Year of Publication


Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation




Mining Engineering

First Advisor

Dr. Jhon Jairo Silva-Castro


Prediction of blast damage radius is integral in the optimization of mining safety and production. The damage radius can be related to blasting variables such as fragmentation size as well as overbreak in hard rock. Various methods have been developed to predict and assess damage radius extension for individual holes to aid in blast design. These methods range from experimental and observational techniques to theoretical applications. Some of these methods have been used with a degree of success. However, many of them lack a comprehensive combination of experimental and theoretical contributions. Since post-blast environments are not conducive to assessing whether the predicted damage radius was correct, this research actively strives to determine the extension of fractures post-blast and compare it to the predicted value. The predictions are based on the use of current fundamental methods in conjunction with a novel methodology proposed in this research.

Numerical modeling has become a promising field within fracture extension analysis and prediction. While methodologies such as Discrete Element Modeling (DEM) and Finite Element Analysis (FEA) have proven effective in fracture prediction, this research delved into the Displacement Discontinuity Method (DDM). The DDM setup is simple as only the crack (fracture) itself is discretized, saving computational time and increasing efficiency when solving. The crack, which for these purposes can be visualized as an infinitesimally small line crack, is divided into an arrangement of nodes and elements. From there, pressure, such as an explosive detonating in a borehole is applied, and the iterative time step process begins to propagate the fracture. This methodology is based upon S.L. Crouch’s book “Boundary Elements Methods in Solid Mechanics.” While the code itself has been used extensively in the petroleum fracking industry, in this research, it has been adapted to blasting. Traditionally only one fracture could be tracked, but this research modified the algorithm to now attempt multiple fracture propagation through coordinate system combination of each fracture. The current build utilizing DDM analysis within this research is highly convenient, and time-consumption for processing is for all intents and purposes almost zero.

Observations of experimental results, as well as modeling analyses, create a large scatter of crack length results depending upon time and loading. In blasting, hard-rock inherently has initial flaws and cracks of which are random in nature. The cracks can be present between grain boundaries in addition to physical voids. These initial natural flaws influence the damage radius around the blasthole in an arbitrary manner; therefore, a random analysis is required to represent any patterns that may be created. This research introduced the use of random parameter distributions and observed the effects these parameters had upon the overall damage radius of the blasthole.

Validation and calibration is a necessity when modeling real physical problems. The dissertation included research for two (2) small-scale experiment that investigated the damage radius of a borehole loaded with an appropriate explosive and calibrated the explosive use in the large-scale test. One (1) six-foot cube of high-strength concrete was manufactured as an analog for in-situ rock. A small-diameter hole (7/8”) was drilled through the center, loaded, and shot. Various instrumentation was utilized to capture the damage radius produced, and this information was used as feedback into the DDM program to model the blast.

The DDM model provided accurate results to assess the extension of the cracks for a single-crack condition, while the multiple-fracture two-crack models proved more conservative when assessing the damage radius. The DDM damage envelope developed from randomization of fracture angle using the two-fracture model provide results closer to that of the single-crack model.

The two-small scale experiments were successful in terms of fracture and fragmentation of the block, as both were completely fractured, and in explosive calibration. The large-block scale test needs improvements; Recommendations and future work are provided for both model and scale-testing improvement.

Digital Object Identifier (DOI)

Funding Information

UKERT: 2017-2020

Central Appalachian Regional ERC: 2016-2020