Calculation types: drained, undrained and fully coupled material behavior. Dr Francesca Ceccato

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1 Calculation types: drained, undrained and fully coupled material behavior Dr Francesca Ceccato

2 Summary Introduction Applications: Piezocone penetration (CPTU) Submerged slope Conclusions

Introduction Porous media Solid grains Liquid Gas Porosity: Void ratio: Saturation degree: n V e V v v V Sr V w v V V s n 1 n Total stresses in saturated soil are

3 Introduction Porous media Solid grains Liquid Gas Porosity: Void ratio: Saturation degree: n V e V v v V Sr V w v V V s n 1 n Total stresses in saturated soil are distributed between liquid and solid grains according to the effective stress principle: σ = σ + p Liquid pressure F Intergranular forces Total stress Effective stress Pore pressure

Drainage type Porous media Dry Saturated Unsaturated 1-phase: M dry a

drag,l F int F drag,g M s a s = F ext F int M l a l M g a g Drained

M l a l = F ext l F int F drag M s a s = F ext F int M l a l Total

4 Drainage type Porous media Dry Saturated Unsaturated 1-phase: M dry a = F ext F int 3-phase: M l a l = Fl ext M g a g = F g ext l F int g F drag,l F int F drag,g M s a s = F ext F int M l a l M g a g Drained 1-phase: M sat/dry a = F ext F int Undrained Fully coupled l 2-phase: M l a l = F ext l F int F drag M s a s = F ext F int M l a l Total stress analysis σ = D ε Effective stress analysis σ = D ε σ = σ + p p = K l ε vol

5 Drainage type

6 Constitutive model Be aware that not all the material models are appropriate for all the material types! For undrained total stress analysis use linear elastic or Tresca model.

function of κ, ρ L, μ d : k = κ ρ Lg μ d Reference values for water Temp. [ C] Dyn. Viscosity x10-3 [Pa s] Density [g/cm³] 5 1.

7 Fully coupled The intrinsic permeability of the soil (κ), depends only on properties of the solid matrix The dynamic viscosity of the liquid (μ d ) and the density of the liquid (ρ L ), depends on the temperature The hydraulic conductivity or Darcy permeability is a function of κ, ρ L, μ d : k = κ ρ Lg μ d Reference values for water Temp. [ C] Dyn. Viscosity x10-3 [Pa s] Density [g/cm³]

8 Applications Simulation of cone penetration in different drainage conditions

9 Piezocone penetration The Piezocone Penetration Test (CPTU) is an in situ test, widely used to characterize the soil profile. The device penetrates the soil with a velocity of 2cm/s. Measurement of: tip resistance q c sleeve friction f s pore water pressure u u f s q c

10 Dissipation test The dissipation test consists of stopping the penetration and monitoring the pore pressure dissipation with time. The test allows to estimate the consolidation coefficient and the permeability. t 50 time corresponding to a degree of consolidation of 50% I r =G/s u rigidity index u u i 0.5 Robertson et al. (1992) t 50 log (t)

11 Drainage conditions Drainage conditions influence q c, u Saturated - drained Saturated fully coupled Saturated - undrained V = vd c v Resistance ratio q net /q ref Drained Partially drained Undrained Normalized velocity V Centrifuge tests (Oliveira et al. 2011) v = penetration velocity d = cone diameter c v = consolidation coefficient c v = k m v γ w k = Darcy s permeability m v = soil mpressibility q net q ref q net = q c s v0 = net cone resistance q ref = undrained net cone resistance s v0 = in situ vertical effective stress

index [-] l 0.205 Recompression index [-] k 0.04 Effective Poisson s ratio [-] n 0.

12 Numerical model Geometry and discretization s y0 =50kPa s x0 =34kPa OCR=1 s v0 =50kPa 20 14d 8d elements MP Modified Cam Clay model Parameter Symbol Value Virgin compression index [-] l Recompression index [-] k 0.04 Effective Poisson s ratio [-] n 0.25 Slope of CSL on p-q plane [-] M 0.92 Initial void ratio [-] e Saturated density [kg/m 3 ] r sat 1700

13 Numerical results: tip resistance The penetration velocity is constant: v = 2 cm/s. We vary the Darcy permeability k to change the normalized velocity Saturated drained: k, V 0 Saturated undrained effective stress: k 0, V Saturated-fully coupled k>10-3 m/s Saturated drained drained Saturated-fully coupled k<10-8 m/s Saturated undrained k V V=1.2 (k=10-5 m/s) V=12 (k=10-6 m/s) undrained V = vd c v c v = k(1 + e 0)σ v0 λγ w Soil-cone friction coefficient: m=0.3

14 Numerical results: excess pore pressure Excess pore pressure around the cone for different drainage conditions. The pore pressure decreases with the normalized velocity. Partially drained (V=1.2) Partially drained (V=12) Undrained

15 Resistance ratio Normalized pore pressure Numerical results: pore pressure and resistance Effect of normalized penetration velocity V on the resistance ratio and normalized pore pressure. q c,net = q c,drained q c,ref 1 + V V c 50 q c,ref u = 1 u ref V V c 50 Soil-cone friction coefficient: m=0.3 u ref = excess pore pressure in undrained conditions

16 Numerical results: comparisons with experiments m=0.3 The numerical results are in good agreement with experimental results on kaolin! m=0.3

dissipation Pore pressure distribution at the

17 Simulation of dissipation test We can stop the cone penetration and observe the pore pressure dissipation Pore pressure distribution at the cone shoulders Excess pore pressure dissipation 150kPa 0

18 Numerical results: dissipation test The dissipation of excess pore pressure with time depends on the considered position of the pressure filter. This is due to the bidimensional characteristics of the water flow. In the normalized chart Du/Du ini -T*, increasing V the curves move to the left V Du = excess pore pressure Du ini = excess pore pressure at the beginning of dissipation test

19 Numerical results and comparisos with experiments Evolution of excess pore pressure at cone shoulder for different normalized penetration rate and comparison with experimental data.

20 Applications Simulation of submerged slope failure

21 Experimental slope failure Initial configuration (experiment)

22 Experimental slope failure Final configuration (experiment)

23 The numerical model In the numerical model the slope failure is triggered by uniformly distributed increase of pore pressure at the bottom of the mesh. The pore pressure increases linearly from 0 to 10kPa in 5s and then is set to elements, 4545 nodes, 1567 active elements, 6252material points p w

24 The numerical model Material type: saturated fully coupled Constitutive model: Mohr-Coulomb Parameter Symbol Value Unit of measure Saturated unit weigth g sat kn/m 3 Water unit weigth g w 9.81 kn/m 3 Submerged unit weigth g 8.90 kn/m 3 Young s modulus E 5000 kpa Effective Poisson s ratio n Bulk modulus of water K w kpa Porosity n Darcy s permeability k 10-4 m/s Cohesion c 0 kpa Friction angle j 32 deg Dilatancy angle y 0 deg

25 Gravity loading Generate initial stresses via gravity loading ($$APPLY_QUASI_STATIC) F ext F int = 0 KE = 0 static equilibrium F ext F int F ext KE W ext < tol < tol Convergence condition

26 Local damping Local damping accelerates the convergence to static equilibrium Ma = F ext F int + F damp F=50kPa f damp = α f ext f int sign(v) α= damping factor f damp m v

27 Gravity loading Submerged weight is used: g = g sat - g L The gravity force of the liquid is neglected: F g,l = 0 Vertical effective stress distribution 0kPa 12kPa

28 Numerical results Displacement at material points

29 Numerical results Final configuration predicted by MPM and comparison with the experiment.

30 Summary Anura3D can currently be used to simulate Dry soil Saturated soil in drained and undrained conditions Fully coupled solid-water interactions in saturated soil These features have been validated with theoretical and experimental results Advanced features are available to improve the simulation (quasi-static convergence, local damping ) Usaturated conditions are under development

31 References Ceccato F., Beuth L., Simonini P. (2016). Analysis of piezocone penetration under different drainage conditions with the two-phase Material Point Method. Journal of geotechnical and Geoenvironmental engineering DOI: /(ASCE)GT Ceccato F., Beuth L, Vermeer P.A., Simonini P. (2016). Two-phase material point method applied to the study of cone penetration. Computers and Geotechnics DOI: /j.compgeo Ceccato F., Simonini P. (2016). Numerical study of partially drained penetration and pore pressure dissipation in piezocone test. Acta Geotechnica (published online). DOI: /s Ceccato F., L. Beuth, P. Simonini. (2015) Study of the effect of the drainage conditions on the cone penetration with the Material Point Method. XV pan-american conference on soil mechanics and geotechnical engineering, Buenos Aires (Argentina), November 2015 Ceccato F., L. Beuth, P. A. Vermeer, P. Simonini, (2014). Two-phase Material Point Method applied to cone penetration for different drainage conditions. In: International Symposium on Geomechanics from Micro to Macro, Cambridge (United Kingdom), 1-4 September 2014 Ceccato F., A. Rohe, P. Simonini, (2014) Simulation of slope failure experiment with the Material Point Method. In: IARG Chieti, July 2014

32 Thank you for your attention!

MPM Research Community. Anura3D MPM Software. Verification Manual

MPM Research Community. Anura3D MPM Software. Verification Manual MPM Research Community Anura3D MPM Software Verification Manual Version: 2017.1 12 January 2017 Anura3D MPM Software, Verification Manual Edited by: Miriam Mieremet (Deltares Delft, The Netherlands) With