A. Benardos Mining Engineer, Lecturer, NTUA D. Papakonstantinou Mineral 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 (~2.500m 2 ) UHWR (~2.500m 2 ) Access tunnel (~170m) Access tunnel (~170m) Shaft (~35m) Shaft (~35m)

Impermeable low strength formations of the overthrusted nappe (schists, phyllites, graphic schist, layers) Impermeable low strength formations of the overthrusted nappe (schists, phyllites, graphic schist, layers) “Upper marble” formation “Upper marble” formation Water table at approximately +0m Water table at approximately +0m UHWR site Geologic setting

Room and Pillar method Limestone (upper marble) Graphic schist Shale, Phyllite Tectonic Nappe Limestone mi9669 σ ci (MPa) E i (MPa) E m (MPa) GSI s mbmb α Upper marble Ground

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/m 3 γ=26 kN/m 3 Wp/Hp =1,27 Wp/Hp =1,27  Evaluation of pillar strength for stone mines ignores the effect of σ 3 ignores the effect of σ 3  Satisfactory SF for limestone Empirical formulae

 Simulating the effect of the cross-cuts (3d geometry) the concept of an additional equivalent vertical stress increased unit weight of rocks L p : pillar length, W p : pillar width, W o : width of the opening (room width) 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 N-S E-W Numerical Analysis Two model sections created based on actual field observations 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 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 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 Using the concept of increased unit weight of rocks SF within pillar SF at roof Section 1

Section 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 1Section 2 Stress (kPa)Displacements (mm) Safety FactorStress (kPa)Displacements (mm) Safety Factor PhasePlaxisPhase2PlaxisPhase2PlaxisPhase2PlaxisPhase2 Plaxis Phase2Plaxis

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 selected procedure for the safety factor estimation (Strength Factor and Safety Factor)  The horizontal to vertical stress ratio (K o ) assumption

Numerical tools have the ability to assess in a clearer and a more definite manner pillar stability, comparing to empirical solutions. 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 Good agreement between two different software packages Major identified failures share the same characteristics Major identified failures share the same characteristics At 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 Phase 2 simulates pillar behavior better than Plaxis