A. Benardos Mining Engineer, Lecturer, NTUA D. Papakonstantinou Mineral Resources Engineer, MSc...
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Transcript of A. Benardos Mining Engineer, Lecturer, NTUA D. Papakonstantinou Mineral Resources Engineer, MSc...
A. Benardos Mining Engineer, Lecturer, NTUA
D. PapakonstantinouMineral Resources Engineer, MSc
Pillar stability analysis using the finite element method at the Lavrion
Technological and Cultural Park underground hazardous waste repository
The LTCP underground hazardous waste repository
UHWR (~2.500m2) Access tunnel
(~170m) Shaft (~35m)
Impermeable low strength formations of the overthrusted nappe (schists, phyllites, graphic schist, layers)
“Upper marble” formation
Water table at approximately +0m
UHWR site
Geologic setting
Room and Pillar method
Limestone(upper marble)
Graphic schist
Shale,
PhylliteTectonic Nappe
Limestone
mi 9 6 6 9σci
(MPa) 50 20 20 30Ei
(MPa) 7804 5649 4500 5000Em
(MPa) 3126 258
GSI 50 20 20 40
s 0.0039 0.0001 0.0001 0.0013
mb 1.509 0.345 0.345 1.056
α 0.506 0.544 0.544 0.511
Upper marble
Ground
7m
7m
6m
6m
7m
7m
Rock pillars
Access tunnel
Graphic schist intrusion
The upper layers of the hill are comprised by low strength formations as shales, phyllites and graphic schists
At the lower part, a layer of “upper marble” limestone formation is located
A tectonic contact lies between them
A geology issue
Tributary area method γ=26 kN/m3 Wp/Hp =1,27
Evaluation of pillar strength for stone mines ignores the effect of σ3
Satisfactory SF for limestone
10 15 20 25 30 35 40 45 500
2
4
6
8
10
Graphic Schist C1=13 MPa
C1 (MPa)
SF
20 30 40 50 60 70 800
2
4
6
8
10
12
14
16Limestone C1= 32,5 MPa
C1 (MPa)
SF
66.0
46.0
pH
pW
mC
pC
2
1
pWR
Wh
p
Empirical formulae
Simulating the effect of the cross-cuts (3d geometry)
the concept of an additional equivalent vertical stress
increased unit weight of rocks
Lp : pillar length,
Wp : pillar width,
Wo : width of the opening (room width)
PP
pop
WL
WWL
hγ
P
o
WW
1γγ2D
Numerical Analysis
Types of analysis 2D strain softening analysis using the Hoek-
Brown criterion 2D elastic perfectly plastic analysis using
Mohr-Coulomb failure criterion
Phase2
Plaxis v.8
Two sections created based on actual field observations
Tectonic contact
Limestone (upper marble)
Graphicschist
Shale, phyllite
Limestone
Limestone (upper marble)
Graphicschist
Shale, phyllite
Tectonic contact
N-S E-W
Numerical Analysis
Two model sections created based on actual field observations
Strength Factor
Phase 2 strain-softening analysis
Using the concept of increased unit weight of rocks
Yielded elements Vertical displacement
Phase 2 strain-softening analysis
Using the concept of increased unit weight of rocks
Plastic points Vertical displacements
Plaxis elastic-perfectly plastic analysis
Using the concept of increased unit weight of rocks
SF within pillar SF at roof
Se
ct
io
n
1
Se
ct
io
n
2
SF within pillar = 3.5 SF at pillar ribs = 1.05
Vertical displacements Plastic points
Plaxis elastic-perfectly plastic analysis
Phase2 vs Plaxis v.8
In situ measurements
Section 1 Section 2
Stress (kPa)
Displacements (mm)
Safety Factor
Stress (kPa) Displacements (mm)
Safety Factor
Phase Plaxis
Phase2
Plaxis
Phase2
Plaxis
Phase2
Plaxis
Phase2
Plaxis Phase2
Plaxis
2500 1800 3 3 2 3.5 2000 1300 5 2.5 2 3.5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
Date
Dis
pla
cem
ents
- D
y (m
m)
Α21Α22Α23Α24Α25Α26Α27Α28
Dissimilarities in the approaches used in each of the finite elements software
The different failure criterion used (Hoek-Brown, Mohr-Coulomb)Hoek-Brown non-linear envelope fits better the tests results, whereas the Mohr-Coulomb linear failure envelop presents larger deviations
The different attained material behavior Pillar failure is a progressive cohesion loss process usually starting from the pillar ribs and in the absence of confinement it propagates toward pillar core (strain-softening behavior)
The selected procedure for the safety factor estimation (Strength Factor and Safety Factor)
The horizontal to vertical stress ratio (Ko) assumption
Conclusions
Numerical tools have the ability to assess in a clearer and a more definite manner pillar stability, comparing to empirical solutions.
Good agreement between two different software packages
Major identified failures share the same characteristicsAt the pillar core area the strength and safety factors are satisfactory, thus, allowing the pillar to bear the loading of the overburden
The pillars do not appear to experience any significant problems, apart from some localized slabbing issues.
Protection against gravity failures
Instability problems due to the presence of the graphic schist formation occur at the southeastern part of the repository
Phase 2 simulates pillar behavior better than Plaxis