Introduction. Introduction. Frozen/unfrozen soils: Cold regions Climate change Artificial ground freezing

Transcription

1 Properties and a constitutive model for frozen and unfrozen soil Ronald Brinkgreve, Delft University of Technology / Plaxis Authors: Manuel Aukenthaler, Ronald Brinkgreve, Adrien Haxaire Content Introduction Characteristics of frozen soils Starting from particle size distribution Soil-Freezing Characteristic Curve Hydraulic conductivity Validations Constitutive model for frozen / unfrozen soil Model parameters Applications Conclusions 2/24 Copyright Plaxis bv

2 Introduction Frozen/unfrozen soils: Cold regions Climate change Artificial ground freezing 3/24 Introduction Research on modelling of frozen/unfrozen soils i.c.w. NTNU Constitutive model (NTNU) Parameters and Validation (Plaxis/ TUDelft) 4/24 Copyright Plaxis bv

3 Characteristics of frozen soils Transition pore water > pore ice (and vice versa): Gradual process (in tand T) Transition zone: Frozen fringe Unfrozen water content θ uw (T) (Soil Freezing Characteristic Curve, SFCC) Pressure melting θ uw (p) Change of hydraulic conductivity k(t,p) Change of stiffness and strength Expansion / compression 5/24 Characteristics of frozen soils Problem: Temperature-related parameters are uncommon for geotechnical engineers Solution: Derive them from common soil data (Particle Size Distribution) 6/24 Copyright Plaxis bv

4 Starting from particle size distribution Selection of soil type > PSD > SSA 7/24 Soil-Freezing Characteristic Curve SSA > Unfrozen water content θ uw : (after Anderson & Tice, 1972) ρ w = bulk density of water ρ b = bulk density of unfrozen soil T = temperature T f = freezing temperature of water 8/24 Copyright Plaxis bv

5 Soil-Freezing Characteristic Curve Pressure-dependence of the freezing temperature: (Clausius-Clapeyron equation) p ice = p w = ρ ice = L = pore ice pressure pore water pressure bulk density of ice latent heat Cryogenic suction s c : (1) 9/24 Soil-Freezing Characteristic Curve Melting pressure for ice p melt : (after Wagner et al., 2011) (T= T f ) (vapour-liquid-solid triple point) (2) 10/24 Copyright Plaxis bv

6 Soil-Freezing Characteristic Curve Pressure melting: (pressure in MPa) For a given p w and T: s c, p ice and T f can be calculated by solving eq. (1) and (2) iteratively 11/24 Soil-Freezing Characteristic Curve Final result: SFCC for different soils at different pressures Increasing pressure Fine grained Coarse grained 12/24 Copyright Plaxis bv

7 Hydraulic conductivity PSD > k sat > k(θ uw ): (after Tarnawski& Wagner, 1996) Permeability of partially frozen soil: m i = mass fractions of clay, silt, sand d i = particle size limits θ uw = unfrozen water content θ sat = saturated water content 13/24 Validations (soil mass fractions after Smith & Tice, 1983) SFCC based on SSA 14/24 Copyright Plaxis bv

8 Validations Pressure-dependence: (after Zhang et al., 1998) Lanzhou Loess: m cl = 0.12 m si = 0.80 m sa = 0.08 e 0 = /24 Validations Hydraulic conductivity: (after Burt & Williams, 1976) 16/24 Copyright Plaxis bv

9 Constitutive model for frozen/unfrozen soil Solid state (grains + ice) stress σ*: Similarities with BBM In unfrozen state: MCC σ = net stress S uw = unfrozen water saturation p w = pore water pressure ε m = solid phase strain component ε s = cryogenic suction strain component 17/24 Constitutive model for frozen/unfrozen soil Elastic strains: s c = cryogenic suction Frozen soil properties: ice saturation ν f = frozen Poisson s ratio Temperature-dependent (but stress-independent) Young s modulus of frozen soil 18/24 Copyright Plaxis bv

10 Constitutive model for frozen/unfrozen soil Plastic strains: Loading-collapse Segragation M 19/24 Model parameters Elastic parameters Strength Primary loading - isotropic stress - freezing 20/24 Copyright Plaxis bv

11 Model parameters Parameter determination: From oedometer test (frozen/unfrozen): (p y0* ) in, p c*, β, κ 0, λ 0, r From simple shear test: G 0, M From axial compression test: E f,ref, E f,inc, ν f, k t From frost heave test: (s c,seg ) in, κ s, λ s 21/24 Applications Frost heave Chilled pipeline 253 K Temperature distribution a. 40 days b. Long time Frost heave after long time 22/24 Copyright Plaxis bv

12 Applications Thaw settlement Footing on frozen soil T = 2 K 500 kpa Ice saturation a. Initial b. After warming Settlement a. Initial b. After warming 23/24 Conclusions Practical approach for θ uw (T,p)and k(t,p)of frozen soils Validated against data from literature PSD seems to enable a good estimate of properties of frozen soils Constitutive model for frozen / unfrozen soil Typical phenomena of frozen soil Successful applications: Frost heave Thaw settlement 24/24 Copyright Plaxis bv