the verification on the numerical results with another experiments. They adopted two slab models geometry, the first was 2000 mm × 1000 mm × 100 mm with reinforcement ratio of 1.34 % and the second was 1200 mm × 1200 mm × 90 mm using 10 mm steel bar in the bottom for flexure. They concluded that the maximum displacement decreases significantly with using FRP [3].

Zhao and Chen [4] implemented experimental and numerical studies for RC slab to investigate the mechanism of failure under blast load [4]. They selected slab model has dimensions of 1000 mm × 1000 mm × 400 mm with reinforcement ratio of 1.43%. The authors analysed the slab model using LS-DYNA-software. They concluded that the slab failure mode was affected by increasing the TNT charge weight significantly.

In this study, the numerical modelling of ordinary reinforced concrete one-way slab is adopted. The ABAQUS-software is used to analyse the structural model under blast loads. The verification of the adopted model is made with reference to

Blast Loading Response of a Special Concrete Slab Reinforced with . . . . 3805


Zhao and Chen [4] which has the experimental results. Moreover, the reinforcement method is replaced using a proposed method of an embedded CNC steel plate instead of the ordinary reinforcement. The CNC means Computer Numerical Control used to configure the steel plate with the opening in any required shapes for different thicknesses. This method of reinforcement is implemented to investigate the dynamic nonlinear behaviour of concrete slab and the mode of failure under blast loading.

2. Numerical Model of Ordinary RC One Way Slab Structure The adopted model in the present study is one way reinforced concrete slab with dimensions of 1000 mm × 1000 mm and thickness of 40 mm, as shown in Fig. 1. The selected model was adopted by Zhao & Chen (2013) in their research and they implemented both numerical and experimental investigation [4]. The one-way slab model is supported as fixed in two opposite sides and free for other. The reinforcement used in the model is a one layer in two directions with 6 mm bar diameter at distance of 75 mm to with reinforcement ratio of 1.43%.

Fig. 1. Structural geometry of the adopted model using ordinary steel reinforcement [4].

The concrete material properties of the adopted model are Modulus of Elasticity of 28.3 GPa and the cylinder compressive, tensile strength of 39.5 MPa, 4.2 MPa, respectively, as listed in Table 1. While, the steel bar has the modulus of elasticity of 200 GPa and yield strength of 600 MPa, as listed in Table 1. This case study is called the standard case for next discussion.

Table 1. Material properties of the adopted structural model. Concrete [4] Steel rebar [4]

Young's Modulus (GPa) 28.3 200 Compressive strength (MPa) 39.5 ---- Tensile strength (MPa) 4.2 ---- Yield strength (MPa) ---- 600 Poisson's ratio 0.2 0.3

The Finite Element (FE) model of the slab structure is simulated using ABAQUS-software, as shown in Fig. 2. The finite element model has divided to two parts, the first represents the concrete model and the second represents the steel reinforcement. The numbers of elements for first and second part are 5000 and 2800, respectively.



a) FE model for concrete material b) FE model for steel reinforcement

Fig. 2. Finite element model of the steel reinforced concrete slab.

2.1. Material model In the current study, the concrete damage plasticity (CDP) model was selected in ABAQUS explicit software to describe appropriate dynamic response of the structural RC slab model under blast loading. The concrete damage plasticity model assumes that the two main failure mechanisms in concrete are the tensile cracking and the compressive crushing. In this damage model, the appropriate tensile and compressive relationship of the concrete material, the damage parameters (cracking and crushing parameter) and other parameters should be defined.

For concrete material, the mass density is 2400 kg/m3 and other parameter are listed in Table 2.

Table 2. Values used of the concrete damage plasticity parameters [5, 6]. Dilation angle Eccentricity Fb0/fc0 K Viscosity

30 0.1 1.16 0.667 0.001

The concrete behaviour in tension, as mentioned in Belarbi and Hsu [7] for both elastic and inelastic behaviour, is explained, as shown in Fig. 3. The tensile strength in the descending part of the stress-strain relationship is given in Eq. (1):

4.00

0

=

t

ttt ε

εσσ (1)

where tσ is the tensile strength of inelastic strain, 0tσ is the maximum elastic tensile strength, 0tε is the maximum elastic tensile strain, and tε is the inelastic strain.

The compressive behaviour of concrete material is represented in this study as mentioned in Popovics [5] and Thorenfeldt et al. [6], the relation between compressive stress and strain is given in Eq. (2):

nk

cm

c

ccc

n

nE

+−

=

εε

εσ

)1(

(2)

The modulus of elasticity is calculated based on compressive strength cmf as given in Eq. (3):



69003320 += cmc fE MPa (3)

The parameter n represents the relation is calculated from Eq. (4):

+=

178.0 cm

fn (4)

The parameter k is calculated based on the concrete strain

−=

1'

nn

Ef

c

cmcε ,

then the k parameter as given in Eq. (5):

≤→

〉→

+

=0.10.1

0.162

67.0

'

'

c

c

c

ccmf

k

εε

εε

(5)

a) For tensile b) For compression

Fig. 3. Stress-strain curve of concrete in the damage concrete plasticity model [7, 8].

In the concrete damaged plasticity model, the reduction of the elastic modulus is assumed in terms of a scalar degradation variable d , as given in Eq. (6) [9]:

0)1( EdE −= (6)

where 0E is the undamaged modulus of elasticity. The stiffness degradation variable, d is a function of the stress state. The uniaxial damage variable for both tension and compression is given in Eq. (7) and Eq. (8), respectively [8, 9]:

c

t

t

plt

c

t

t

Eb

Ed

σε

σ

+

−

−=

111 (7)



c

c

c

plc

c

c

c

Eb

Ed

σε

σ

+

−

−=

111 (8)

where tb = 0.1 and cb = 0.7 and they are close to the experimental test and to

produce a convergent solution and the plastic strain is calculated by inccplc b εε = .

For reinforcement steel bar material, the mass density is 7800 kg/m3 [4]. For the stainless steel, the yield stress yσ is equivalent to the value of 0.2% of proof

stress as 2.0σ , as shown in Fig. 4. [10]. The relationship of stress-strain curve can be estimated as shown in Fig. 4. from Eq. (9), as mention in the reference [10]:

〉⋅⋅+

−

−+

−

≤⋅

+

=

2.02.02.0

2.0

2.0

2.0

2.02.0

002.0

σσεσσ

σσε

σσ

σσσ

σσ

ε

forE

forE

m

uu

n

o (9)

Fig. 4. Stress-Strain curve for stainless steel [10].

where uσ is the ultimate tensile strength, uε is ultimate strain calculated by

uu σ

σε 2.01−= and n, m is given in Eqs. (10) and (11) by trial and error from the

stress-strain relationship:

=

01.0

2.0ln

)20ln(

σσ

n (10)



um

σσ 2.05.31+= (11)

where the modulus of elasticity of 0.2 stress is given in Eq. (12):

en

EE o002.01

2.0+

= (12)

where e is the non-dimensional stress, 0

2.0

Ee σ= and the strain at 2.0σ is given in

Eq. (13):

002.02.02.0 +=oE

σε (13)

For austenitic and duplex alloys, the best approximate line equation to represent the relationship is given in Eq. (14) [10]:

eu

⋅+= 1852.02.0σσ

(14)

However, for all alloys the relationship could be presented by Eq. (15):

)5(0375.011852.02.0

−−⋅+

=n

e

uσσ

(15)

The accuracy of the results for all structural types of stainless steel alloys were obtained since they were compared with experimental tests [10]. For alloys material, there is needed to convert nominal stress to the true stress using the following equation [9]:

)1( normnormtrue εσσ += (16)

Then, the converted true strain from the nominal strain is given in the following equation:

)1ln( normtrue εε += (17)

To convert the true plastic strain, use the following equation:

Etrue

trueplσ

εε −= (18)

2.2. Blast loading As mentioned before, ABAQUS/Explicit-software is used to simulate air blast loading on the adopted structural model without need to model the fluid medium. The CONWEP (Conventional Weapon Effects Program) model is included in ABAQUS-software to represent the waves produced by an explosion [11]. The



external propagation shock wave is generated from the interaction between the ambient air and gas mass composed from the blast. The CONWEP simulates blast loading by empirical data to define the effects of such type of loading for both spherical and hemispherical surface waves of incident [11]. The Lagrangian method is represented in the CONWEP model and this method allows the user, by specifying the time, location and the surface of blast, to estimate the pressure loading generated from the blast without need to the computation of propagation in the air [12]. This is the main advantage of this model.

To estimate the applied load in the CONWEP, the empirical calculation is based on manual TM5-855-1 [13, 14]. The data of CONWEP model are verified by using full scale, by recording the incident pressure caused by the blast propagation from experiments [12, 14].

In the CONWEP model, the distance from the surface to the blast load and its weight should be defined. This distance is called "standoff" and has to provide by selecting the maximum overpressure, time, phase duration and the coefficient of exponential decay for both types of pressure, incident and reflected. The time history of those pressures is shown in Fig. 5. and it is adopted in this study and the total time of detonation was defined.

Fig. 5. Blast loading history [11].

3. Verification of Numerical Model To verify the results of the adopted structural model, the comparison with the reference [4] is carried out. From the results, the maximum displacement at of the model is very close to experimental result in the reference [4] under 0.2 kg TNT and the difference is less than 1%, as listed in Table 3.

Table 3. Comparison in maximum displacement between numerical and experimental slab model.

Numerical model

Experimental Model

Difference (%)

Displacement at of bottom face (mm) 9.927 10.00 0.73



It is obvious from Table 3, that the numerical analysis procedure in this study is validated. The dynamic response of the midpoint in the slab model extracted numerically is shown in the Fig. 6. It is clear from Fig. 6. that a maximum displacement is close to the initial time of the explosion.

Fig. 6. Displacement time history in the of the slab model.

The comparison in results of damage area between the adopted numerical model and experimental model included in reference [4] is shown in Fig. 7. The both models were subjected to blast load of 0.2 kg TNT.

Upp

er su

rfac

e

Low

er su

rfac

e

(a) Adopted numerical model (b) Experimental test ref. [4]

Fig. 7. Comparison between the numerical and experimental damage mode of the slab model for TNT charge weight of 0.2 kg.



It is evident from Fig. 7(b), that the upper surface has low effect generated by blast load. However, the lower surface has significant damage represented by the crack and small indentation in the of slab. This large effect is caused from the direct exposure of explosion as shown in the Fig. 7(b). The results of numerical modeling, as shown in Fig. 7(a), show the comparable modes of damage area for both upper and lower surface. This means the accuracy of the numerical simulation is satisfied.

4. Parametric Study on Ordinary RC One Way Slab Model The parametric study is implemented to investigate the effect of four parameters on the maximum displacement at the of slab. These parameters are the ratio of steel reinforcement, the material properties represented by compressive strength of concrete, the stiffness of the structure represented by the thickness of the slab and the standoff distance effect. The standard case has the following properties; 0.2 kg weight of TNT charge, 40 mm slab thickness, 6 mm steel bar diameter represents steel reinforcement ratio of 1.43%, 39.5 MPa compressive strength of concrete material and 400 mm standoff distance.

4.1. Effect of steel reinforcement ratio The effect of the reinforcement ratio on the dynamic response of RC slab model is significance, as shown in Fig. 8. It is clear from figure, the increase in the displacement of the of the slab model is due to decrease the steel reinforcement ratio.

Fig. 8. Effect of the reinforcing ratio on the maximum displacement

in the of the slab model for TNT charge weight of 0.2 kg.

The values of increasing the displacement in the of slab model are listed in Table 4. Figure 8 shows the slowly nonlinear behaviour of the displacement with the changing in the reinforcement ratio.

Table 4. Displacement values for different reinforcement ratios in the of the slab model.

Steel bar Diameter (mm) 4 6 10 12 Max. displacement at the (mm) 12.086 9.927 6.033 4.854

The percentage of increase between the minimum and the maximum extracted displacement is about 149% corresponding to the decrease in reinforcement bar diameter from 12 mm to 4 mm. Also, the permanent deformation decreases by percentage of 98.6% with increasing reinforcement ratio. Evidently, the reinforcement has significance by reducing the displacement under blast load and thereby, the proposed new reinforcement method is investigated.



4.2. Effect of compressive strength The effect of the compressive strength, which represents material properties, on the dynamic response of RC slab model is also significance, as shown in the Fig. 9. It is evident from figure; the decrease of compressive strength causes increase in the displacement of the centre of the slab model.

The values of increasing the displacement in the centre of slab model are listed in Table 5. Figure 9 shows the nonlinear behaviour of the displacement with the changing in the compressive strength of concrete material. The results show that the higher compressive strength concrete improved the level of protection. The displacement values dropped by 29.8% with increasing the compressive strength between (20-50) MPa. Hence, it can be observed that high strength of concrete was effective in reducing the level of response.

Fig. 9. Effect of the compressive strength on the maximum

displacement in the of the slab model for TNT charge weight of 0.2 kg.

Table 5. Displacement values for different concrete compressive strength in the of the slab model.

Compressive strength (MPa) 20 30 39.5 50 Max. displacement at the (mm) 12.16 10.93 9.927 9.37

4.3. Effect of standoff distance The effect of the standoff distance of blast load on the dynamic response of RC slab model is also significance, as shown in the Fig. 10. It is obvious from figure, the increase in the displacement of the of the slab model by percentage of 144% is due to decrease the standoff distance from 700 mm to 300 mm.

Fig. 10. The effect of the standoff distance on the maximum




The values of increasing the deflection in the of slab model are listed in Table 6. Figure 10 shows the nonlinear behaviour of the displacement with the changing in the standoff distance.

Table 6. Displacement values for different standoff distance in the of the slab model.

Standoff distance (mm) 300 400 500 700 Max. displacement at the (mm) 11.33 9.927 7.17 4.64

4.4. Effect of thickness of slab The effect of the thickness of slab model, represents geometric properties, on the dynamic response of RC slab model is also significance, as shown in the Fig. 11. It is clear from figure, the decrease of the slab thickness causes increase in the displacement of the of the slab model by percentage of 660%.

Fig. 11. The effect of the thickness of slab on the maximum


The values of increasing the deflection in the of slab model are listed in Table 7. Figure 11 shows the nonlinear behaviour of the displacement with the changing in the slab thickness.

Table 7. Displacement values for different slab thickness in the of the slab model.

Thickness of slab (mm) 30 40 50 70 Max. displacement at the (mm) 20.169 9.927 5.441 2.654

To compare the effect of studied parameters on the maximum displacement in the of slab model, the coefficients of variation (COV) for all four parameters were estimated. The values of COV for steel reinforcement ratio, compressive strength, standoff distance and thickness of slab are 35.4%, 10%, 31.1% and 69.7%, respectively. It is evident from the results of the parametric study, the slab thickness is more significance than the others and the compressive strength has less effect.

5. Proposed Model Using Embedded CNC Steel Plate Reinforcement The proposed model of one-way concrete slab is built by replacing the ordinary reinforcement rebars by embedded steel plate with openings cutting using CNC method. The authors suppose that the need of using embedded CNC steel plate reinforcement in slab model instead of ordinary reinforcement is to improve the



ductility of the structural model which is important to resist such type of blast loading. Increasing ductility means large displacement before collapse and more efficient to dissipate energy. Also, other benefits of use of CNC method are to provide the reinforcement for structural member by reducing the cost and mistakes in the reinforcement operations by workers. As well, this new reinforcement method increases the stiffness of the slab model and reducing the concentrated of tensile stress in steel reinforcement. Moreover, it could be useful to increase the bonding and transfer stresses between the concrete and reinforcement and thereby reducing the slipping. Furthermore, this new reinforcement method has more durability than the external strengthen method because it is embedded and protected from any external environment.

Present study assumed that the material properties of the embedded CNC steel plate have the same properties of ordinary reinforcement. The new proposed structural model is analysed under blast loading. The CNC method is used to configure the steel plate with openings for different shapes and sizes. In this type of new reinforcement, the CNC embedded steel plate was configured to has 36 circular opening in the whole area of slab model, as shown in Fig. 12.

a) CNC steel plate reinforcement b) Concrete slab with embedded CNC

Fig. 12. FE Models of the embedded CNC steel plate reinforcement with 36-circular opening in the slab model.

The cross section of the CNC steel plate is selected to be equivalent to the area and the moment of inertia of the cross section of ordinary steel reinforcement and the modelling of the CNC steel plate is represented as 3D solid exclusion element.

The comparison between the ordinary and new steel reinforcing is investigated. The dynamic nonlinear behaviour of concrete slab is shown in Fig. 13. The comparison is done for the standard case study of material properties under blast loading of 0.2 kg.

It is clear from Fig. 13, that the new steel reinforcement method reduces the maximum displacement in the of concrete slab model about 12.1%. Moreover, the new reinforcing method reduces the permanent deformation which occurred in the RC slab model. In other hand, the investigated maximum tensile stresses for both reinforcement methods was not reached the yield stress.



Fig. 13. Comparison between ordinary and embedded CNC steel plate reinforcement on the maximum displacement in the of the slab model for

TNT charge weight of 0.2 kg.

A parametric study was carried out to investigate the appropriate configuration of the embedded steel plate. The first configure has 36-circular opening and the second one has 36- square opening with a length of the side equal to the diameter of the circular opening and keeping equivalent moment of inertia of steel reinforcement cross section, reinforcement ratio and other structural properties unchanged, as shown in Fig. 14. This study is made to get the indication about effect of shape on the maximum displacement in the of slab model.

Fig. 14. Effect of opening shape in the embedded CNC steel plate reinforcement on the maximum displacement in the of the slab model for

TNT charge weight of 0.2kg.

The results show that the model with circular opening has better behaviour than the model with square opening by decreasing percentage in the maximum displacement of 25%, as shown in Fig. 14. This situation occurs due to the effect of distribution of the middle area of steel between openings to increase the bonding.

Also, the appropriate number of circular opening in the slab model is checked. Two numbers were studied, 36-opening with diameter of 155.7 mm and 625-opening with diameter of 37.4 mm in the entire model. The number of 625-opening has the better results than the other, as shown in the Fig. 15.

It is clear from Fig. 15, the decrease of opening diameter, means increase number of circular openings, increase the bonding between the concrete and steel material by reducing the slipping. This will lead to higher efficiency in transferring stresses between concrete and steel, thereby reducing the displacement. The



decreasing percentage in the maximum displacement for this effect of diameter size is 11%.

Fig. 15. Effect of circular opening diameter in the embedded CNC steel plate reinforcement on the maximum displacement in

the of the slab model for TNT charge weight of 0.2kg.

Finally, the variations in the maximum displacement of the proposed model are produced from the efficient distribution of steel reinforcement within volume unit of concrete slab and the enhanced bonding between steel reinforcement and concrete of the slab. Those lead to redistribute the tensile stresses by increasing the resistance ratio of the steel corresponding to concrete material. Therefore, the observed maximum tensile stresses in embedded CNC steel plate is higher than on the steel bars and the both are less than the yield stress value. Thus, the ductility of the proposed structural slab model is improved.

6. Conclusions A new steel reinforcement method using embedded CNC steel plate configuration has been investigated for a one-way concrete slab model under blast loading. The validation of the numerical analysis procedure for the ordinary steel reinforced concrete slab model is verified using ABAQUS-software with the experimental results from reference [4]. Some observed conclusions are given below.

• The verification study gives the value of the maximum displacement in the of the slab model is very close with difference less than 1%.

• A parametric study is carried out to investigate the effect of four parameters in the slab model with ordinary reinforcement. The effect of changing in material properties, blast load properties, reinforcement ratio and geometry of the slab model is considered in the parametric study. The change in slab thickness has a significant effect on the maximum displacement in the of the slab model, while the compressive strength has less effect.

• A parametric study is carried out to investigate the new method of embedded CNC steel plate reinforcement. The effects of the number and shape of openings in the new reinforcement of embedded CNC steel plate model are included. The circular shape and small size are more significant, where the decreasing ratios in the maximum displacement for both the shape and the size are about 25% and 11%, respectively.

• The results show that the new reinforcement method using embedded steel CNC plate instead of the ordinary steel reinforcement in the one-way slab models subjected to blast load is promising and particularly for military structures.



Nomenclatures cb Constant parameter for compression state

tb Constant parameter for tension state

cd Stiffness degradation variable for compression

td Stiffness degradation variable for tension

cE Modulus of elasticity of concrete material, MPa

oE Modulus of elasticity of elastic region of steel material, MPa

Fb0/fc0 Ratio of the strength in the biaxial state to the strength in the uniaxial state. cmf Maximum compressive strength of concrete material, MPa

K Shape factor controls the dependence of the yield surface on the value of the intermediate principle stresses.

k Parameter calculated based on the concrete strain from Eq. (5) n Parameter represents the relation calculated from Eq. (4) Greek Symbols

cε Inelastic strain produced by compression stress plcε Compressive plastic strain

cmε Strain at the maximum compressive strength

tε Inelastic strain produced by tensile stress

0tε Maximum elastic tensile strain pl

tε Tensile plastic strain

cσ Compressive strength of concrete material, MPa

tσ Tensile strength of concrete material, MPa

0tσ Maximum elastic tensile strength, MPa

uσ Ultimate stress, MPa

yσ Yield stress of steel reinforced material, MPa

2.0σ Yield stress of the steel equivalent to the value of 0.2%, MPa

Abbreviations CDP Concrete Damage Plasticity. CNC Computer Numerical Control CONWEP Conventional Weapon Effect Program

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