*3.4. Analysis of Finite Element Calculation Results*

#### 3.4.1. Explosion Load Analysis

Based on the simulation results, the load distribution on the impact surface of the RC slabs at the scaled distance of 0.56 m/kg1/3 is obtained, as shown in Figure 12. In the figure, the X-axis and Y-axis represent the directions of the short span and long span of the slab, respectively.

**Figure 12.** Contour plots of load distribution in RC slab: (**a**) peak overpressure, (**b**) specific impulse.

According to Figure 12a, the peak overpressure on the impact surface of the RC slab is large in the center and gradually decreases at both ends along the long-span direction. Due to the ground reflection effect, the peak overpressure at the end near the ground is slightly larger than that at the top, but along the short-span direction it is basically the same. Different from the peak overpressure distribution, the specific impulse of the impact surface of the RC slab in Figure 12b gradually reduces along the long-span direction, and

the impulse near the ground is about two times that at the top. It shows that the ground makes the shockwave appear to be strengthening and creates a convergence effect at the bottom of the component. Therefore, the load distribution in the RC slab in the close-in explosion experiment is affected by many factors, such as the ground, the distance from the explosion center, and the angle of incidence. Although peak overpressure and impulse are unevenly distributed, there exists a distribution law.

#### 3.4.2. Damage Analysis of RC Slab

The contour plots of the plastic damage of the two slabs are presented in Figure 13, where (a) front face and (b) rear face.

**Figure 13.** Comparison of damage contours of slab A and slab B: (**a**) Front face, (**b**) Rear face.

As can be seen from the figure, the damage distribution of the two RC slabs is similar. Taking the damage distribution of the blast face as an example, whether it is plate A or plate B, the damage is basically distributed along the reinforcement around the frame and the lateral constraint direction. The damage distribution of RC slabs is mainly along the transverse and longitudinal reinforcement and is obviously affected by frame constraints. The damage degree of RC plates with different reinforcement ratios is significantly different. The damage range and damage degree of the plates with small reinforcement ratios are significantly higher than those of the plates with large reinforcement ratios, regardless of the blast front or back surface. There is a large rectangular plastic strain zone in the center of the back blasting surface of the small reinforcement ratio plate, and several plastic strands appear along the short-span direction. The concrete in some areas is in almost complete failure, showing typical bending failure characteristics.

#### 3.4.3. Residual Displacement Analysis

Figure 14 shows curves of the residual displacement distribution of the two slabs along the long-span direction.

From the figure, the curves of their residual displacement along the long-span direction under shockwave loading take the shape of a parabola, but the displacement of slab A is obviously smaller than that of slab B. At the symmetrical position along the slab center, the displacement at the end near the ground is slightly larger than that at the other end, mainly because of the ground reflection effect, which is consistent with the phenomenon observed in the experiment.

**Figure 14.** Comparison of residual displacement of the RC slabs along the long−span direction.

3.4.4. Residual Bearing Capacity Analysis

To further quantitatively evaluate the degradation of the bearing capacity of damaged RC slabs, the residual bearing capacity of damaged RC slabs was simulated by restarting in LS-DYNA, and the quasi-static loading was carried out by slowly applying the displacement perpendicular to the panel at each node of the component face. The method of applying a displacement load is shown in Figure 15.

**Figure 15.** Schematic diagram of application method of displacement load.

Extract the reaction force at the support, and finally get the curve of the residual bearing capacity of the damaged member with displacement, as shown in Figure 16.

From Figure 16, the residual load-bearing capacity curves of the two damaged RC slabs under the same blast-loading conditions are obviously different. For slab A, when the mid-span displacement increases to 20 mm, its bearing capacity reaches the maximum, about 2000 kN; when the mid-span displacement increases to 50 mm, its bearing capacity almost decreases to 0, indicating that the slab has been completely damaged at this time. For slab B, when the mid-span displacement increases to 45 mm, its bearing capacity reaches the maximum, around 2250 kN, and when the displacement continues to increase to 105 mm, its bearing capacity is close to zero. The above data fully shows that increasing the reinforcement ratio can not only ensure that the RC slab has a high residual bearing capacity after explosive loading, but also ensures that the damaged members have better ductility and good energy-absorption effect.

**Figure 16.** Residual load-bearing capacity curves of the two damaged RC slabs.

Figure 17 gives the comparison of the load-bearing capacity of the two RC slabs before and after the blast-loading test.

**Figure 17.** Comparison of load−bearing capacity between undamaged and damaged slabs: (**a**) slab A with low reinforcement ratio, and (**b**) slab B with high reinforcement ratio.

It can be seen from the figure that the shape of the bearing capacity-displacement curves of the RC slabs after blast loading have changed to some extent; specifically, the peak bearing capacity decreases to varying degrees, and the mid-span displacement corresponding to the peak bearing capacity increases, which is mainly due to the degradation of the bending stiffness after cracks appear in the damaged slabs. From the values, the bearing capacity of slab A decreases by 750 kN, or 26% compared to the undamaged slab; the residual load-bearing capacity of slab B decreases by 600 kN, or 20% compared to the undamaged slab, which is slightly smaller than that of slab A.

#### **4. Conclusions**

In this paper, the blast-loading experiment and numerical simulation were performed for reinforced concrete (RC) slabs with two typical reinforcement ratios. The environmental parameters of relevant loads and the damage data of displacement response of the specimens were obtained, and the calculation model was verified based on the measured data. Finally, the residual load-bearing capacity of the damaged RC slabs was analyzed. The main conclusions are as follows:


**Author Contributions:** Writing—review and editing, L.W.; visualization, S.C.; supervision, Z.L.; project administration, K.L.; data curation, S.C. and W.Y.; resources, Z.L.; investigation, K.L.; funding acquisition, W.Y.; methodology, L.M.; validation, T.W. and D.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** The study did not require ethical approval.

**Informed Consent Statement:** The study did not involve humans.

**Data Availability Statement:** The study did not report any data.

**Conflicts of Interest:** The authors declare no conflict of interest.
