Estimating Mining
Induced Stress
Penny Stewart BEng(Mining) PhD
Estimation of Elastic Stress

All empirical design tools, across all disciplines of engineering have one
thing in common – They must be applied consistently

Now that 3D models are commonly used, it is worth checking how this
affects 2D derived mining induced stresses upon which stability charts are
based.

1980s to late 1990s, induced stresses were estimated using 2d plain-strain
charts (Stewart and Forsyth, 1995)- Kirsch equation closed form linear
elastic solution.

Charts not applicable for low aspect ratios in the database

Map3d boundary element

Most authors used 2d stress estimation methods
 Need to check Map3d against 2d model
eg Phases2d
Example: South Crofty mine: Stope 320 15H
Map3d Stress Estimation
Span = 32 m
Width = 17m
Height = 75 m
Hangingwall
Stress Resolution
Grid 3
3
-0.94 MPa
Example: Stope 320 15H
Phases 2d Stress Estimation
3
-3.2 MPa
3
Estimation of Elastic Stress II

2d Phases hybrid boundary element/finite element estimated larger tensile
stresses than Map3d

Difference between Phases2d and Map3d could not be explained for stopes
approaching 2d geometry

ie. Aspect ratio >5
Estimation of Elastic Stresses III

Further investigation required

South Crofty case study used to compare numerical modelling
programs

High aspect ratio = 83 (strike span to width)
 Theoretically, 2d should be very similar to 3d model results

Compare FLAC3D (finite element) with Map3d (boundary element)
FLAC3D Stress Estimation
F L A C 3D 2.00
S te p 3 3 7 6 M o d e l
1
4 :0
4 M on M ay
P1e:1
rsp
e ctive
13 2002
C e n te
R o ta tio
r:X :
nX: :
Y
:
7 .5 0 0 e + 0 0 1
0Y.0: 0 0
1Z.2: 5 0 e + 0 0 2
0Z.0: 0 0
D
ist:
M
ag
1 .0
00e+002
0 .0
0 .:
0
A
n
g
8 .5 4 9 e + 0 0 2
4 .7 5.:
2 2 .5 0 0
P la n e
P la n e
X
:
O rig in :
NXo: rm a l:
0Y.0: 0 0 e + 0 0 0
0Y.0: 0 0 e + 0 0 0
0Z.0: 0 0 e + 0 0 0
1Z.0: 0 0 e + 0 0 0
0 .0 0 0 e + 0 0 0
0 .0 0 0 e + 0 0 0
C ontour of
la n e :
SPGM
ax
ra d ie n t
on
0 0ne + 0 0 7
C a-4
lcu.0la0tio
-3
3 .5.5000000ee++000077
-3
3 .0.0000000ee++000077
-2
2 .5.5000000ee++000077
-2
2 .0.0000000ee++000077
-1
1 .5.5000000ee++000077
-1
1 .0.0000000ee++000077
-5
5 .0.0000000ee++000066
.0000000ee++000000
00.0
.0000000ee++000066
55.0
.0000000ee++000077
11.0
In1 te
.2rva
0 0 0l e=+ 0 0 7
5 .0 e + 0 0 6
JK M R
C
to
to
to
to
to
to
to
to
to
to
to
-
Stope
3=-1.99 MPa
3=-7.59 MPa
Comparison of Stress Estimation Method:
South Crofty
Stress Estimation
Method
Minimum Tangential
Stress (MPa)
2d Plain-strain
-13.8
Map3d
-2.4
2d Phases
-7.8
FLAC3D
-2.0
2d FLAC
-3.9
Some difference
between FLAC3D
and FLAC
Comparison of Stress Estimation Methods
@ Bottom of Stope
Stress Estimation
Method
Minimum Tangential
Stress (Mpa)
2d Plain-strain
-
Map3d
- 5.0
2d Phases
-13.5
FLAC3d
-7.6
2d FLAC
-7.6
Bottom of stope
less sensitive to
element size
Conclusions: Comparison of Stress
Estimation Methods

FLAC3d, 2d FLAC and Map3d produce similar
values


Map3d stress estimates of induced stresses will be
used, not Phases2d
Further investigation is required to explain why
Phases2d is predicting larger tensile stresses than
Map3d, FLAC3d and 2d FLAC
 Comparison
of codes