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Lassonde Mineral Engineering
Design and Support of Underground Mine Excavations MIN565S Fall 2020 Mid‐Term Exam: November 2, 2020 1.00 pm to 3.05 pm (EST) John Hadjigeorgiou Ph.D., P.Eng., ing., FCIM, ICD.D Pierre Lassonde Chair in Mining Engineering
Instructions: This is an open book exam. You are provided with a PDF document stating the questions and a Word file where you can insert your answers. A series of design charts that may be of some use, are also provided in the Word document. In all cases, you must upload your final responses to the questions within the allotted examination time. In answering the questions, you should justify any assumptions that you make and, where possible, provide appropriate references. For all questions you must include all calculations and steps used to arrive at your answers. Acknowledge the Faculty’s Code of Behaviour on Academic Matters: I, , pledge upon my honour that I will not violate our Faculty’s Code of Behaviour on Academic Matters during this assessment by acting in any way that would constitute cheating, misrepresentation, or unfairness, including but not limited to, using unauthorized aids and assistance, impersonating another person, and committing plagiarism. I acknowledge that providing unauthorized
assistance to someone else is also considered a serious academic offence
.
Question 1 /30 Question 2 /20 Question 3 /30 Question 4 /20 Total 100Student Name: _________________________ Student No: _________________________
2 Question 1: (30 points) The Butch Cassidy and the Sundance Kid mining company is currently reviewing the optimization of the Hole in the Wall pit design. As part of this, a review has been made of the large, currently open XYZ stope below the pit which has previously caved but is presently stable. You have been provided the results of recent underground mapping campaign in the vicinity of the stope and have been mandated to investigate the stability of the surface crown. Parameters Lower Quality Case Intermediate Quality Case Upper Quality Case Current Pit Extension Current Pit Extension Current Pit Extension Modeled Maximum Stress σ1 (MPa) 18.0 20.0 18.0 20.0 18.0 20.0 Strength to Stress Ratio σc/σ1 7.8 7.0 7.8 7.0 7.8 7.0 Stress Reduction Factor SRF 0.6 0.7 0.6 0.7 0.6 0.7 Joint Water/SRF Jw/SRF 1.7 1.4 1.7 1.4 1.7 1.4 Rock Mass Quality Q 14.2 12.1 26.4 22.6 39.6 33.9 Crown pillar span (m) S 80 80 80 80 80 80 Rock mass Unit weight (t/m3) Y 2.7 2.7 2.7 2.7 2.7 2.7 Thickness of Crown pillar (m) T 200 155 200 155 200 155 Strike Length (m) L 110 110 110 110 110 110 Orebody Dip (deg) Alpha 80 80 80 80 80 80 Based on the results of your analyses make appropriate follow up recommendations, including exposure guidelines. ANSWER
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As sinking of the shaft progressed to greater depths, the ground control engineer at the Last Hope Mine became concerned with the wall stability. The shaft has a 6 m diameter and is planned to reach a depth of 1,800 m. Based on stress measurements, the major and intermediate principal stresses, σ1 and σ2, are
horizontal and oriented North‐South, and East‐West, respectively. The minor principal stress σ3 is vertical. The magnitude of the principal stresses is defined based on depth: 1 = 2Vertical 2 = 1.7Vertical 3 = Vertical
where Vertical = H; ≈ 0.027 MPa/m, and H = depth below the surface in meters.
The rock mass is composed of metamorphic basalt. A reasonable approximation of the rock mass behaviour around the shaft can be estimated by applying the Hoek‐Brown (1988) failure criterion using m = 10 and s = 0.25. Based on preliminary testing results, the uniaxial compressive strength of the metamorphic basalt is 140 MPa. Hoek and Brown Criterion (1988)
1=
3+
m
c
3+
s
c2 Given the stress conditions, and the geomechanical properties of the rock mass, use an analytical solution to estimate the maximum extent of the fracture zone around the shaft. Discuss the importance of the obtained results in the selection of suitable reinforcement for the shaft. Make appropriate recommendations to mitigate any potential problems. Identify the limits of your analysis and any assumptions that you make.
ANSWER
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Question 3: (30 points)
You are a consultant working on the Preliminary Economic Assessment of a nearly flat and tabular mineral deposit in Australia. Your mandate is to design appropriate dimensions for square pillars. The orebody is 5 m thick on average and located about 300 m below the surface elevation. The current mining plan calls for the ore to be extracted using the room‐and‐pillar mining method with room dimensions of 5 m wide by 5 m high. At this stage of the project, you have access to a limited amount of geotechnical information to assist in your design. • Unit weight: 27 kN/m3 • RQD: 70 – 80 • QTypical : 12 • Qmax: 14 • Qmin: 8 • Uniaxial compressive strength: 145 MPa • Tensile strength: 5 MPa • Young ’s modulus: 52 GPa • Poisson’s ratio: 0.26 Suggest appropriate pillar dimensions for this mining layout and calculate the resulting extraction ratio. Justify your choice of factor of safety based on observations of pillar failures reported by Lunder and Pakalnis. ANSWER5 Use the provided technical information in the course, and supplier data for the rock reinforcement elements presented in the tutorial/laboratory sections, to provide a trade‐off comparison between different rock bolts to be used as part of the ground support strategy or a shallow depth mining drive in the Canadian Shield. You should address both operational and capacity considerations. ANSWER
