ACI 370R-14 Report for the Design of Concrete Structures for Blast Efects.
5.4.4 Analwical methods—Analytical methods have been developed to predict blast loads. These methods fall into two groups: semi-empirical and hydrocode. The semi-empirical approach uses a physics-based model to compute selccted blast parameters with coefficients that are tuned to match test data. These models arc limited to configurations and charge weight ratios for which data are available, but offer the advantage of quick run times compared with more detailed techniques. BLASTX is an example of this approach. Semi-empirical codes may offer limited abilities to model shock diffraction, shielding, and reflection. Semi-empirical methods have been developed primarily by defense-related agencies and are restricted to distribution to government and its contractors.
Flydrocodes use a grid of computational cells to track detonation propagation through an explosive charge and shock wave propagation through a medium based on models of material behaviors and fundamental thermodynamics and fluid dynamics to predict pressure, density. and other key parameters. Hydrocodes that have been developed by both government agencies and private industries are available to analysts developing loads for commercial projects. This type of analysis is much more complex than the use of empirical relationships. Some of the available tools have user interfaces that greatly simplif’ the analysis, especially for standard materials, but considerable effort and expertise is typically required to conduct a competent analysis.
Output from hydrocodes will be in the form of pressure- time histories for selected probes or nodes in the model. Application of these loads to the structural model can be tedious. If the structural analysis involves a time history calculation, the time-varying loads may be transferred into the structural analysis but the number of data points to be transferred may be excessive.
5.5—Bursting pressure vessels
Ilursting pressure blast predictions are most commonly conducted in one of two ways: simplified analytical methods or computation fluid dynamics models. In either case, it is necessary to select the conditions under which the vessel would be expected to fail—overpressure/overfIlling. rnnaway reaction, external heating, mechanical or impact load, corrosion, or other mechanisms. This selection is important because it determines the composition, pressure. temperature. phase. and energy of the vessel contents, all of which can have a significant elThct on the predicted blast loads. In any case, as long as the vessel pressure is above 2 atmospheres at failure and the pressure is released abruptly. the resultant blast will be a shock wave (that is, suddenly applied).
The most recent simplified method was published by Tang et al, (1996) and consists of a series ol’nondimensionalized curves to predict the side-on pressure and impulse at a particular stand-off These curves depict pressure and impulse as a function of:
a) Pressure ratio (defined as burst pressure divided by ambient pressure)
b) Ratio of specific heats of the vessel Contents (a properly of the gaseous contents of’ the vessel)
c) Expansion energy potential ol’ the vessel contents
d) The temperature ratio (the ratio of the vessel internal temperature at failure to the ambient temperature)
The vessel energy term in this analysis should be corrected for ground reflection. liquid fraction in the vessel, and energy consumed by fragment production. In addition, the side-on pressures need to be modified to account for reflection and clearing efl’ects: this is typically accomplished by using the methods outlined in UFC 3-340-02.ACI 370R pdf download.