Dynamic performance of ultra-high performance fiber-reinforced concrete panel exposed to explosive loading

Abstract

Ultra-high performance fiber reinforced concrete (UHPFRC) is a cement-based composite material mixing with reactive powder and steel fibers. It is characterized by its high strength, high ductility, and high toughness and such characteristics enable its great potential in protective engineering against severe dynamic loads. In the current research, the dynamic performance of the concrete panel made with ultra-high performance fiber subjected to explosive loading was investigated. For this purpose, several concrete panel samples were considered and modeled in ABAQUS finite element software. The accuracy of the numerical model is verified by comparing the numerical simulation results with available testing data. First, the considered panel was modeled with normal concrete then it was modeled with UHPFRC concrete, and the effect of using this type of concrete on the behavior of concrete panels was investigated. After analyzing and examining the models, their behavior such as the degree of vulnerability, more vulnerable points and changes in the locations that occurred in each of the models were obtained and compared. The results demonstrate that the use of UHPFRC significantly improves the blast performance of RC panels by reducing maximum and residual displacements, enhancing damage tolerance, and increasing energy absorption. The results also indicate that the increase in the intensity of explosion has increased the base reaction force in all panels.

Keywords

Vulnerability ultra-high performance concrete panel explosive loading ABAQUS

Introduction

The behavior of concrete structures under explosion loading is a topic of major concern in both civil and material engineering (Mao, 2015). With the strain rate effect, the concrete behavior subjected to high strain rate loading will be different from that under static loading (Lin, 2018; Li, 2015a). Due to the brittle nature of concrete materials, several methods have been developed to further increase the concrete resistance to high strain rate loading, such as adding fiber reinforcement to the concrete or use of high-strength concrete materials. UHPFRC has been recently developed and has material properties which are much improved from those of conventional concrete (Mao, 2014).

The first application of super-strength concrete was the construction of a pedestrian bridge in Sherbrooke, Canada. The span of this bridge is 60 m and it is designed as a pre-tensioned space truss. In fact, the implementation of this bridge was part of a long-term study and a research program was conducted to study the changes in shapes and stresses in the bridge’s prestressed beams in the long term. In 1997, the use of super strong concrete in a project in France confirmed the very good durability of this type of concrete. In the French Catnum power plant, the metal beams of the cooling towers were replaced with beams made of high-strength concrete. The environment was very corrosive and the experts expected that due to the very high durability of this concrete, the failure and as a result the costs of repair and maintenance of these beams would be minimized. After 3 years, a specialized group from the French Engineers Association reviewed the said beams at the power plant site and no signs of damage were seen on the beams. The first bridge made of high-strength concrete for the passage of vehicles in France was put into operation in 2001. The span of this bridge is about 44 m. In the United States, in 2001, super-strength concrete was used instead of metal coating to build the roofs of clinker silos. Twenty-four trapezoidal pieces with a thickness of 13 mm covered the roof of the silo with a diameter of 17.5 m. This reduced manpower and project implementation time compared to the case of covering with metal.

UHPFRC concrete

In the early 1980s, the idea of using a very fine granularity along with a homogeneous and solid matrix of cement material appeared. This idea was found because research showed that the weakest area of concrete is the junction of cement paste and aggregate, or the transfer zone. Mainly, the small cracks that are created in this area cause the concrete to break after spreading to other areas. Now, by removing the coarse grain, this weakness is actually removed, and the small cracks in the transfer zone, which cause the final rupture of the concrete, will also be limited. The UHPFRC concrete contain Portland cement, microsilica, quartz powder (also called quartz powder), quartz sand, super lubricant, water, and fibers. UHPFRC is a concrete material with both high-strength concrete and fiber reinforcement (Lin, 2018; Li, 2015b). It has high cement content and low water/cement ratio. Fine silica sand and short steel fibers are also included in the material. UHPFRC has high compressive strength of up to 200 MPa and tensile strength of about 20–40 MPa (Lai, 2015).

In general, special operations are considered for making high-strength concrete, which include:

(1) Removing coarse-grained stone materials to achieve a more homogeneous structure

(2) Increasing the density of concrete by optimizing and grading the grains of materials used in this concrete

(3) Applying special processes, compressing fresh concrete and applying heat treatment on this concrete

(4) Adding steel fibers to increase ductility and remove the brittleness of concrete

(5) Reducing the water-cement ratio to 0.2 or even less, using new generation superlubricants

(6) Using other cement and pozzolanic materials to replace some of the cement

(7) Reducing the ratio of CaO to SiO₂ by adding silica materials

The characteristics and specifications of super strong concrete that have been proposed in the world are:

(1) The compressive strength is 150 MPa and even more (with heat and pressure treatments before setting, the compressive strength has reached 800 MPa).

(2) Tensile strength of 25 MPa and even more.

(3) Flexural modulus (ultimate bending strength) of about 40 MPa with steel fibers.

(4) High plasticity and very high energy absorption, which is comparable to some metals; (If there are steel fibers, its plasticity is about 250 times that of ordinary concrete). This enables the construction of tall and reliable structures against additional loads and earthquakes.

(5) The very high durability of this concrete, which leads to an increase in life and a reduction in its maintenance.

Literature review

Under the effects of blast load, numerous studies were conducted using either normal concrete or high-strength concrete (Liu, 2022; Taha, 2020; Xu, 2021; Wan, 2021; Abedini, 2020). However, tests on UHPFRC members under blast load are extremely limited as a result of the high technical requirements and high costs associated with the fabrication of UHPFRC. Under the influence of a blast load, Burrell conducted an experiment with a total of thirteen half-scaled steel fiber reinforced concrete columns (Burrell, 2012). They discovered that fiber played a crucial impact in lowering the number of secondary explosion pieces that were produced. In addition, the maximum and residual deflection of UHPFRC columns is significantly reduced in comparison to that of conventional concrete columns. Ellis et al. undertook an experimental program on UHPFRC panels to validate a multi-scale model (Ellis, 2014). They came to the conclusion based on the findings that packing, volume fractions, and the geometry of the fibers are all parameters that have a major influence on the resistance of UHPFRC panels when they are subjected to blast loading. The behavior of UHPFRC columns when they were subjected to blast load was investigated by Juechun et al. (Xu, 2016). For the purpose of their research, a large number of field experiments were carried out in order to explore the behavior of UHPFRC columns when subjected to blast stress. UHPFRC columns not only showed more resistance under the over pressures and shock waves generated from explosives than high-strength concrete columns, but they also minimized the maximum displacements. This is in comparison to high-strength concrete columns.

In 2020, Sharma et al. addressed the effect of critical parameters on UHPFRC structural elements under blast loading (Sharma, 2020). They came to the conclusion that ultra-high performance fiber reinforced concrete (UHPFRC), in comparison to high-strength concrete and standard concrete, enhanced capacity to dissipate a huge amount of energy during blast loading and reduced the severe damage in the structure after blast load. In order to examine the behavior of UHPFRC panels when subjected to blast loads, Mao et al. (Mao, 2014) used the Concrete Damage Model in LS-DYNA. This model took into account the influence that strain rate had on the material. Experimental experiments were conducted by Cavil et al. (Cavili and Rebentrost, 2006) on a total of seven UHPFRC panels. The effectiveness of these panels was evaluated using stand-off distances of 30, 40, and 50 m, respectively. In general, the obtained results demonstrated a positive reaction of UHPFRC panels when subjected to blast stress, demonstrating strong ductility and exhibiting no trace of serious damage. In addition, the exceptional energy absorption of the UHPFRC panel was proved by comparing the peak deflection to the span of the panel. Despite the fact that the achieved results are noteworthy, the specific designs of the UHPFRC panel were not disclosed because to the requirement that security limitations be adhered to.

A numerical simulation method is required in order to achieve more accurate predictions of the dynamic behavior of UHPFRC structures in general and UHPFRC panels in particular while they are subjected to blast stress. This can be accomplished by simulating the structures numerically. The use of numerical models leads to a reduction in the enormous number of expensive experiments being conducted. This study reveals that UHPFRC material has the potential to be used for the purpose of protecting significant structures that are subjected to blast load. In this research, the investigation of the response of UHPFRC panels to catastrophic explosions was carried out using numerical models. These models were implemented to investigate the response. It is important to model the UHPFRC panel using a computer-aided program when it is being subjected to blast load in order to provide supplemental knowledge for blast loading resistance design. The numerical simulation was carried out by employing the ABAQUS program in conjunction with a subroutine that was created by the authors of the study. This technique relies on an explicit numerical model to solve issues that arise in settings with many loading conditions and significant amounts of deformation. In order to determine whether or not the subroutine was accurate, the findings were compared to previous tests. As was already indicated, there have only been a handful of tests done on the UHPFRC structure in this industry, and the ABAQUS software has not supported the input parameters for the UHPFRC. In order to calibrate these input parameters such that they follow the structural behavior of UHPFRC when it is subjected to blast load, selecting the appropriate material model and making use of the supported subroutine are both essential.

In 2021, Gao et al. investigated the performance of a concrete retaining wall with super-strength concrete under blast loading. In this study, a three-dimensional numerical simulation was performed using autodyn-3D. In this simulation, a high explosive (TNT) is detonated against two concrete slabs. This model was first validated using experimental tests conducted by Lee and showed good results. Two numerical models were conducted to investigate the effect of using high-strength concrete in reducing the effect of blast waves. Reflected pressure and damage were observed after testing. The results showed that UHPC retaining walls perform better in blast loading than conventional concrete retaining walls (NSC). In addition, the damage to the concrete retaining wall after blasting is greatly reduced because UHPC affects the integrity of the concrete wall and limits the amount of fragments protruding from the concrete retaining wall. Because it is one of the serious harmful effects that causes human casualties and damage to structures.

In the current research, the dynamic performance of the concrete panel made with ultra-high performance fiber subjected to explosive loading was investigated. For this purpose, several concrete panel models were considered and modeled in ABAQUS finite element software. The accuracy of the numerical model is verified by comparing the numerical simulation results with available testing data. First, the considered panel was modeled with normal concrete, and then it was modeled with high-strength fiber concrete, and the effect of using this type of concrete on the behavior of concrete panels was investigated. After analyzing and examining the models, their behavior such as the degree of vulnerability, more vulnerable points, and changes in the locations that occurred in each of the models were obtained and compared.

Finite element modeling

Table 1 In this section, finite element modeling of UHPFRC panel under high strain rate loading is considered and the applied variables in the panels are discussed. First, the considered panel will be modeled with ordinary concrete, and then it will be modeled with UHPFRC concrete to investigate the effect of using this type of concrete on the behavior of concrete panels. After analyzing and examining the models, their behavior such as the level of vulnerability, deflection time history, energy absorption, and reaction force will be analyzed and compared. The considered concrete panel model is a 200 × 300 cm panel with a thickness of 15 cm. The variables considered to investigate the behavior of the concrete panel against the explosion are the type of concrete (normal and UHPFRC concrete). Also, the amount of explosive charge will be variable in the models, and three types of explosives with different weights of TNT will be used. The following Table shows the characteristics of the considered models along with the applied variables.

Table 1.

Specifications of the considered panels.

Models	Pane dimensions (cm)	Horizontal rebar	Vertical rebar	Concrete type	TNT (kg)
Cp-oc-10	300x200x15	φ25@10	φ25@10	NC	10
Cp-oc-20	300x200x15	φ25@10	φ25@10	NC	20
Cp-oc-50	300x200x15	φ25@10	φ25@10	NC	50
Cp-uhpfrc-10	300x200x15	φ25@10	φ25@10	UHPFRC	10
Cp-uhpfrc-20	300x200x15	φ25@10	φ25@10	UHPFRC	20
Cp-uhpfrc-50	300x200x15	φ25@10	φ25@10	UHPFRC	50

To model the concrete part of the panel, the cubic element (Solid) with extrusion type is used, and for the modeling of the rebar’s, the linear element (Wire) is used in the form of a truss (through this element, we can give a specific area to the cross-section of a linear element). Elements under sever distortion may cause numerical instability (Zhang, 2020). To stop this type of instability, highly distorted elements can be removed from the simulation using element erosion technique. For a severe distortion problem like the present study, the erosion method is generally applied. Element erosion is a process that eliminates elements from the analysis when they meet some failure criteria (Abedini and Zhang, 2021a). This method produces discontinuities in the material due to both brisance effect and fracture induced. The keyword *Mat Add Erosion with failure criteria of minimum pressure at failure (P_min), and maximum principal strain (ε_max) are used to consider the element deletion for the concrete material.

The rebar’s in this part are first modeled as horizontal and vertical rebar’s separately, then in the assembly part, they are integrated into a uniform mesh.

Mesh convergence is an important consideration in both ABAQUS/Standard and ABAQUS/Explicit. It is important that you use a sufficiently refined mesh to ensure that the results from your ABAQUS simulation are adequate. Coarse meshes can yield inaccurate results in analyses using implicit or explicit methods. The numerical solution provided by the model will tend toward a unique value as the mesh density is increased. The computer resources required to run your simulation also increase as the mesh is refined. The mesh is said to be converged when further mesh refinement produces a negligible change in the solution. In this study, convergence test is performed with different element size and 20 mm mesh size is selected as model baseline.

The contact between the metal bars and the concrete beam is defined in the software by specifying the Embedded region. By means of this clause, one part can be placed inside another part so that the degrees of freedom of the inner part are interpolated from the outer part using its degrees of freedom. The Figure 1 shows the construction of different panel parts and the considered concrete panel formation.

Figure 1.

Finite element modeling of (a) concrete, (b) rebar’s and (c) RC panel.

Boundary conditions represent any relationship between the external points of the model and the surrounding space. In fact, in this section, the support conditions of the model are defined. In order to apply the support conditions, sometimes the movement of the modeled concrete panel is prevented in the lower and side part. The figure below shows the boundary conditions considered for the modeled concrete panel Figure 2.

Figure 2.

Boundary conditions in the modeled concrete panel sample.

Material models

In order to define the characteristics of concrete materials, the plastic damage model will be used (Mai, 2021; Abedini and Zhang, 2021a). The concrete grade C30 was used for normal concrete. For the model made with high-strength fiber concrete, a high-strength concrete model whose mechanical characteristics have already been obtained will be used (Abedini and Zhang, 2021b). As we know and it was mentioned before, high-strength fiber concrete has various advantages such as high compressive strength, and the presence of fibers in it increases its plasticity, tensile strength, and strength against dynamic loads (Li, 2016).

JH-2 is the second version of the Johnson–Holmquist (JH-1) damage, which is able to simulate the behavior of brittle materials such as concrete under blast load including the strain rate effects, dilatation and pressure-strength dependence caused by damage. Based on the JH-2 model, the yield strength degrades with damage accumulation. In the JH-2 model, it is assumed that in case of undamaged and fully damaged material state, the equation of the strength can be expressed as a function of the pressure and strain rate. Q960 high-strength steel, because of its good comprehensive performance, can meet the requirements of the steel for engineering machinery and has high added value, which is the key research of steel in large steel works. The following tables show the specifications of the materials used Tables 2 and 3.

Table 2.

Properties of concrete and rebar’s.

Materials	Modulus of elasticity (GPa)	Density (kg/m³)	Strength (MPa)	Yield stress (MPa)	Ultimate stress (MPa)	Ultimate strain %
Rebar	210	7800	-	340	500	25
Concrete	25	2350	30	-	-	-

Table 3.

Properties of UHPFRC concrete.

Material	Volume percentage of fibers (%)	Modulus of elasticity (GPa)	Compressive Strength (MPa)	Tensile Strength (MPa)	Maximum initial compressive strain	Ultimate compressive strain	Maximum initial tensile strain	Ultimate tensile strain
UHPFRC concrete	2	56	152	9.9	0.004	0.008	0.004	0.01

Blast loading

In order to apply an explosive load on the concrete panel, TNT will be used with a certain weight and a certain distance (Zhang and Abedini, 2021). The explosion distance and TNT weight have been chosen in proportion to match each other and the explosive load has a good effect on the panels with weak, medium and strong explosions (Li, 2016). Therefore, the distance between blast location and the panel is 4 m, and the height of the explosion from the ground is 1.5 m. The TNT charge weights are 10, 20, and 50 kg. The blast load applied to the panel will be applied to the concrete panel as an air blast through the CONWEP constraint (Fan, 2022). Figure 3 presents the simulation of blast load on the panel. The red dot shows the place where the TNT was drawn and the explosion occurred, and the purple surface shows the place where the blast wave entered, which is a concrete panel. The analysis performed is an explicit dynamic type (Zhang and Abedini, 2022).

Figure 3.

Applying the blast load to concrete panel.

Validation of the finite element model

Validation with reinforced concrete beam

In order to validate the numerical model, a laboratory sample of reinforced concrete beam against explosive load has been investigated by Zhang et al. in 2013 at China Defense University (Zhang, 2013; Zhang and Abedini, 2022). The beam sample that has been used for verification purposes in this research is a reinforced concrete beam with a length of 1100 mm and a square cross-section of 100 mm. The Figure below shows the cross-section and characteristics of the reinforcement of the RC beam Figure 4.

Figure 4.

Considered reinforced concrete beam.

In order to apply an explosive charge to the sample of the considered beam, 0.75 kg TNT charge weight will be placed at a distance of 400 mm from the center of the beam Figure 5.

Figure 5.

Explosive load applied to the beam.

Finite element modeling of validated beam

The initial stage is the construction of different parts of the beam. To model the concrete part of the beam, the cubic element (Solid) with extrusion type is used, and to model the rebar’s, the linear element (Wire) is used. The rebar’s in this part are first modeled as horizontal and vertical rebar’s separately, and then in the assembly section, they will become an integrated reinforcement network. The following Figure show the construction of different parts in the software Figure 6.

Figure 6.

Finite element modeling of concrete and rebar’s.

One of the important parts of modeling in ABAQUS software is sample meshing. Choosing the type of element and its dimensions can have an impact on the analysis process and the results of the analysis. As described before, the concrete beam is modeled by the cubic element and the rebar’s are also modeled by the linear element. In order to mesh the beam, eight-node cubic element with reduced integral C3D8R is used, and two-node linear element B31 is used for meshing the rebar’s. The Figure 7 shows the sample meshing.

Figure 7.

Meshing of the model.

The specifications of steel members will be defined in two lines to the software. The specifications of concrete materials will also be defined in the form of concrete plastic damage model. The tensile stress of the rebar’s mesh is 395 MPa and the ultimate stress is 501 MPa. The average compressive strength of concrete is 40.45 MPa. The contact between the rebar’s and the concrete is defined in the software by specifying the Embedded region. The TNT with a weight of 750 g and a distance of 40 cm will be used to apply an explosive charge on the beam. The explosive load applied to the beam will be applied in the ABAQUS software through the CONWEP approach. Through this approach, one or more explosions in the air with a certain amount of TNT can be applied at a certain distance from the desired point or object. Burst pressure decreases with time. The following relationship shows this.

P (t) = P_{s o} [1 - \frac{t - T_{a}}{T_{0}}] \exp [\frac{- A \times (t - T_{a})}{T_{0}}

which in relation p(t) is the pressure at time t, P_so is the maximum pressure, T₀ is the duration of the positive phase of the explosion, A is the reduction parameter, and T_a is the arrival time of the explosion wave. The CONWEP method, which is used in ABAQUS, predicts and calculates the pressure load caused by the explosion for a certain weight of TNT at a certain distance from the desired location and applies it to the desired location.

Validation results

After analyzing the model, we will compare the results of the laboratory sample with the finite element model. The Figures below show the compressive and tensile damage to the beam and the comparison with the laboratory sample Figures 8 and 9.

Figure 8.

Compressive damage of the validated model.

Figure 9.

Tensile damage of the validated model.

It can be seen that in the part of the beam that is close to the explosive charge (the middle of the beam), a compressive failure has occurred due to the blast wave. Also, at both ends of the beam and at the place of the supports, due to the pressure applied to the beam, compressive failure has occurred in the concrete section. Also, there is a tensile failure in the beam below and in the middle, which is the result of the beam being stretched from this area. Tensile damage is also observed at the beam supports. Figure 10 also shows the damage in the laboratory sample, which matches well with the finite element model.

Figure 10.

Blast damage of the experimental model.

The following Figure also shows the comparison of the displacement–time curve of the laboratory results with the finite element model. In a short time after the explosion wave reaches the beam, the middle of the beam opening starts to increase its displacement, and after that, with the change of air pressure due to the wave caused by the explosion, the negative pressure in the air has caused a distortion in the beam. According to Figure 11, it can be seen that the laboratory results are in good agreement with the finite element model. The maximum displacement in the laboratory sample was 36.2 mm and in the finite element model was 38.8 mm, which is about 7% difference between the two samples.

Figure 11.

Comparison of displacement time-history between experimental results and FEM.

Validation with reinforced concrete panel

In order to verify the accuracy and reliability of the numerical model described above, the numerical model is used to simulate the responses of a concrete panel to blast load obtained in a field blasting test. Muszynski and Purcell (Muszynski and Purcell, 2003) conducted a field test on the concrete cubicles with a 150 mm thick roof and floor as shown in Figure 12. Two RC panels without or with FRP strengthening are tested. In this paper, only the un-strengthened RC panel is modeled. The FRP strengthened RC panel is modeled in the part 2 of this study . The 2700 mm high, 2500 mm wide and 200 mm thick un-strengthened concrete wall is reinforced with 9 mm rebar at 300 mm center to center spacing. An explosive charge of 830 kg TNT equivalent is detonated at 14.6 m standoff distance from the structure. The blast load is not presented in Muszynski & Purcell (Muszynski and Purcell, 2003), but with the charge weight and standoff distance, it can be accurately predicted with standard approaches. In this study, the blast load was calculated using the empirical formulae given by Wu and Hao (Wu and Hao, 2005), which gives similar predictions as UFC-3-340-02. Figure 13 displays the six blast pressure time histories calculated for the nine segments corresponding to the charge weight and the standoff distance used in the test. These blast loads are applied to the RC panel to calculate its responses.

Figure 12.

(a) Isometric view of cubicle concrete structure, and (b) Retrofitted and non-retrofitted wall displacement measurement locations (Muszynski and Purcell, 2003).

Figure 13.

Calculated blast pressure time histories.

A numerical model of RC walls similar to those in the test is developed as shown in Figure 14. The boundary condition is very important in the analysis hence the concrete slab, side walls, middle column and roof are also included to mimic the actual tested structure model. Figure 15 and Table 4 show the comparison of the calculated and field measured residual deflection of the un-strengthened RC wall at locations illustrated in Figure 12. As shown, the predicted residual deflections in the present analysis agree well with the measured residual deflection in the field test. The largest error is 33%, but the 35.11 mm of the average residual deflection obtained in the analysis is nearly the same as the 35 mm residual deflection recorded in the field test. Flexural crack patterns are illustrated in Figure 16. The predicted crack patterns (Figure 12(b)) developed from middle span towards the corner of the wall is similar to the crack patterns observed in the field test (Figure 12(a)). These confirm the reliability of the numerical model to predict the un-strengthened concrete slab response to blat loads.

Figure 14.

Numerical model of the cubicle concrete.

Figure 15.

Comparison of un-strengthened RC panel residual displacement contour, (a) Muszynski and Purcell (Muszynski and Purcell, 2003) field test result and (b) present analysis.

Table 4.

Residual displacement of un-strengthened RC panel.

Displacement locations	Muszynski and purcell (Muszynski and Purcell, 2003) residual displacement results (mm)	Present analysis residual displacement results (mm)	Percentage of error (%)
d1	25	26	4
d2	34	28	-18
d3	39	29	-26
e1	30	39	30
e2	52	67	29
e3	52	50	-4
f1	22	22	0
f2	36	29	-19
f3	39	26	-33
avg	35	35.11	0.00

Figure 16.

Comparison of crack patterns for un-strengthened RC wall, (a) Muszynski and Purcell (Muszynski and Purcell, 2003) field test result and (b) failure strain contour in the present analysis.

Results and discussion

Evaluation of damage on panels

The blast pressure from the front is applied to the reinforced concrete panels. After a fraction of a second, the explosive charge reaches to concrete panel, and with increasing time, the amount of pressure applied to the panel increases. The greater TNT weight cause the greater pressure wave on the concrete panel and cause more damage. As an example, Figure 17 shows the pressure wave applied to the panel after 0.01 and 0.02 s with normal concrete and 20 kg TNT charge weight. After this time, the pressure wave caused by the explosion decreased to zero.

Figure 17.

Pressure counter by the blast wave after 0.01s and 0.02 s with 20 kg TNT.

As we know, damage to concrete occurs in the form of compression damage (caused by compressive forces in concrete) and tensile damage (caused by tensile forces in concrete). After analyzing the models, the compressive and tensile damage contours applied to each panel were obtained. The Figures below show the compressive and tensile damage contours applied to each panel Figures 18, 19, 20, 21, 22, 23.

Figure 18.

Compressive and tensile damage to concrete panel with normal concrete and 10 kg TNT charge weight.

Figure 19.

Compressive and tensile damage to concrete panel with normal concrete and 20 kg TNT charge weight.

Figure 20.

Compressive and tensile damage to concrete panel with normal concrete and 50 kg TNT charge weight.

Figure 21.

Compressive and tensile damage to UHPFRC concrete panel and 10 kg TNT charge weight.

Figure 22.

Compressive and tensile damage to UHPFRC concrete panel and 20 kg TNT charge weight.

Figure 23.

Compressive and tensile damage to UHPFRC concrete panel and 50 kg TNT charge weight.

After the start of the explosion, the first effect of the explosion is a sudden increase in air pressure, which causes rapid movement of air and the generation of strong waves due to the explosion. The pressure of the environment around the explosion point increases in a very short time and reaches its maximum. This value is called the maximum overpressure P_so. The created overpressure gradually decreases and finally the ambient pressure returns to its initial pressure. After reducing the pressure, a negative pressure or suction condition is created in the environment and finally the air pressure returns to its normal state. In the panels, when the pressure wave from the explosion reaches the panel, considering that the panel is restrained from around and on the ground, it starts to deform from its upper and middle parts, so the most deformation can be seen in the central and upper part of the panel. The stronger explosive charge is more deformation occurs in the panel and more destruction occurs in different parts of the panel.

In the panel model with normal concrete against the explosive load of 10 kg TNT, compressive damage is observed in the middle part of the panel, and a lot of tensile damage has occurred in the middle and side parts of the panel, and some deformation in the panel is also observed. Deformation has occurred in this panel against the explosive load of 20 kg TNT, and extensive compressive and tensile damage has occurred on the entire surface of the panel. In this panel, against the explosive load of 50 kg TNT, the deformations were very high and there was complete destruction in it.

In the model of the panel with high-strength fiber concrete, it was not damaged much against the explosive load of 10 kg TNT, and the resistance of the panel against this explosive load was very high and showed good resistance. Only in the central part of the wall, a little compressive damage is observed and a little tensile damage is also observed in the boundary points of the wall, and the displacement caused in different parts of this panel is small. This panel also has a good resistance against the explosive load of 20 kg TNT and the deformation of this panel is very small. The compressive and tensile damage in this model is the same as the panel model against the explosion of 10 kg TNT, and the damage caused in it is slightly more. In this panel, against the explosive load of 50 kg TNT, compressive and tensile damage is seen more widely, and compressive damage is observed throughout the wall and tensile damage is also observed in many parts of it, and the deformation of the panel is also quite evident. By comparing the contours of compressive and tensile damage in the two cases of panel with normal concrete and panel with high-strength fiber concrete, the better performance of the concrete panel with high-strength concrete is evident, and this model has a much higher resistance than the model with normal concrete.

Panel displacements

In this section, the results of the displacement are discussed in the panels due to the explosion. The displacements are provided for two points, the middle part of the top of the panel and the center of the panel. The following Figures show the graphs of displacement versus explosion time for each models Figures 24 and 25.

Figure 24.

Displacement time history of middle and upper part of panels with normal concrete against explosive loads.

Figure 25.

Displacement time history of middle and upper part of panels with UHPFRC concrete against explosive loads.

Table 5 By observing the displacement time history diagrams of the panels, it can be seen that the increase in the weight of TNT (explosive charge) causes an increase in displacement in different parts of the panel. The change in the location of the upper part in all considered panels was greater than the middle part at the end of the analysis time. Also, it can be seen that the change of location in the model of the panels made with super strong fiber concrete compared to the samples with normal concrete has been significantly reduced and the use of super strong concrete has been completely effective in reducing the vulnerability of the panel. The Table below shows the maximum changes in places that occur in each of the panels.

Table 5.

Comparison of maximum deflection in the panels.

Models	Middle part deflection (mm)	Top part deflection (mm)
Cp-oc-10	91	112
Cp-oc-20	283	319
Cp-oc-50	1000	1084
Cp-uhpfrc-10	25	31
Cp-uhpfrc-20	55	65
Cp-uhpfrc-50	330	413

According to the above table, it can be seen that the displacement of the concrete panel with high-strength fiber concrete against the explosive load of 10 kg TNT has decreased by 72% in the middle part and 72% in the upper part compared to the model with normal concrete. The displacement of the concrete panel with high-strength fiber concrete against the explosive load of 20 kg TNT has decreased by 80% in the middle part and 79% in the upper part compared to the model with normal concrete. The displacement of the concrete panel with high-strength fiber concrete against the explosive load of 50 kg TNT has decreased by 67% in the middle part and 62% in the upper part compared to the model with normal concrete.

Reaction force

As we know, boundary conditions are defined for each panel, and the movements of the panels are limited at these points, so when the pressure force caused by the explosion enters the panels in the parts connecting the panel to the ground and its surroundings, a reaction force is created. The following Figures show a comparison of the base reaction force curves applied to the panels Figures 26 and 27.

Figure 26.

Comparison of reaction force for panels made with normal concrete against explosive loads.

Figure 27.

Comparison of reaction force for panels made with UHPFRC concrete against explosive loads.

Table 6 By observing the base reaction force diagrams for each panel, it can be seen that the maximum base reaction force in each panel occurred at the initial moments of the explosion and when the blast wave reached the panel, and after that with the passing of time, the amount of base reaction force is reduced. The increase in the weight of TNT and the intensity of explosion has increased the base reaction force in all panels. The Table below shows the maximum value of the base reaction force for each panel.

Table 6.

Maximum base reaction force of panels.

Models	Reaction forces (kN)
Cp-oc-10	5599
Cp-oc-20	7196
Cp-oc-50	12994
Cp-uhpfrc-10	6900
Cp-uhpfrc-20	11981
Cp-uhpfrc-50	21310

According to the above table, it can be seen that the panels made with high-strength fiber concrete, due to their greater resistance to explosion, have transferred more force from the explosive load to their boundary parts, and therefore, the maximum reaction force increases. The reaction force of the base of the concrete panel with high-strength fiber concrete against the explosive load of 10 kg TNT was 19% higher than the model with normal concrete. The reaction force of the base of the concrete panel with high-strength fiber concrete against the explosive load of 20 kg TNT was 40% higher than the model with normal concrete. The reaction force of the base of the concrete panel with high-strength fiber concrete against the explosive load of 10 kg TNT was 39% higher than the model with normal concrete.

Absorbing energy

In this part, we will examine the amount of energy absorption for each panel. Energy absorption shows the amount of force applied to it due to the explosive charge. Of course, it should be noted that the greater explosion pressure, create more amount of energy entering the panels, and naturally, the amount of energy absorption increases. The following Figures show the energy absorption diagrams for each panel Figures 28 and 29.

Figure 28.

Comparison of energy absorption for concrete panels made with normal concrete against explosive loads.

Figure 29.

Comparison of energy absorption for concrete panels made with UHPFRC concrete against explosive loads.

It can be seen that with the increase in the weight of TNT and consequently the increase in explosive pressure, the amount of energy absorption for each panels have increased. The concrete panels made with normal concrete have absorbed more energy from the blast wave than the models made with high-strength fiber concrete, and in fact, the models of concrete panels made with high-strength fiber concrete have more explosive force. The highest amount of energy absorption is observed in the model made with normal concrete against the explosive charge weight of 50 kg TNT.

Conclusions

In the current research, dynamic performance of ultra-high performance fiber-reinforced concrete panel exposed to explosive loading is numerically investigated. After modeling the concrete panels with normal concrete and UHPFRC concrete and analyzing the panels against explosive loads with different intensities, various factors are evaluated including vulnerability of the panels, displacements, reaction force, and their energy absorption rates. Validation study is conducted based on the experimental test available in the literature to investigate the accuracy of finite element models using ABAQUS to present the behavior of the models. The results showed that the use of UHPFRC significantly improves the blast resistance of panels, resulting in a better control of maximum and residual displacements at equivalent blast loads, and an ability to sustain larger blast loads before failure. Also the results demonstrate that the use of UHPFRC significantly improves the blast performance of RC panels by reducing maximum and residual displacements, enhancing damage tolerance, and increasing energy absorption.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Ministry of Science and Technology of China (Grant No. 2019YFE0112400), the Department of Science and Technology of Shandong Province (Grant No. 2021CXGC011204), and the State Key Laboratory of Precision Blasting of Jianghan University.

ORCID iD

M Abedini

References

Abedini

(2020) Large deflection behavior effect in reinforced concrete columns exposed to extreme dynamic loads. Frontiers of Structural and Civil Engineering 14: 532–553.

Abedini

Zhang

(2021a) Dynamic performance of concrete columns retrofitted with FRP using segment pressure technique. Composite Structures 260: 113473.

Abedini

Zhang

(2021b) Performance assessment of concrete and steel material models in ls-dyna for enhanced numerical simulation, a state of the art review. Archives of Computational Methods in Engineering 28: 2921–2942.

Burrell

(2012) Performance of Steel Fibre Reinforced Concrete Columns under Shock Tube Induced Shock Wave Loading. Canada: University of Ottawa.

Cavili

Rebentrost

(2006) Ductal–a high-performance material for resistance to blasts and impacts. Australian Journal of Structural Engineering 7(1): 37–45.

Ellis

(2014) Experimental investigation and multiscale modeling of ultra-high-performance concrete panels subject to blast loading. International Journal of Impact Engineering 69: 95–103.

Fan

(2022) Experimental study of damage to ultra-high performance concrete slabs subjected to partially embedded cylindrical explosive charges. International Journal of Impact Engineering 2022: 104298.

Lai

Guo

Zhu

(2015) Repeated penetration and different depth explosion of ultra-high performance concrete. International Journal of Impact Engineering 84: 1–12.

(2016) Experimental investigation of ultra-high performance concrete slabs under contact explosions. International Journal of Impact Engineering 93: 62–75.

10.

Hao

(2015a) An experimental and numerical study of reinforced ultra-high performance concrete slabs under blast loads. Materials and Design 82: 64–76.

11.

Hao

(2015b) Investigation of ultra-high performance concrete slab and normal strength concrete slab under contact explosion. Engineering Structures 102: 395–408.

12.

Lin

(2018) Numerical simulation of blast responses of ultra-high performance fibre reinforced concrete panels with strain-rate effect. Construction and Building Materials 176: 371–382.

13.

Liu

(2022) Investigation of geopolymer-based ultra-high performance concrete slabs against contact explosions. Construction and Building Materials 315: 125727.

14.

Mai

V-C

(2021) Investigate the structural response of ultra-high performance concrete column under the high explosion. Defence Science Journal 71(2): 256–264.

15.

Mao

(2014) Numerical simulation of ultra high performance fibre reinforced concrete panel subjected to blast loading. International Journal of Impact Engineering 64: 91–100.

16.

Mao

(2015) Response of small scale ultra high performance fibre reinforced concrete slabs to blast loading. Construction and Building Materials 93: 822–830.

17.

Muszynski

Purcell

(2003) Use of composite reinforcement to strengthen concrete and air-entrained concrete masonry walls against air blast. Journal of Composites for Construction 7(2): 98–108.

18.

Sharma

(2020) Influence of critical parameters on UHPFRC structural elements subjected to blast loading. SN Applied Sciences 2(3): 1-12.

19.

Taha

(2020) Response of a new structural ultra-high performance concrete barrier wall subjected to blast loading. Australian Journal of Structural Engineering 21(2): 154–161.

20.

Wan

(2021) Determination and evaluation of Holmquist-Johnson-Cook constitutive model parameters for ultra-high-performance concrete with steel fibers. International Journal of Impact Engineering 156: 103966.

21.

Hao

(2005) Modeling of simultaneous ground shock and airblast pressure on nearby structures from surface explosions. International Journal of Impact Engineering, 2005. 31: 699–717.

22.

(2016) Behaviour of ultra high performance fibre reinforced concrete columns subjected to blast loading. Engineering Structures 118: 97–107.

23.

(2021) Experimental investigation and numerical simulation on the blast resistance of reactive powder concrete subjected to blast by embedded explosive. Cement and Concrete Composites 119: 103989.

24.

Zhang

(2013) Experimental study on scaling of RC beams under close-in blast loading. Engineering Failure Analysis 33: 497–504.

25.

Zhang

Abedini

(2021) Time-history blast response and failure mechanism of RC columns using Lagrangian formulation. Structures. 34, 3087–3098.

26.

Zhang

Abedini

(2022) Development of PI model for FRP composite retrofitted RC columns subjected to high strain rate loads using LBE function. Engineering Structures 252: 113580.

27.

Zhang

Abedini

(2022) Application of Lagrangian approach to generate PI diagrams for RC columns exposed to extreme dynamic loading. Advances in Concrete Construction 14(3): 153.

28.

Zhang

Abedini

(2023) Strain rate influences on concrete and steel material behavior, state-of-the-art review. Archives of Computational Methods in Engineering 30: 1–28.

29.

Zhang

Abedini

Mehrmashhadi

, Development of pressure-impulse models and residual capacity assessment of RC columns using high fidelity Arbitrary Lagrangian-Eulerian simulation. Engineering Structures 224: 111219.