# Stress analysis Design Problem

MINE5502 Numerical Analysis Lab                                                 25 September

Provide a brief memo report, identifying the process you followed, the modelling methodology and software, the purpose of the modelling analysis, the constraints and limitations of this type of modelling and the assumptions required to apply this type of model for these particular problems.

1. Geotechnical Engineering Practice – Boundary Element Lab Exercise

The geology involves a jointed dolerite, with 3 orthogonal joint sets resulting in a blocky rock mass with fair to good joint conditions. The intact rock itself is strong with a uniaxial compressive strength estimated to be 150 MPa. For the pre-feasibility design required, it is assumed that the minimum pillar thickness (and therefore the maximum extraction) can be assessed treating the rock mass as an equivalent continuum, which maintains a Strength Factor 1.1.

1. Sequencing of a cut and fill stope

The purpose of this exercise is to:

• examine features of 2‐D numerical stress analysis in modeling alternate mining sequences
• develop failure criteria for interpreting analysis results using rockmass data from your field mapping and rockmass classification task.

You are given a mining layout to evaluate location of footwall drives, and mining sequence for a cut and fill mining operation.

The geometry and 1 sequence is shown in Figure 1 below.

Figure 1.   Cut and Fill Stope

 Sill Pillar

Use your classification results and stress gradients from your rockmass classificiton project as input rock property and rockmass parameters for analysis. (Assume all granite and you may use RocLab to determine appropriate rockmass strength criteria for your analysis – include screen capture of your output if you do). Assume a depth to the midpoint of the pillar of 1000 m. What is the Strength Factor in the centre of the pillar after each mining stage? Are there alternative sequences which may be better?

1. Assessment of mining shapes

An existing mine is planning on sinking a new shaft to access a recently discovered high‐grade zone. The shaft is to be sunk from surface (0 m Elevation) to a depth of ‐1200m. There are four proposed shaft geometries, as shown in Figure 1.

Based on in‐situ stress measurements, field mapping and laboratory testing the following information is available:

In Situ Stresses

Stress Magnitude at 1000 m: σ1 = 2.5 x v = 0.027 x 1000 x 2.5 = 67.5 MPa, σ2 = 1.75 x v = 47.25 MPa,  σ3 = 27 MPa

Stress Orientation: σ1 trend=090, plunge=15, σ3 trend=000, plunge=75

Rock Properties

Rock Type: Granite UCS =150 MPa

Elastic Modulus = 50 GPa

Poisson’s Ration = 0.25

Friction Angle = 40

Coh=12.1

Given the information above and your rockmass assessment completed from the field mapping and core logging, determine the following using Rocscience’s Phase2 or Examine2D:

1. Discuss the relative design merits of each cross‐section in terms of rock mechanics principles, and hence provide recommendations for the optimal shape (and in the case of profile b), c) and d), optimal orientation) for the excavation for the shaft geometry at 1000m depth and explain why. Show Principal stress orientations/trajectories on plan view.
2. By employing undisturbed values for the Hoek‐Brown Failure Criterion, determine the thickness of the pillar between the shaft and a stope having dimensions 20m x 20 m x 100m vertical, such that the center of the pillar has a Strength Factor of 1.5 (i.e. how far away from the shaft does the stope need to be?).