Dynamic performances of ultra-high-performance fiber-reinforced concrete–strengthened concrete columns subjected to blast impacts

Abstract

Normal functionality of common concrete structures such as bridges and buildings relies heavily on the structural resistance under accidental or anthropogenic blast events. As one of the widely used structural types, reinforced concrete columns need to be highly considered when blast events occur to avoid severe socio-economic losses. To improve the blast–impact resistance of conventional reinforced concrete columns, this article makes the following contributions: (1) proposes to adopt the advanced ultra-high-performance fiber-reinforced concrete to strengthen the columns as a protective layer; (2) validates the superiority of ultra-high-performance fiber-reinforced concrete–strengthened columns through comparative study and specifies the controlling design parameters through sensitivity analysis; (3) implements and compares various ultra-high-performance fiber-reinforced concrete reinforcement methods; and (4) develops a numerical formula to predict the residual capacity of ultra-high-performance fiber-reinforced concrete–strengthened columns under blast impacts as a suitable alternate of the complicated and time-consuming finite element simulations.

Keywords

blast impacts dynamic performances protection and reinforcement reinforced concrete columns ultra-high-performance fiber-reinforced concrete

Introduction

Recently, many blast events happened on infrastructure have been reported worldwide causing large quantities of casualties and economic losses (Abdollahzadeh and Nemati, 2014; Al-Thairy, 2016). Zhu and Xing (2015) reviewed several blast events and pointed out the seriousness of the problem. As one of the principal construction materials, reinforced concrete (RC) is widely used in civil and military engineering (Tai et al., 2011). Among various elements of RC structures threatened by blast, columns take up a large proportion (Voyiadjis and Kattan, 2017). For example, dynamic response of bridge columns (i.e. piers) under blast impacts is of great importance, since column failures may lead to partial or even progressive collapse of the whole bridge (Shi and Stewart, 2015). As for buildings, abrupt failure of one or more load-bearing structural columns could typically initiate the collapse of the structure (Codina et al., 2017; Sideri et al., 2017). Therefore, exploring the dynamic performances and inherent regularity of RC columns under blast impacts play an important role in the normal operation during the life cycle for most civil structures.

Many researchers focused on the study of dynamic response and failure behaviors of RC structures subjected to blast loads analytically, numerically, and experimentally (Astarlioglu et al., 2013; Fouche et al., 2016; Liu et al., 2018; Yuan et al., 2017). All these studies showed that conventional RC columns were susceptible to blast due to the low impact-resistance. According to the fact, various kinds of retrofit measures have been put forward. For instance, aluminum foamed sacrificial layer and fiber-reinforced plastic (FRP) cover (Liang et al., 2019; Schenker et al., 2008) are proposed as feasible ways to strengthen columns that are vulnerable to blast loads. However, some disadvantages have been found. For example, steel is susceptible to corrosion and the epoxy resin adhesive used in the FRP wrapping is of poor durability. Considering this, it is valuable to find an alternate. Ultra-high performance fiber-reinforced concrete (UHPFRC) is considered to be a good choice to strengthen conventional RC structures and increase its blast-resistance. Since created in 1990s (Habel et al., 2006), UHPFRC has been demonstrated to be high-strength, durable and energy-absorbed, and can contribute to improving durability, service life, and performance of structures. It is regarded as a promising material to bear extreme loads especially impact loads (Guo et al., 2018; Yoo and Banthia, 2016, 2017). Since UHPFRC is capable of preventing catastrophic failure like progressive collapse and reducing fragmentation due to projectiles, it is selected to strengthen the normal RC columns resisting blast impacts. Furthermore, structural components with UHPFRC can be designed with smaller sizes, which can largely reduce the amount of materials used (Xu et al., 2016). Thus, exploring the potential use of UHPFRC in anti-blast design of RC columns is of interest. A common practice for structural reinforcement is to use UHPFRC as the protective layer. Therefore, UHPFRC is adopted as the protective layer for normal reinforced concrete columns under blast impacts in this article. The effectiveness of UHPFRC layer and dynamic response of UHPFRC-strengthened concrete columns under blast impacts are studied carefully.

In addition, the effective estimation of dynamic response is a problem needed to be dealt with considering the parametric variability and high occurrence uncertainty of blast. Different parameters including layer strength, thickness, length, and reinforcement ratio of UHPFRC-strengthened columns contribute differently to the reinforcement effect (Hao et al., 2010). Identifying the controlling design parameters of UHPFRC can be useful in the design process of conventional RC columns under blast impacts. Therefore, it is necessary to carry out parametric sensitivity analysis. What’s more, accurate prediction of simulated blast response of UHPFRC-strengthened columns is meaningful to further facilitate the future optimization of blast-resistant design and replace complicated and time-consuming three-dimensional (3D) simulations.

In this article, the use of the UHPFRC to strengthen the RC columns as a protective layer is put forward. The conventional RC and UHPFRC-strengthened columns are modeled in 3D in ANSYS/LS-DYNA (ANSYS/LS-DYNA. R10.0., 2017). Results obtained from simulation were validated against the experimental data to ensure the credibility of the research. Comparative study is carried out to show the superior performance of UHPFRC-strengthened columns subjected to blast loads. To identify controlling design parameters, parametric sensitivity analysis has been performed using Tornado diagram (TD) and first-order second moment (FOSM) methods. Effectiveness of different UHPFRC strengthening methods for RC columns are investigated and effective strengthening length has been figured out. In addition, dynamic response of UHPFRC-strengthened concrete columns is quantified through response surface model (RSM) considering the residual capacity as the response variable. Research results have proved the effectiveness of strengthening RC columns with UHPFRC layer subjected to blast impacts.

Finite element model and simulation verification

Finite element model

Based on existed research works, typical column models are adopted (Thilakarathna et al., 2010) to investigate blast-resistance and conduct comparative analysis between conventional RC and UHPFRC-strengthened columns. Finite element (FE) models are developed as presented in Figure 1 using ANSYS/LS-DYNA. RC columns with square section of 0.4 m × 0.4 m and height of 4.0 m are established. A 16-mm longitudinal reinforcement and 200-mm spacing stirrups with 10-mm diameter are deployed. Concrete and reinforcements are modeled using solid and beam elements, respectively. Reinforcement and concrete are built separately with ignorance of the bond–slip effect between them. The nodal degrees of freedom at the bottom are all fixed without considering the influence of soil–structure interaction, and all the degrees of freedom at the top are constrained except the axial transitional displacement.

Figure 1.

FE models of (a) conventional RC column and (b) UHPFRC-strengthened column.

Two models with various concrete cover are established to compare the blast resistance of conventional RC columns with the UHPFRC-strengthened columns. One of the models uses normal concrete for the whole cross section (Figure 1(a)), and the other uses 80-mm UHPFRC as the protective layer (Figure 1(b); Nguyen et al., 2017). For UHPFRC, the uniaxial compressive strength considered in comparative analysis is 160 MPa with steel fibers at a dosage of 2.0% by volume. As a comparison, the normal concrete with C40 strength grade is used without any added steel fibers. All materials are modeled using elastic-plastic material models. Material 159 (∗MAT_CSCM) is used to simulate normal concrete and UHPFRC. Material 3 (∗MAT_PLASTIC_KINEMATIC; Livermore Software Technology Corporation (LSTC), 2014), which could reflect isotropic and kinematic hardening plasticity with strain rate effect based on Cowper–Symonds, is employed to simulate the longitudinal and transverse reinforcements. All the material parameters used in the FE models are listed in Table 1. And the input material parameters for UHPFRC and the normal concrete are shown in Appendix 1.

Table 1.

Material models adopted in the FE analysis.

Material type	Material model	Main parameters
Concrete	*MAT_CSCM	Appendix 1. Concrete material parameters (Fan et al., 2018)
Longitudinal reinforcement	*MAT_PLASTIC_KINEMATIC	ρ (kg/m³)	E (GPa)	ν	fy (MPa)
		7850	206	0.3	400
		E_T (GPa)	SRC	SRP	fs
		3.0	7.27E7	11.22	0.2
Transverse reinforcement	*MAT_PLASTIC_KINEMATIC	ρ (kg/m³)	E (GPa)	ν	fy (MPa)
		7850	206	0.3	300
		E_T (GPa)	SRC	SRP	fs
		3.0	7.27E7	11.22	0.25

ρ: material density; ν: poisson’s ratio; E: modulus of elasticity; fy: yield strength; E_T : tangent modulus; SRC, SRP: strain rate parameters for Cowper–Symonds strain rate model; fs: effective plastic strain.

The continuous surface cap model (CSCM; LSTC, 2014) can achieve the desired mechanical behaviors and material response of concrete and show good agreement with results collected from experimental data (Fujikake et al., 2006; Guo et al., 2018). Therefore, the CSCM is adopted to simulate concrete (Jiang et al., 2012; Nguyen et al., 2017) and are used in this study as well.

Additional axial (18.08 MPa) and gravity load are taken into account during the analysis. Blast loads are calculated by CONWEP program imbedded in the ANSYS/LS-DYNA and applied on the detonation surface of the column. The keyword *SET_SEGMRNT is used to define the loading group. *LOAD_BLAST and *LOAD_ SEGMENT_SET _ID are used to apply blast pressure on the detonation surface. This method is convenient because it can operate without air and explosive models thus leading to high calculation efficiency. Following the blast–impact analysis, axial residual capacity of columns is further determined through the restart module by applying progressive displacement loading in the axial direction on damaged columns until the occurrence of failure.

Simulation verification

The numerical simulation method and material models described in previous section are used to simulate the dynamic response of RC columns under blast. Results obtained are compared with the experimental data published in the literature (Zong et al., 2017) to verify its accuracy. The specimens and test setup are shown in Figure 2. The total length of the specimen is 3.5 m with circular section of 0.4-m diameter. Concrete C40 embedded with longitudinal reinforcement HRB335 (Φ 0.012) are used. The axial compression ratio is 0.15. Blast impact (1 kg trinitrotoluene (TNT)) is applied at the bottom of the detonation surface with 0.33-m height above the ground.

Figure 2.

Test setup and comparison of experiment and simulation results.

Comparison of experiment and simulation results are described in Figure 2. In the real test, significant damage accumulation occurred on the detonation surface of RC column. The protective layer fell off completely within the 0.60 m range at the bottom of the specimen and the failure depth was up to 0.05 m. Concrete at the bottom of the back surface was also damaged to some extent. In numerical simulation, the falling height of protective layer and damage depth are approximately 0.60 and 0.10 m, respectively. The concrete near the blast position is basically peeling off and some of the reinforcements are buckling. Since the numerical simulation results show good agreement with the experimental data, rationality of the simulation method and adopted material models are verified.

Superiority verification of UHPFRC-strengthened columns

To show the effectiveness of UHPFRC protective layer, comparative analysis has been conducted between conventional RC columns and UHPFRC-strengthened columns. The dynamic performances of these columns under various blast scenarios are carefully studied using the FE models in Figure 1. 10 kg TNT with various blast distance of 0.250, 0.375, 0.500, 0.750, 1.000, 1.500, 2.000, and 3.000 m are considered for conventional RC and UHPFRC-strengthened columns. Description of load cases and damage condition are listed in Table 2. Various damage levels (slightly, moderately, seriously, and completely damaged) are quantified based on the existed research (Shi et al., 2008). Damage condition of UHPFRC-strengthened and conventional RC columns are compared in Figure 3. It can be seen that damage condition of conventional RC columns is much more serious than those of UHPFRC-strengthened columns under blast with the same magnitude. When blast occurs at the distance less than 2.0 m, severe damage and large displacement response are observed for the conventional RC column. Moderate damage appeared in the conventional RC column when blast distance is up to 3.0 m. However, visible damage occurred on UHPFRC-strengthened columns when blast distance is less than 0.75 m, and slight or moderate damage are exhibited when blast distance varies from 1.0 to 3.0 m due to the large deformation and damage inside. This demonstrates that the blast–impact resistance of RC columns increases due to the presence of UHPFRC. In addition, the elemental peak stress and displacement response of UHPFRC-strengthened and conventional RC columns are shown in Figure 4. Elemental peak stress decreases with increasing blast distance for all kinds of columns (Figure 4(a)). And elemental peak stress of the UHPFRC-strengthened column increases much more obviously than that of the conventional RC column under certain blast scenario (about 32.7%–91.7%). The maximum displacement at the impact position of the UHPFRC-strengthened column is slightly lower than the conventional RC column. Displacement response decreases with increasing blast distance for both RC and UHPFRC-strengthened columns (Figure 4(b)). Due to the presence of UHPFRC, maximum displacement of UHPFRC-strengthened columns at the impact position are moderately reduced (about 6.57%–23.8%). Thus the effectiveness of UHPFRC layer for improving the impact-resistance of columns are verified.

Table 2.

Comparative study of damage conditions.

Case number	Amount of TNT, M (kg)	Blast distance, D (m)	Scaled distance, Z $({m/kg}^{1/3})$	Damage condition
Case number	Amount of TNT, M (kg)	Blast distance, D (m)	Scaled distance, Z $({m/kg}^{1/3})$	Normal concrete	UHPFRC
1	10	0.250	0.116	Completely damaged	Completely damaged
2		0.375	0.174	Completely damaged	Completely damaged
3		0.500	0.232	Completely damaged	Completely damaged
4		0.750	0.348	Completely damaged	Seriously damaged
5		1.000	0.464	Seriously damaged	Moderately damaged
6		1.500	0.696	Seriously damaged	Moderately damaged
7		2.000	0.928	Seriously damaged	Moderately damaged
8		3.000	1.392	Moderately damaged	Slightly damaged

UHPFRC: ultra-high-performance fiber-reinforced concrete; TNT: trinitrotoluene.

Scaled distance $Z = D / M^{1 / 3}$ , where D is the distance between the explosive center and the target detonation surface, and M is the equivalent mass of TNT. For all the loading cases listed, blast occurs at 1.5-m height above the ground.

Figure 3.

Effective plastic strain of conventional RC and UHPFRC-strengthened columns after blast impacts.

Figure 4.

Comparison of dynamic response for different blast scenarios: (a) elemental peak stress and (b) displacement at the impact position.

To evaluate the residual capacity of these columns subjected to blast, the restart analysis module is used to apply the displacement-control load in axial direction on the column. Residual capacities of the conventional RC and UHPFRC-strengthened columns after blast are presented in Figure 5(a). Residual capacity of the UHPFRC-strengthened columns are almost 2–4 times of those for conventional RC columns. The residual capacity of conventional RC columns shows nearly linear tendency to decline with the decreasing scaled distance. Instead, residual capacity of UHPFRC-strengthened columns shows the nonlinear tendency to decline with the decreasing scaled distance. The damage index which is defined as the difference between unity and ratio of the residual axial capacity of the impact-damaged column and the ultimate capacity of the undamaged column is used (Shi et al., 2008). Damage indexes of various blast scenarios are shown in Figure 5(b). Generally, damage index of the UHPFRC-strengthened columns is smaller than those of the conventional RC columns under different scaled distances. When scaled distance equals to 0.232 m/kg^1/3, damage index for the two columns remains the same. However, at this condition, the residual capacity of UHPFRC-strengthened column is almost 2 times of the conventional RC column. Therefore, residual capacity is much more reasonable for comparison analysis of columns with same sectional dimensions and different ultimate capacities, and is adopted for further study in the following sections: “Identification of the controlling design parameters,” “Effectiveness of various strengthening methods,” and “Prediction of response of UHPFRC-strengthened columns” in this article.

Figure 5.

(a) Residual capacity and (b) damage index for different blast scenarios.

Identification of the controlling design parameters

To investigate the influence of parameters of UHPFRC-strengthened columns under blast loads, parametric study is performed using the FE models of UHPFRC-strengthened columns in section “Finite element model.” Based on the previous research in section “Superiority verification of UHPFRC-strengthened columns,” blast load (10 kg TNT) is set to occur at 1.5-m height above the ground and 0.5 m away from the side of columns. Four parameters including UHPFRC thickness (t), UHPFRC strength (s), longitudinal reinforcement ratio (ρl), and transverse reinforcement ratio (ρt) are considered (Table 3). In Table 3, μx and σx are mean and standard deviation, respectively. Considering the complexity and time-consuming characteristic of 3D FE analysis for concrete structures, numerical methods including TD and FOSM are adopted (Tae-Hyung Lee, 2006). Dynamic responses including maximum horizontal displacement at the impact position, elemental peak stress at the detonation surface and residual axial loading capacity are considered for UHPFRC-strengthened columns. Considering the mean value of each parameter together as the basic loading scenario, the 4 × 5 = 20 nonlinear time history analysis in total is carried out by changing each variable for four other values orderly. It is validated that the relationship between structural response and each variable shows obviously linear or slightly nonlinear behavior, thus confirming the rationality of the applied FOSM method.

Table 3.

Variation coefficient and range of parameters involved in the sensitivity analysis.

Independent variable	Symbol	Unit	Variation coefficients COV = σx/μx	Range
Independent variable	Symbol	Unit	Variation coefficients COV = σx/μx	μx – 2σx	μx – σx	Μx	μx + σx	μx + 2σx
Transverse reinforcement ratio	ρt	%	0.39–1.19	0.39	0.60	0.79	0.99	1.19
Longitudinal reinforcement ratio	pl	%	0.769–1.900	0.77	1.05	1.34	1.62	1.90
UHPFRC strength	S	MPa	160–200	160	170	180	190	200
UHPFRC thickness	T	mm	40–80	40	50	60	70	80

UHPFRC: ultra-high-performance fiber-reinforced concrete.

Results for sensitivity analysis are shown in Figures 6 –8. Vertical lines marked represent blast response of the basic loading scenario. The influence of various parameters on impact-induced response of the UHPFRC-strengthened columns can be clearly identified. In general, the residual capacity increases significantly with the increase of UHPFRC thickness. Higher UHPFRC thickness can improve the residual capacity and control the structural deformation (Figures 6 and 8). It is seen that the influence of longitudinal reinforcement ratios is considerably greater for displacement and stress response (Figures 6 and 7). The abovementioned research results are consistent with the results presented by other researchers (Dong et al., 2019; Duc-Kien et al., 2019; Qasrawi et al., 2016). To be specific, following observations can be made:

Figure 6.

Displacement at the impact (mm): (a) Tornado diagram and (b) relative variance contribution.

Figure 7.

Elemental peak stress (MPa): (a) Tornado diagram and (b) relative variance contribution.

Figure 8.

Residual capacity (MN): (a) Tornado diagram and (b) relative variance contribution.

As for the maximum horizontal displacement at the impact position, UHPFRC thickness, strength, and longitudinal reinforcement ratio are controlling parameters. Contribution of these parameters to response variance is 39%, 27%, and 34%, respectively (Figure 6).

As for the elemental peak stress on the detonation surface, UHPFRC strength and longitudinal reinforcement ratio are controlling parameters with the same contribution of 48%, and two other parameters reflect low sensitivity (Figure 7).

As for the residual capacity, UHPFRC thickness is the most sensitive parameter with contribution to the response variance of 90%, and transverse reinforcement ratio ranks the second with response variance of 9% (Figure 8).

Effectiveness of various strengthening methods

In this section, two different strengthening methods of UHPFRC protective layer for blast resistance of RC columns are investigated. One is the local strengthening method for which the column is strengthened symmetrically vertically regarding the blast impact as the center for 0.5-, 1.0-, 1.5-, 2.0-, 3.0-, and 4.0-m length. The other is the integral strengthening method for which the column is strengthened from the bottom for 1.75-, 2.0-, 2.25-, 2.5-, 3.0-, and 4.0-m length. For the two strengthening methods, fixed boundary conditions are arranged at the bottom and all the degrees of freedom at the top of the columns are constrained except the axial transitional displacement. For each strengthening method, six different strengthening lengths of UHPFRC are considered (Figure 9). Blast (10 kg TNT) is set to explode at 1.5-m height above the ground and 0.5-m away from the surface of column. Material models for concrete and reinforcements are the same as those used in section “Identification of the controlling design parameters.” Outer part of the column is strengthened by UHPFRC and inside is normal concrete. The uniaxial compressive strength of UHPFRC considered is 180 MPa. Blast analysis is performed first and then restart analysis is carried out to obtain the residual capacity for all the columns. Response of UHPFRC-strengthened columns subjected to blast is obtained including the maximum displacement at the impact position and elemental peak stress at the detonation surface. Damage index can be calculated according to the literature (Shi and Stewart, 2015).

Figure 9.

Two different strengthening methods for UHPFRC-strengthened columns: (a) local strengthening method and (b) integral strengthening method.

Computed results are shown in Figures 10 and 11. It is seen that residual capacity increases when the strengthening height of UHPFRC is up to 4.0 m (Figures 10(a) and 11(a)), but the damage index decreases to about 0.73 (Figures 10(b) and 11(b)) which means the damage condition of the column is greatly reduced. Residual axial loading capacity and damage index for other cases do not change much for the two strengthening methods since the weakest part of the column is always the un-strengthened region. Regarding the blast-induced response of UHPFRC-strengthened column with the minimum strengthening length as the reference, the ratios of maximum horizontal displacement at the impact position and elemental peak stress at the detonation surface are shown in Figures 10(c), (d) and 11(c), (d). The displacement response of UHPFRC-strengthened columns slightly increases for the first five strengthening cases of local and integral strengthening methods. Large decrease about 19.7% and 3.84% occurs when UHPFRC are used for full column length (Figures 10(c) and 11(c)). Besides, when length of UHPFRC adopted is up to 3.0 and 4.0 m, 30.0% and 32.1% increase appears in the elemental peak stress for local strengthening method (Figure 10(d)). A 13.59% and 13.34% increase appears in the elemental peak stress for integral strengthening method (Figure 11(d)). Thus, it can be summarized that while considering the structural performance, large strengthening height of UHPFRC can effectively improve the blast resistance of RC columns due to reduction of displacement and damage condition, and give full play to the function of UHPFRC. Considering this, UHPFRC-strengthening is adopted for full column length in the following study without special instructions.

Figure 10.

Dynamic response and damage condition of concrete columns using local strengthening method: (a) (d) Strengthening height of UHPFRC (m).

Figure 11.

Dynamic response and damage condition of concrete columns using integral strengthening method: (a)–(d) Strengthening height of UHPFRC (m).

Prediction of response of UHPFRC-strengthened columns

Response surface model and factorial design

In this part, essential design parameters of UHPFRC protective layer divided into three levels under various blast impacts are considered to conduct the sensitivity analysis and predict the residual capacities of UHPFRC-strengthened columns. RSM is combined with the central composited design (CCD) method to reduce the number of required FE simulations and improve the computational efficiency (Fan et al., 2018; Fang et al., 2017; Gunst, 1996; Hou et al., 2007).

In this study, involved parameters and related CCD are listed in Tables 4 and 5. Blast (10 kg TNT) is set to occur at 1.5-m height above the ground with varied horizontal distances away from the surface of column. The influence of varying parameters including UHPFRC thickness, strength, and scaled distance are investigated and related RSM of residual capacity is established. Accordingly, performance of various parameters of UHPFRC can be identified and evaluated.

Table 4.

Parameters for RSM.

Parameters	Symbol and unit	Lower bound (−1)	Middle (0)	Upper bound (1)
UHPFRC thickness	t (mm)	40	60	80
UHPFRC strength	s (MPa)	160	180	200
Scaled distance	Z (m/kg^1/3)	0.232	0.290	0.348

RSM: response surface model; UHPFRC: ultra-high-performance fiber-reinforced concrete.

Table 5.

CCD design and residual capacity.

Case	X1	X2	X3	Residual capacity (MN)		Relative error (%)
Case	t (mm)	s (MPa)	$Z ({m/kg}^{1/3})$	FE results	Predicted value	Relative error (%)
1	40	160	0.232	3.740	3.688	1.382
2	80	160	0.232	6.520	6.814	4.520
3	40	200	0.232	3.148	3.237	2.830
4	80	200	0.232	6.379	6.806	6.688
5	60	180	0.232	6.986	6.228	10.857
6	60	180	0.290	8.994	9.056	0.686
7	80	200	0.348	11.439	11.499	0.520
8	60	180	0.348	8.989	9.717	8.100
9	60	200	0.290	9.245	8.956	3.121
10	80	180	0.290	10.924	10.225	6.399
11	80	160	0.348	10.833	10.752	0.747
12	40	180	0.290	5.383	6.051	12.417
13	60	160	0.290	8.550	8.808	3.015
14	40	160	0.348	6.393	5.974	6.557
15	40	200	0.348	6.564	6.278	4.357

CCD: central composited design; FE: finite element.

Predictions and verifications from RSM

From Table 5, the RSM of residual capacity (Equation (1)) is established for UHPFRC-strengthened columns considering variables including UHPFRC thickness and strength, and scaled distance. Predicted values based on the proposed RSM and relative errors (REs) between FE results and predicted values are listed in Table 5.

The 3D plots are displayed in Figure 12 from which the influence of parameters on the residual capacity of columns can be identified. It is seen that the residual capacity increases with the increase of UHPFRC thickness and scaled distance. Larger UHPFRC layer thickness is much more effective than strength for improving the residual capacity. Both the UHPFRC thickness and scaled distance have significant influence, namely t ≈ Z > s

Figure 12.

Influence of UHPFRC thickness, strength, and scaled distance on residual capacity of UHPFRC-strengthened columns: (a) 3D figure and isograms for thickness, strength of UHPFRC, and residual capacity of column; (b) 3D figure and isograms for thickness of UHPFRC, scaled distance, and residual capacity of column; and (c) 3D figure and isograms for strength of UHPFRC, scaled distance, and residual capacity of column.

\begin{matrix} R (t, s, Z) = 9.0557 + 2.0867 t + 0.0739 s + 1.7400 Z \\ - 0.918 t^{2} - 0.1736 s^{2} - 1.0836 Z^{2} \\ + 0. 1108 t s + 0. 4130 t Z + 0. 1890 S z \end{matrix}

To verify the RSM, additional cases are obtained, and RE and the coefficient of multiple determination R ² are used. In Table 6, residual capacities predicted by using the developed RSM are compared with the corresponding FE results showing that the RE between them is within the range between 0.451% and 27.075%. All the cases including original and additional samples are considered in Figure 13. The value of R ² is 0.9477 and the average RE is 7.43%, which show a good linear fitting characteristic. All these results demonstrate that the developed RSM is capable of predicting the residual capacity of UHPFRC-strengthened columns under blast loads.

Table 6.

Sample points for RSM verification.

Case	X1	X2	X3	Residual capacity (MN)		Relative error (%)
Case	t (mm)	s (MPa)	$Z ({m/kg}^{1/3})$	FE results	Predicted value	Relative error (%)
16	40	160	0.320	6.244	6.216	0.451
17	40	190	0.260	3.905	4.962	27.075
18	60	160	0.232	7.259	6.169	15.018
19	80	170	0.260	9.474	8.732	7.833
20	60	170	0.348	9.252	9.542	3.131
21	40	200	0.290	5.486	5.841	6.474
22	40	200	0.348	6.564	6.278	4.359
23	80	180	0.232	7.129	6.984	2.043
24	60	180	0.320	9.225	9.668	4.806
25	80	190	0.290	10.599	10.274	3.066

RSM: response surface model; FE: finite element.

Figure 13.

Verification of response surface model.

Conclusion

In this article, UHPFRC was proposed to strengthen the conventional RC columns subjected to blast impacts. To show the superiority of this advanced material in the blast protection, comparative study of UHPFRC-strengthened concrete columns and conventional concrete columns subjected to blast was conducted. FE modeling techniques were discussed and validated by experimental results in this article. Parametric sensitivity analysis was performed using TD and FOSM methods to identify the controlling parameters for blast-resistance design of UHPFRC-strengthened columns. Effectiveness of various strengthening methods of UHPFRC was investigated and optimum strengthening length was determined. The influence of design parameters of UHPFRC protective layer under blast was discussed through RSM combined with CCD considering the residual capacity as the response variable. Effective predictions of residual capacity for UHPFRC-strengthened concrete columns were achieved based on the validated RSM. In this article, following conclusions can be drawn:

Displacement response and damage condition of RC columns were reduced due to the presence of UHPFRC protective layer. Up to 24% reduction of maximum displacement at the impact was observed. Thus, the UHPFRC enhancement was verified to be an effective way of increasing the blast-resistance of RC columns.

Sensitivity analysis was carried out and the influence of UHPFRC thickness, strength, longitudinal, and transverse reinforcement ratios on dynamic response of UHPFRC-strengthened columns subjected to blast were investigated. UHPFRC thickness was the most influential factor for residual capacity of columns. Maximum displacement and elemental peak stress were much more sensitive to the variation of longitudinal reinforcement ratio. These controlling parameters should be considered in the design process.

Effectiveness of different strengthening methods of UHPFRC to increase the blast resistance of conventional RC columns was investigated. Large strengthening length of UHPFRC can effectively improve the blast–impact resistance of RC columns while pursuing the better structural performance.

Response surface model was developed to identify the effects of design parameters for UHPFRC, and can be used as the fast prediction of the residual capacity of UHPFRC-strengthened columns under various blast loads. Moreover, predictions based on the established RSM coincided well with the results obtained from the FE simulations. Specifically, larger UHPFRC layer thickness was discovered to be much more effective in improving the residual capacity.

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: The research presented in this article is supported by the Ministry of Science and Technology of China under Grant No. SLDRCE19-B-19; the National Natural Science Foundation of China under Grant No. 51778471, 51978512; and Transportation science and technology plan of Shandong province (2017B75).

ORCID iD

Jingyu Wang

Appendix 1

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