Tangential Induced Stress

The induced stress is defined as the maximum tangential stress acting parallel to the exposed surface at the stope boundary.

The induced stress acting on a stope wall is best estimated by numerical modelling. When such models are not available, Mathews (1981) [1] provided two graphs which describe the stresses induced in the roof and walls of isolated openings. Potvin (1988) [2], making use of his updated database, developed his own curves for induced stress estimation. Later, Vallejos et al (2018) [3] proposed new curves based on tridimensional modelling.

Mathews Curves

Figure 1: Stress curves proposed by Stewart and Forsyth [4], after Mathews et al [1].

Potvin Curves

Figure 2: Stress curves proposed by Potvin [2].

Vallejos Curves

IMG

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GeoAssistant Implementation

Recipe

GeoAssistant works by the word of maximum automatization, meaning that the user doesn’t have to actually call a method to calculate the induced stress of a certain stope wall. Actually, GeoAssistant detects when the necessary inputs are set and automatically calculates the induced stress.

from geoassistant import Stope

stress_tensor = Stress.createStressTensorByDepth(depth=500, density=2.7e6)

stope = Stope.createFromBlock(block=Block(corners=[[0, 0, 0], [width, length, height]]))
stope.setStressTensor(stress_tensor=stress_tensor)

roof = stope.getRoof()
induced_stress = roof.getInducedStress()

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References

[1] (1,2)

K. E. Mathews, E. Hoek, D. C. Wyllie, and S. B. V. Stewart. Prediction of stable excavation spans for mining at depths below 1,000 metres in hard rock. Report, Golder Associates, Ottawa, Ontario, Canada, 1980. Report to Canada Centre for Mining and Energy Technology (CANMET), Department of Energy and Resources.

[2] (1,2)

Yves Potvin. Empirical Open Stope Design in Canada. PhD thesis, University of British Columbia, Vancouver, Canada, 1988. Available online at the UBC Open Collections. URL: https://open.library.ubc.ca/collections/ubctheses/831/items/1.0051179.

[3]

J. A. Vallejos, A. Delonca, and E. Perez. Three-dimensional effect of stresses in open stope mine design. International Journal of Mining, Reclamation and Environment, 32(5):355–374, 2018. doi:10.1080/17480930.2017.1309833.

[4]

S. B. Stewart and W. W. Forsyth. The mathew’s method for open stope design. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 33(4):168, 1996. URL: https://doi.org/10.1016/0148-9062(96)85121-7, doi:10.1016/0148-9062(96)85121-7.