Analysis of tunnel in weak rock
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This presentation is about the properties of rockmass around tunnel in weak rock, before and after excavation. Contact us on www.geotechnicaldesigns.com
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The document discusses several failure criteria for rocks, including:
1) The Mohr-Coulomb criterion, which defines shear strength as a function of cohesion and friction angle.
2) The Hoek-Brown criterion, which models the non-linear relationship between principal stresses and incorporates rock mass quality.
3) The Griffith failure criterion, which postulates that stress concentrations at flaws like cracks cause propagation and failure.
It also briefly mentions the Drucker-Prager yield criterion and that empirical criteria tailored to a specific rock type may provide the most precise failure prediction.
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2) Two main modeling approaches are direct analysis using finite elements for the soil, and indirect substructure analysis using springs/dashpots to represent soil-foundation interaction.
3) Pile foundations are commonly modeled using springs representing the pile stiffness, with properties estimated from empirical formulas accounting for factors like soil properties and pile geometry.
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Analysis of tunnel in weak rock
- 1. Geotechnical DesignsGeotechnical Designs Analysis of Tunnel in Weak Rock www.geotechnicaldesigns.com.au
- 2. Geotechnical DesignsGeotechnical Designs Tunnels in Weak Rock This presentation is based on paper by Hoek : Tunnels in weak rocks Based on basic concepts: ❖ How rock mass surrounding tunnel deforms. ❖ How support systems acts to control this deformation. www.geotechnicaldesigns.com.au
- 3. Geotechnical Designs Advancement Stages of Tunnel – Section-1 Geotechnical Designs Tunnel Shape – Circular Tunnel is advancing in weak rockmass In-situ Stress – Hydrostatic Stress Field (v = h = 0 ) Advancement Stages of Tunnel Section -1 Section -2 Section -3 Section 1- in front of the excavation face. In-situ Stress - Rock mass with no excavated induced stresses. pi = p0 Internal Pressure = In-situ Stresses Deformation = 0
- 4. Geotechnical Designs Geotechnical Designs Advancement Stages of Tunnel Section-2 Section 2 –behind the tunnel face, between the face and tunnel lining. Internal pressure < in-situ stress pi 0 but < p0 (There is support from tunnel face) Deformations start from front of the tunnel face but not to full extent behind the tunnel face. Section -1 Section -2 Section -3
- 5. Geotechnical Designs Advancement Stages of Tunnel Section-3 Geotechnical Designs Section 3 – far away from and behind the tunnel face. The support from tunnel face no longer provided. Therefore now the provided internal pressure is zero and so the deformation is to its full extent. pi = 0 Section -1 Section -2 Section -3
- 6. Geotechnical Designs Tunnel deformation analysis Geotechnical Designs In this analysis it is assumed ➢The surrounding heavily jointed rock mass ➢Mass behaves as an elastic-perfectly plastic material ➢Failure involving slip along intersecting discontinuities is assumed to occur with zero plastic volume change (Duncan Fama, 1993) Support is modelled as an equivalent internal pressure and, although this is an idealised model, it provides useful insights on how support operates.
- 7. Geotechnical Designs Failure Criterion Geotechnical Designs Mohr Coulomb Criterion This criterion is determined through Triaxial test which is conducted over intact rock.
- 8. Geotechnical Designs Failure Criterion Geotechnical Designs increment 3 1 13 32 0 1E-10 0.00 0.00 0.00 1 0.36 1.78 0.64 0.13 2 0.71 2.77 1.98 0.51 3 1.07 3.61 3.87 1.15 4 1.43 4.38 6.26 2.04 5 1.79 5.11 9.12 3.19 6 2.14 5.80 12.43 4.59 7 2.50 6.46 16.16 6.25 Sum 10 29.92 50.46 17.86 The value of k is determined from slope 1 and 3 K = 2.44 The value of friction angle of rockmass was determined from the equation given below = 24.72
- 9. Geotechnical Designs Failure Criterion Geotechnical Designs increment 3 1 13 32 0 1E-10 0.00 0.00 0.00 1 0.36 1.78 0.64 0.13 2 0.71 2.77 1.98 0.51 3 1.07 3.61 3.87 1.15 4 1.43 4.38 6.26 2.04 5 1.79 5.11 9.12 3.19 6 2.14 5.80 12.43 4.59 7 2.50 6.46 16.16 6.25 Sum 10 29.92 50.46 17.86 Determination of global rockmass strength cm Is determined through triaxial test using below equation Determination of cohesion value of rockmass cm = 0.69MPa C= 0.22MpaDetermination Modulus of deformation of rockmass Em = 750MPa
- 10. Geotechnical Designs Support Pressure Geotechnical Designs Failure of the rock mass surrounding the tunnel occurs when the internal pressure provided by the tunnel lining or tunnel face is less the critical support pressure. pcr = 0.96Mpa Therefor to support the tunnel or to stop rockmass failure the support measures Shall be more that this critical pressure
- 11. Geotechnical Designs Support Pressure Geotechnical Designs When the internal support pressure pi is less than the critical support pressure pcr If pi < pcr ➢ Failure occurs around the excavated tunnel ➢ Plastic zone forms around the tunnel with radius rp rp = 6.43m Actual radius of tunnel r0 = 3m
- 12. Geotechnical Designs Radial deformation Geotechnical Designs If pi < pcr For plastic failure, the total inward radial displacement of the walls of the tunnel is: uip = 30.60mm If pi > pcr No plastic failure
- 13. Geotechnical Designs Support Measures Geotechnical Designs The above study and calculation has been adopted from article “Tunnels in Weak Rock” ➢ From this article we have only studied about the analysis of tunnel behavior. ➢Determination of support measures from the analysis of tunnel behavior will be studied next presentation.