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- 1. THEORETICAL AND NUMERICAL INVESTIGATIONS ON SHALLOW TUNNELLING IN UNSATURATED SOILS MEng. Enrico Soranzo, Prof. Wei Wu Institute of Geotechnical Engineering University of Natural Resources and Life SciencesInstitute of Geotechnical Engineering European Geosciences Union General Assembly 2013
- 2. Theoretical and Numerical Investigations on Shallow Tunnelling in Unsaturated Soils 1 Outline Soil properties Theoretical Prediction Numerical Analysis Conclusion OUTLINE Unsaturated soil properties • Water retention properties • Dependance of cohesion on saturation • Dependance of elastic parameters on saturation Stability of the tunnel face in unsaturated soil • Theoretical assessment Numerical modelling • Parameter calibration • Numerical results ConclusionsInstitute of Geotechnical Engineering European Geosciences Union General Assembly 2013
- 3. Theoretical and Numerical Investigations on Shallow Tunnelling in Unsaturated Soils 2 Outline Soil properties Theoretical Prediction Numerical Analysis Conclusion STRENGTH AND STIFFNESS Water retention curve (Soil-Water Characteristic Curve, SWCC) • Degree of saturation depends on suction level • The terms are related with van Genuchtens equation (van Genuchten, 1980): 1S SS r r 1 u u a w n m Dependance of cohesion on saturation • Cohesion can be related to the degree of saturation (Fredlund et al., 1978): cunsat = c + (ua – uw)Sktanf Dependance of elastic parameters on saturation • Youngs modulus can be related to the mean net stress and the suction level (Rahardjo et al., 2011): Eunsat = a(sn – ua)m + b(ua – uw)n + c(sn – ua)(ua – uw)pInstitute of Geotechnical Engineering European Geosciences Union General Assembly 2013
- 4. Theoretical and Numerical Investigations on Shallow Tunnelling in Unsaturated Soils 3 Outline Soil properties Theoretical Prediction Numerical Analysis Conclusion SUCTION AND DENSITY Definition of soil suction […] suction is the negative pressure relative to the external gas pressure on the soil water (Krahn & Fredlund, 1961) • In hydrostatic conditions suction develops linearly from the water table (Lu & Griffiths, 2004): evaporation seasonal unsteady zone (1 – 3m) Soil density suction profile hydrostatic • Soil density depends on suction steady zone (3 - 100m) profile the degree of saturation infiltration and porosity: suction saturated zone profile r = rd + nSrw Figure 1 Suction profilesInstitute of Geotechnical Engineering European Geosciences Union General Assembly 2013
- 5. Theoretical and Numerical Investigations on Shallow Tunnelling in Unsaturated Soils 4 Outline Soil properties Theoretical Prediction Numerical Analysis Conclusion FACE STABILITY OF SHALLOW TUNNEL Face stability C Unsaturated Soil • Which pressure prevents collapse? (Limit face support pressure) Shallow tunnel D pf • C/D ratio lower than 3 Close-form prediction W • Many formulae for homogeneous soil Saturated Soil • Different origin: Figure 2 Problem statement • Limit plasticity theory • Centrifuge testing Vermeers formula (Vermeer & • Numerical analysis Ruse, 2002) • From parametric studies (NA) 1 c p f D 9 tan 0.05 tan Parameters vary with depth! Institute of Geotechnical Engineering European Geosciences Union General Assembly 2013
- 6. Theoretical and Numerical Investigations on Shallow Tunnelling in Unsaturated Soils 5 Outline Soil properties Theoretical Prediction Numerical Analysis Conclusion PARAMETER CALIBRATION Cohesion • CD Triaxial Tests on unsaturated soil were performed to obtain the shear parameters • To best-fit the results, Fredlund et al., 1978 suggest to adopt the SWCC of van Genuchten raised to the power of k: 1S cunsat = c + (ua – uw)Sktanf SS r r 1 u u n m a w • The shape of the curve was retained, but the dependence on physical parameters was abandoned: cunsat = a(ua – uw){1+[(ua –uw)]n}k a n k Figure 3 Cohesion calibration 1.313 0.001698 1.882 -59.735Institute of Geotechnical Engineering European Geosciences Union General Assembly 2013
- 7. Theoretical and Numerical Investigations on Shallow Tunnelling in Unsaturated Soils 6 Outline Soil properties Theoretical Prediction Numerical Analysis Conclusion PARAMETER CALIBRATION Youngs modulus • Youngs modulus has to be calibrated against the mean net stress and the suction value: Eunsat = a(sn – ua)m + b(ua – uw)n + c(sn – ua)(ua – uw)p 4 x 10 12 a b c 10 4.965·103 6.962·103 5.073·10-3 Youngs modulus (kPa) 8 6 m n p 4 2 1.911·10-1 3.713·10-1 1.570 0 150 200 100 150 50 100 Figure 4 Youngs modulus 0 50 Suction (kPa) Mean net stress (kPa)Institute of Geotechnical Engineering European Geosciences Union General Assembly 2013
- 8. Theoretical and Numerical Investigations on Shallow Tunnelling in Unsaturated Soils 7 Outline Soil properties Theoretical Prediction Numerical Analysis Conclusion NUMERICAL MODEL Geometry Suction-Stress Characteristic Curve • A very shallow tunnel has (SSCC) been modelled (C/D = 0.5) • Instead of updating the cohesion, the SSCC-approach has been utilized C=5m • Bishops effective stress (Bishop, 1954) has been combined with Fredlunds cohesion D = 10 m • In doing so, there is no need to update the Mohr-Coulomb failure criterion W=1m c = Sk s = (s – ua) – c(ua – uw) Figure 5 Numerical model t = c + s tan fInstitute of Geotechnical Engineering European Geosciences Union General Assembly 2013
- 9. Theoretical and Numerical Investigations on Shallow Tunnelling in Unsaturated Soils 8 Outline Soil properties Theoretical Prediction Numerical Analysis Conclusion SIMULATION PROCEDURE Tunnel face • A piston is placed in front of the tunnel face and fixed in the direction of the excavation during consolidation • After consolidation, the piston is displaced inwards • Rise of the water can be simulated to assess the tunnel face stability in a worst-case scenario Figure 6 Water table below the tunnel Figure 7 Water table at the tunnel centerlineInstitute of Geotechnical Engineering European Geosciences Union General Assembly 2013
- 10. Theoretical and Numerical Investigations on Shallow Tunnelling in Unsaturated Soils 9 Outline Soil properties Theoretical Prediction Numerical Analysis Conclusion WATER TABLE AT THE TUNNEL CENTERLINE Failure • The soil follows the inward displacement of the piston • The failure is localized at the tunnel face and does not propagate to the Figure 8 Horizontal displacement surface Support pressure • If the soil fails, a limit support pressure has to be provided to the tunnel face, Local which can be computed Failure numerically Figure 9 Vertical displacementInstitute of Geotechnical Engineering European Geosciences Union General Assembly 2013
- 11. Theoretical and Numerical Investigations on Shallow Tunnelling in Unsaturated Soils 10 Outline Soil properties Theoretical Prediction Numerical Analysis Conclusion POSITIVE LIMIT SUPPORT PRESSURE Face pressure • As the pressure applied to the tunnel face decreases, • At a certain value of the face the inward displacement pressure, the inward increases displacement increases indefinitely (limit support pressure) • The limit support pressure for the present case is 16.8 kPa • Pressures greater than 75 kPa lead to an opposite deformation of the tunnel face (passive failure) Figure 10 Limit support pressureInstitute of Geotechnical Engineering European Geosciences Union General Assembly 2013
- 12. Theoretical and Numerical Investigations on Shallow Tunnelling in Unsaturated Soils 11 Outline Soil properties Theoretical Prediction Numerical Analysis Conclusion WATER TABLE BELOW THE TUNNEL Stable face • Soil density as well as strength in saturated conditions are kept constant • The water table is set below Figure 11 Gap between the piston the tunnel bottom and the tunnel face Support pressure • Under these conditions the tunnel face is stable and no support pressure is needed to prevent collapse Figure 12 Transverse settlementInstitute of Geotechnical Engineering European Geosciences Union General Assembly 2013
- 13. Theoretical and Numerical Investigations on Shallow Tunnelling in Unsaturated Soils 12 Outline Soil properties Theoretical Prediction Numerical Analysis Conclusion NEGATIVE LIMIT SUPPORT PRESSURE Horizontal displacement • At pf = 0kPa the displacement of the soil is negligible Figure 13 Horizontal displacement Face pressure at pf = 0kPa • As the pressure applied to the tunnel face decreases, the inward displacement increases • At pf = 0kPa the displacement has a finite value meaning that the tunnel face is stable Figure 14 Limit support pressureInstitute of Geotechnical Engineering European Geosciences Union General Assembly 2013
- 14. Theoretical and Numerical Investigations on Shallow Tunnelling in Unsaturated Soils 13 Outline Soil properties Theoretical Prediction Numerical Analysis Conclusion RESULTS OUTLINE Water table below the tunnel • In the NA a gap occurs between the tunnel face and the piston • The closed-form formula predicts a negative support pressure Water table at the tunnel centerline • The NA predicts failure of the tunnel face and a certain limit support pressure is required • The theoretical prediction of the support pressure agrees fairly well with the numerical prediction Numerical Theoretical Water Table Analysis Predictions (kPa) (kPa) 0.5m below the tunnel 0 <0 At the tunnel 16.8 16.6 centerlineInstitute of Geotechnical Engineering European Geosciences Union General Assembly 2013
- 15. Theoretical and Numerical Investigations on Shallow Tunnelling in Unsaturated Soils 14 Outline Soil properties Theoretical Prediction Numerical Analysis Conclusion CLOSED-FORM PREDICTION Vermeers formula 1 c p f D 9 tan 0.05 tan • Parameters variation can be considered Water table below the tunnel • The formula returns negative values except at the tunnel invert Water table at the centerline • The formula returns mainly positive valuesInstitute of Geotechnical Engineering European Geosciences Union General Assembly 2013
- 16. Theoretical and Numerical Investigations on Shallow Tunnelling in Unsaturated Soils 15 Outline Soil properties Theoretical Prediction Numerical Analysis Conclusion CONCLUSIONS Numerical Analysis • A method has been developed to numerically analyse the face stability of shallow tunnels in unsaturated soils considering the spatial variation of soil strength, density and Youngs modulus Closed-form formula • An existing formula for the prediction of the limit support pressure has been extended to the unsaturated case and compared to the numerical results • The results obtained with both methods agree fairly-wellInstitute of Geotechnical Engineering European Geosciences Union General Assembly 2013

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