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