Shock and Vibration

Volume 2017 (2017), Article ID 9181729, 13 pages

https://doi.org/10.1155/2017/9181729

## Study of the Similarities in Scale Models of a Single-Layer Spherical Lattice Shell Structure under the Effect of Internal Explosion

College of Civil Engineering, Huaqiao University, Xiamen 361021, China

Correspondence should be addressed to Xuanneng Gao

Received 5 November 2016; Revised 1 January 2017; Accepted 28 February 2017; Published 16 March 2017

Academic Editor: Isabelle Sochet

Copyright © 2017 Wenbao Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The similarity of each scale model is verified based on the theory of similarity, deriving the similarity law of internal explosions in a single-layer spherical lattice shell structure via dimensional theory, calculated based on models with scaling coefficients of 1, 0.8, 0.6, 0.4, 0.2, and 0.1. The results show that the shock wave propagation characteristics, the distribution of the overpressure on the inner surface, the maximum dynamic response position, and the position at which the earliest explosion venting occurs are all similar to those of the original model. With the decrease of scaling coefficients, the overpressure peak value of the shock waves of each scale model, and the specific action time of the positive pressure zone, as well as specific impulse are increasingly deviated from the original model values; when the scaling coefficient is 0.1, the maximum relative error between the overpressure peak value at the measurement point and the specific action time of the positive pressure zone as well as the specific impulse and the original model value is 4.9%. Thus, it is feasible to forecast the internal explosion effect of the original structure size model by using the experiment results of the scale model with scaling coefficient .

#### 1. Introduction

In recent years, worldwide terrorist activities have become increasingly frequent, with an increasing number of bombing assaults. On January 24, 2016, the Moscow Airport in the Russian capital exploded under a terrorist attack; 35 people were killed and hundreds of people were injured. On March 22, 2016, an explosion occurred at the Brussels Airport in Belgium, killing 17 people. On June 28, 2016, an explosion occurred at the Turkey Ataturk International Airport, killing 41 people. It can be seen that steel structures with large space, high visitor flowrate, and significant symbolic value are more likely to become a target of explosion attack, and once subject to a terrorist attack, heavy casualties, property damage, and adverse social impacts are likely [1–3]. The explosion effect of explosives in the structure is much more complex than that of an external explosion, primarily because of the multiple reflection and diffraction phenomena that occur during the transmission of shock waves when meeting the roof, walls, and a variety of structures and constructions within the structure; such phenomena cause continuous superposition or offset of the reflected waves and incident waves in the structure, with gas flow fields within the building exhibiting irregular movement, thus making it difficult to determine the shock wave pressure field acting on the roof [4–6]. Therefore, it is necessary to conduct experimental study on the single-layer spherical lattice shell structure under the action of internal explosion; however, because of the constraints of the experimental techniques, research funds, and other conditions, it is difficult to conduct an internal explosion experiment in a full-scale model. A scale model experiment is a commonly used experimental method currently, and it is necessary to study whether the scale model experiment of a single-layer spherical lattice shell structure under the action of internal explosion will meet the similarity law and whether it will be affected by the size effect.

Currently, scholars have conducted experimental research studies on the damage in a structure or component under explosive impact. In foreign studies, Zyskowski et al. [7] studied the distribution of explosion load in structures. Ngo et al. [8] conducted a large 5000 kg explosion experiment in southern Australia and conducted a quantitative analysis of the parameters obtained. Spranghers et al. [9] studied a numerical simulation of the dynamic response of an aluminium plate under free-space explosion, conducted experimental verification, and studied the effect of different parameters on the simulation results. Remennikov and Uy [10] conducted a near-field explosion experiment. Dey and Nimje [11] conducted experimental research on a full-size sandwich panel explosion and performed numerical simulation analysis of the results. Ichino et al. [12] conducted a 1/20 scale model internal explosion experiment in an underground ammunition depot; the characteristics of the air shock waves and the ground vibration were analysed and verified via a 1/10 scale model experiment. In domestic research, Yang et al. [13, 14] simulated the shock waves propagation law of an internal explosion in closed-wall vault tunnel operation via a numerical computation method and determined the propagation law of an air shock wave along the tunnel and obtained the formulas of the shock wave overpressure and action time in the tunnel; the calculated results were found to be in good agreement with the experimental results. Wei et al. [15] studied the load law of an internal explosion experiment by establishing a small volume simplified chamber. Fan et al. [16] fitted out the forecast formula of the explosive shock waves characteristic parameters of the centre of the inner structure through numerical simulation and analysis under the same working conditions as those in a straight tunnel explosion experiment. Cheng et al. [17] conducted theoretical analysis and experimental study of the large plastic deformation response of rectangular steel plates with four-sided restraints under explosive shock waves; the theoretical calculations were compared with the experimental results and the numerical calculations, revealing that the elastic-plastic analysis method had better calculation accuracy and applicability. Gao et al. [1, 4, 18, 19] conducted a series of studies on the shock wave propagation characteristics, the distribution of the pressure field, the structural dynamic response, and the explosion venting measures under internal explosion of large-space cylindrical reticulated shells, spherical reticulated shells, and other structures; the effect of various parameters, such as structure height, span, structure-to-span ratio, TNT equivalent weight, location of explosion, and hole arrangement on the explosion, was studied. Experimental researches on destruction of structures or components under explosion have gained some achievements. However, there are few studies on destruction under explosion in large-space steel structures, and, limited by such constraints as experimental techniques and scientific research funds, it is much hard to carry out an explosion experiment in full-scale model. Therefore, it is necessary to make a similarity research for scaled model experiment.

In this paper, we derived the similarity law of an internal explosion in a single-layer spherical lattice shell structure by using dimensional theory and constructed a finite element model with the scaling coefficients of 1, 0.8, 0.6, 0.4, 0.2, and 0.1 based on LS-DYNA software. The shock wave propagation characteristics, the distribution law of the overpressure peak on the inner surface, the maximum dynamic response position, and the reticulated shell explosion venting phenomena of the scale models were studied. The similarity of the scale models was verified according to the critical TNT quantity of explosion venting at the connection between the wall and the reticulated shell of the model structure, providing a reference for internal explosion research.

#### 2. Establishment of the Finite Element Model and Selection of the Material Parameters

##### 2.1. Establishment of the Finite Element Model and Selection of Material Parameters

A K6 single-layer spherical lattice shell model was established by using ANSYS/LS-DYNA finite element software, which is mainly composed of the following: air, explosives, ground, reticulated shell bars, beams, columns, connecting structure, and envelope. The unscaled model is shown in Figure 1; the model has the following characteristics: a span of 40 m, vector height of 8 m, a rise span ratio of 1/5, a frequency number of 5, a lower support structure height of 10 m, and a sectional dimension of the seamless steel tubes of the main bar, cross bar, and diagonal bar of ; all the beam columns adopt the H-section. Because the air and explosives are considered as uniform and continuous media, Solid164 is chosen as the calculation unit, and because the ground and envelope are regarded as rigid bodies, Shell163 element is adopted; Beam161 element is adopted for the structural bars, beams, and columns, and Link160 element is used for the purlin hanger. The air and explosives adopt the ALE algorithm, the air, structure, and ground use adopt the fluid-solid coupling algorithm, and the air boundary adopts the transmission boundary to avoid arithmetic errors caused by the reflection of shock waves in the air domain boundary and to improve the calculation accuracy [19]. However, when terrorist attacks and other explosions occur, the location of the explosion point is often unascertainable; considering the complexity of the explosion analysis, it is assumed that the explosion is located in the centre of the structure, 1 m above the ground, and the explosive charge is spherical. A finite element model with scaling coefficients of 0.8, 0.6, 0.4, 0.2, and 0.1 was established for numerical simulation and analysis.