Abstract
To compare the damage zones of spherical and cylindrical charges in rock and soil, a quasistatic spherical model was established to predict the characteristic dimension of the cavity. The results indicated that the damage zones of cylindrical charges were larger than those of spherical charges. Furthermore, the cavity development of two charges with different shapes was obtained by numerical simulation, and a comparison of the prediction results between the quasistatic model and numerical simulation was made. The comparison showed that the model could predict the damage zones exactly and faster than numerical simulation. Ultimately, the influence of explosions and soil media was discussed by the quasistatic model. It was observed that larger damage zones were generated by smaller values of the product of pressure and exponential expansion. However, the influence of soil media was complex, and larger damage zones were usually generated by the harder soil media.
Highlights
E research methods for the damage zones caused by these two kinds of charge mainly include the analytical method, numerical analysis, and explosive test method in soil
Zhang derived the analytical expressions for the crushed zone generated by two charge forms based on the theory of explosion shock wave and suggested that the size of the crushed zone was related to the initial charge radius [7]
The dynamic method often takes much more time in the process of calculating the damage zones, which is not suitable for the analysis of seismic wave field, while the quasistatic method can quickly calculate the damage zones and it is more suitable for the analysis of seismic wave field
Summary
Based on the above assumptions, the shear stress is zero and the annular stress is equal under the condition of spherical cavity expansion in the elastic medium; the equilibrium equation can be expressed as follows: dσr + 2σr − σφ 0,. Μ and λ are Lame’s coefficients, and the stress in the equilibrium equation is expressed as a function of displacement as follows:. Erefore, in the elastic region, the displacement u0 on the boundary b0 can be expressed as follows: u0(t) 2μσ0b0(t). The simplified equilibrium equation of cylindrical charge is expressed as follows: dσr + σr − σφ 0. According to the above assumptions, the equilibrium equation under the condition of cylindrical charge can be expressed as follows: dσr + σr − σφ 0. E displacement u0 on the boundary of the elastic region b0 can be expressed as follows:
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