Rockmass Instabilities Induced by Mining Excavations in El Teniente

1
Rockmass Instabilities Induced by Mining
Excavations in El Teniente

• F. Alvarez, J. Dávila, A. Jofré, R. Manásevich.
• Center for Mathematical Modeling
• Universidad de Chile.
• March 2005.

2
Outline

• Part I Project overview
• Part II Asymptotic analysis of a limit stress
  state.
• Part III Differentiation with respect to the
  domain

3
Part I Project Overview
4
The mine

• Worlds largest underground copper mine.
• Located at 2.100 masl and 80 km SSE of Santiago.
• 1.500 km of tunnels and underground excavations.
• 355.000 ton/year.

El Teniente
5
The rockmass
Secondary mineral near the surface, soft and
highly fragmented. Poor in copper.
Primary mineral deeper, much harder than the
secondary ore. Rich in copper.
6
The caving method

• Panel caving the gravity force helps rock
  fragmentation and block extraction

7
Evolution of the cavity
8
Drawbacks

• Excavations induce deformations and high stress
  conditions within the surrounding rockmass.
• Consequences
• Damages to the surrounding excavations
• Rockmass instability.
• Seismic activity and rockbursting.

9
The challenge
To develop quantitative and qualitative mathematic
al tools to assist the determination of mining
parameters

• Geomechanical properties of the rockmass
• Dynamical aspects of the mining process.

10
The team
Mining Engineers S. Gaete R. Molina
Differential Equations J. Dávila R. Manásevich
Optimization Equilibrium F. Alvarez A. Jofré
11
Part II Asymptotic analysis of the limit stress
condition
12
Linear elasticity PDE
Equilibrium eqs.

• Assumption elastic, isotropic and homogeneuous
  material

Hookes law
13
Mixed boundary conditions
rockmass
cavity
14
Shear stress a numerical example

• High stress concentrations at the underminning
  front

15
Quasistatic stress evolution
16
Limiting process
- Real situation hgt0 - Displacements uh
- Limit situation h0 - Displacements u0
17
Limit solution
Singular domain
Solution

• u1,u2 are explicit and
• Intensity factors

18
Singular stress
19
Analytic vs. numerical solution
20
Asymptotic development for hgt0
x hy
x fixed
21
Part III Differentiation with respect to the
domain
22
Domain perturbations
Perturbation f(x)
Original domain W Perturbed domain W t f
23
Derivative
Perturbed solution
First order estimate for small t
where
24
PDE for u
25
PDE for u'
Traction boundary condition
26
Derivative of the energy
Elastic energy
Perturbed energy
Derivative
27
Explicit formula
Normal-tangent decomposition
Derivative
If
then it is possible to prove that