Post-Liquefaction Strength. State Parameter Approach. 22 January, from. Framework & Experience

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1 Post-Liquefaction Strength from State Parameter Approach Framework & Experience Mike Jefferies, P.Eng. 22 January, 27

2 Soil State versus Soil Properties Soil properties are independent of density, fabric or stress level Μ, Γ, λ, ρ, e min Can measure on reconstituted samples Soil state measures the current conditions of the soil e, σ, K Must determine from insitu it or test t conditions Soil Behaviour = f(soil state) X g(soil properties)

3 What is an appropriate measure of state? psi_piccy.xls maximum void ratio Critical State Locus (CSL) void ratio ψ = e - e c Current void ratio of the soil minimum void ratio mean effective stress ψ is a simple index to characterize particulate materials that is independent of grain shape, size, mineralogy, silt content etc ψ is something internal to every good constitutive model for soil

4 Example of soil behaviour dependent on ψ on, φ peak -φ c Stress dilatancy frictio State Parameter, ψ Erksak 33/.7 Erksak 355/3 Erksak 32/1 Isserk 21/2 Isserk 21/1 Isserk 21/5 Nerlerk 27/1 Alaska 24/5 Alaska 24/1 Castro B Castro C Hilton Mines Leighton Buzz Monterey # Ottawa 53/ Reid Bedford Ticino Toyoura Oil Sands Tail Chek Lap Kok

5 Range of soil type applicability.75 Conventional semi-log idealization of CSL.7.65 Void ratio.6.55 Initial state of samples Critical state at end of test.5 Improved (curved) idealization of CSL Gid GuindonB.xls Mean effective stress, p ' (kpa)

6 4 Constitutive Modelling Modelling tests the truth of concepts Deviator stre ss, q (kpa) NorSand The validated model 1 gives a vehicle on 2 2 which to hang the conceptual framework, q (kpa) Axial strain 8(%) NorSand Mean stress, p' 8(kPa) The model gives a way forward to detailed analysis through finite element and finite Axial strain (%) Mean stress, p' (kpa) 2 2 difference methods Deviator stress15 Deviator stress s, q (kpa) NorSand Axial strain (%) Mean stress, p' (kpa) Liquefaction is simply another aspect of soil constitutive behaviour. All good constitutive models for soil include the state parameter

7 History 1864 Tresca Plasticity 1936 Casagrande Existence of Critical State 1939 Lyman Franklin Falls Dam 1942 Casagrande Large slide, Magna Utah 1948 Taylor Dilation as work transfer 1957 Drucker et al Associated soil plasticity Roscoe et al Critical State Soil Mechanics 1969 Castro Reliable laboratory testing

8 CPT to determine ψ insitu CPT because repeatable, precise reference test offshore q c (MPa) quasi-static allows easy math 5 BUT 1 q c is not a soil property Influence of stress level Influence of soil type Depth (m) 15 2

9 Insight on CPT from constitutive model 1 Q p ( q p) p ( ) = ψ = ln Q p / k m p = σ v + t ( 2K ) 3 1 Q p 1 35 G = 64 MPa, p = 1 kpa G = 64 MPa, p = 1 kpa G = 64 MPa, p = 1 kpa 3 k = 6.2 ln(i r ) - 8 CPT invesrion coefficients k,m ψ 1 m= ln(i r ) Soil rigidity, I r k, m = f(m, λ )

10 Chamber tests 1 Q ψ

11 ψ = ln ( Q p / k ) m Post-liquefaction strength s σ r. for semi-log CSL v = 1 + 2K 3 M 2 exp ( ) m ( ψ λ ) ψ = ln Q p / k for all drained penetration of soils o Q = ( q t σ v ) σ v sr σ 1 1 mλ 1+ 2Ko M Q = 3 k σ v 2 1/ mλ Caution: (1) M(θ) (2) k, m, λ depend on soil gradation, type etc (3) K depends on soil deposition and geological history

12 Variability q c (MPa) Denser zone 1 Depth (m) Looser zone 2 MAC31 MAC4 MAC5 & 32 MAC6 MAC7 MAC8 & 33

13 Effect of variability on soil behaviour (1) Popescu et al (1997)

14 Insitu post-liquefaction strength Calaveras NorSand using soil properties typical of clean sand Fort Peck - no penetration Calaveras data available Undrained in small scale (no localization,) Residu ual strength ratio o, r / σ' Residua al strength ratio o, s vo r /σ' vo Jamuna Jamuna Mochikoshi 2 La Palma Zeeland Coast Hokkaido Nerlerk Lower San Fernando Mochikoshi 1 Sullivan La Marquesa La Marquesa Wachussett Sullivan La Palma Zeeland Wachussett Lower San Increasing plastic hardness (decreasing λ) Nerlerk Mochikoshi 2 Hokkaido Mochikoshi Increasing plastic Sheffield hardness Fort Peck Sheffield Characteristic CPT Q Characteristic state parameter, k ψ / λ

15 Post-liquefaction strength No unique relation between penetration resistance and strength Profession, as a whole, not doing enough in measuring relevant things when investigating case histories Substantial uncertainty in characteristic values Should move beyond total stress stability evaluations into full stochastic finite element/difference analyis

16 25 years work Shameless commerce Many papers Archived data Methodology Theory Data Limit State Case-Histories i Files to Download

17 Engineering Earth s Development. Preserving Earth s Integrity.

18 Effect of variability on soil behaviour (2) Onisiphorou, 2. g new /g nt on slope face (m m) average settleme.8.1 stochastic deterministic (d) d.12