Since longhole stoping under CRF is uncommon, the optimum CRF span for longhole stoping is not well known. The optimization of CRF spans will help maintain safe working conditions, minimize ore dilution from CRF, and reduce overall CRF placement. Mining operations commonly have backfill unconfined compressive strengths, so the development of a method for estimating the maximum CRF span from the laboratory compressive strengths could be a significant benefit. The objective of this study is to develop guidelines for designing optimal CRF spans.
The analysis of Cemented Rock Fill (hereafter, CRF) spans begins with recognizing the CRF represents a constructed beam or arch that forms the back of the open stopes as shown in Figure 1. Two common methods utilized for analyzing spans in geological materials are the elastic beam model and the voussoir beam model (Evan, 1941). Modeling from the previous studies ranges from simple analytical solutions to complex multi-variable solutions. Numerous authors have studied the use of elastic beam and voussoir beam models in underground excavations, but there has been limited use of the models as applied to CRF. A review of past research assists in presenting the basics of each model and summarizes the model versions that could be applied to CRF. In 1972, Wright conducted extensive studies on the arching action of cracked beams with finite element modeling backed up with physical model testing. He developed a series of equations to solve for the thrust, deflection, and maximum compressive stress. Factor of safety equations for sliding near the abutments and compressive failure of the rock were also suggested, and the validity of the equations was verified in a comparison with physical model results. He proposed a beam could fail in one of three ways: block sliding, crushing at points of high compressive stress, and elastic buckling (Figure 2).
Figure 1 Stope cross section of a CRF(available in full paper)
2. COMPARISON OF ANALYTICAL BEAM MODELS
The analytical methods of Evans (1941), Wright (1972), Sterling (1977), Ran (1993), and Deidrichs and Kaiser (1999) are compared utilizing the CRF beam scenario shown in Figure 1. The scenario consists of two 10-ft thick levels of CRF with assumed parabolic loading from the overlying rock formation. The top CRF level is assumed to act as only added weight to the lower CRF level along with the loading from the overlying rock. The parabolic loading is calculated from a loading height of 1.5 times the span with a rock unit weight of 2. 64 g/cm3 (165 lb/ft3) Total calculated load on the lower CRF level or beam is converted to a uniform load, and the total load not including self weight of the beam for various spans is listed in Table 1. The CRF material properties are shown in Table 2.
Figure 2 CRF failure modes (Wright, 1972) (available in full paper)
Table 1. CRF loading conditions (available in full paper)
Table 2. CRF Material Properties (available in full paper)