Thesis Defense: Kinley Seabaugh

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Title: Development of a Material-Informed Equation for Predicting the Normal Coefficient of Restitution in Rockfall Using Vertical Impact Tests

Program: Civil Engineering MS

Committee Chair: Nick Hudyma

Committee: Nick Hudyma, Bhaskar Chittoori, Mary MacLaughlin

Abstract: Users of rockfall trajectory modeling software commonly assign coefficients of restitution (COR) based on generalized ground-surface descriptions, which may not adequately represent differences in the geotechnical properties of natural soils. This research developed a material-informed equation for predicting the normal coefficient of restitution (CORn) using instrumented controlled drop tests accompanied by field and laboratory soil characterization. Controlled vertical drop tests were conducted at 36 sites in southwest Idaho to capture the variation of the normal coefficient of restitution. The tests were performed using an instrumented concrete sphere of 21.84 cm diameter, with a mass of 8.6 kg, released from a height of 1.83 m. Three drops were conducted at each site to obtain an average rebound of the concrete sphere impacting the horizontal ground surface. The rebound was measured using high-speed video with particle tracking. The normal coefficient of restitution was calculated using the square root of the ratio of measured rebound to initial drop height. An inertial measurement unit was embedded in the concrete sphere which measured the three components of acceleration and rotational velocity. Before- and after-photogrammetry was used to measure the impact crater. Field soil characterization consisted of bulk density measurements using a Voluvessel and dynamic modulus measurements using a lightweight deflectometer. Soil samples were brought to the laboratory for field moisture contents, grain size distribution, fines content, median grain size, sorting coefficient, shear strength parameters (from direct shear tests), and Atterberg limits testing. Measured CORn values ranged from 0.033 to 0.221. Pearson correlation analysis identified statistically significant positive relationships between CORn and in-situ density, dynamic modulus, fines content, and peak friction angle. Of the 36 soil conditions investigated, 25 were used to develop the regression equation, while the remaining sites were evaluated separately based on their soil characteristics and suitability for regression development. The selected regression equation incorporated dynamic modulus, in-situ density, and fines content, producing an R^2 of 0.6034, an adjusted R^2 of 0.5468, and a leave-one-out cross-validation R^2 of 0.4483. Although peak friction angle was significantly correlated with CORn, its inclusion did not improve the adjusted or cross-validated performance when included with other variables and was therefore excluded from the regression equation. Evaluation of the regression equation showed that 20 of the 25 calibration sites fell within the calculated 70% prediction intervals. The equation produced mean absolute errors of 0.0427 for three withheld representative soils, 0.0285 for four excluded large-grained soils, and 0.0960 for two excluded fine-grained soils. Three additional tests conducted on the same soil material under different density and moisture conditions produced a mean absolute error of 0.0143. Additional analyses indicated that soils with similar grain-size distributions did not consistently exhibit similar CORn values or regression prediction errors. Furthermore, the relationship between fines content and CORn weakened when three higher-fines observations were excluded, suggesting that fines content alone does not fully describe rebound behavior. Comparisons with representative CORn ranges from RocFall2 and Rockyfor3D showed that the measured values were consistently lower than the generalized reference ranges, while the regression equation generally provided estimates closer to the measured values. These findings demonstrate the potential for geotechnical soil properties to provide more representative estimates of CORn than generalized ground-surface classifications. However, additional field testing and independent validation are necessary to establish the equation's applicability beyond the investigated soil and impact conditions.