Background - Symbols

Ced

Parameter defined in equation: εvol_dm0 = 0.001 exp[(I_D1 – I_D) / Ced]

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D₅₀

Median grain size = grain diameter for which half the sample is smaller  and half is larger

[μm]

D₁₅

Grain diameter for which 15% of the sample is finer

[μm]

D_r

Relative density on the basis of n: D_r = R_n = (n_max – n) / (n_max – n_min)

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e

Void ratio: e = n / (1 – n)

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(x)

e_max

Maximum e.

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e_min

Minimum e.

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f(s)

Form of the dilatation curve as a function of s: f(s) = εvol_d / εvol_dm

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I_D

Relative density on the basis of e: I_D = R_e = (e_max – e) / (e_max – e_min)

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I_D1

Parameter defined in the following equation: εvol_dm0 = 0.001 exp[(I_D1 – I_D) / Ced]

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Ks

Elastic modulus for isotropic unloading

[kN/m²]

Ks₀

Value of Ks at average stress p’₀

[kN/m²]

Ks₀₁

Parameter defined in the following equation: Ks₀ = Ks₀₁ + ∂Ks₀ / ∂I_D × I_D

[kN/m²]

m

Parameter describing f(s), defined in the following equation: f(s) = A.s^m – B.s^r / (s_max – s)

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n

Porosity: n = e / (1 + e)

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n_max

Maximum value of n.

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n_min

Minimum value of n.

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p’

Mean effective stress (or isotropic effective stress): p' = (σ'₁ + σ'₂ + σ'₃) / 3

[kN/m²]

p’_CON

Mean effective stress after consolidation.

[kN/m²]

p’₀

Reference value for p’.

[kN/m²]

q

Deviatoric stress (or equivalent shear stress): q = (s₁ – s₃)

[kN/m²]

R_e

Relative density on the basis of the void ratio: R_e = I_D = (e – e_min)/(e_max – e_min)

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r

Parameter describing f(s), defined in the following equation:

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S_r

The degree of saturation of the soil (0 \< S_r \< 1). For sand (generally dry) S_r = 0 and for clay (generally completely saturated) S_r = 1.

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s

Relative shear strength: s = q / p'

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s₂

Value of s at maximum contraction

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s_max

Maximum value of s. The value of s_max matches the friction angle φ, through the following equation: s_max = 6 sin φ/ (3 – sin φ)

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s_m2

s_m2 = s_max – s₂  

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s_m2-0

Parameter defined in equation s_m2 = s_max – s₂ = s_m2-0 + ∂s_m2 / ∂I_D . I_D

Parameter s_m2-0 can be obtained from samples with different values for I_D.

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u

Parameter describing the influence of p’ on K_s defined in equation: Ks = Ks₀ . (p' / p₀')^u

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v

Parameter describing the influence of p’_CON on evol_dm, defined in equation: εvol_dm = εvol_dm0 . (p_CON' / p₀')^v

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w

The water grade: The water grade: w = S_r . e . γ_w / γ_s

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ε_cor

Correction on the measured volumetric strain with respect to the membrane, defined by the following equation:
ε_cor = 32.4 D₅₀ [(σ’_h2 – 10)^0.64 – (σ’_h1 – 10)^0.64) ]

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εvol

Volumetric strain (defined as positive for compaction).

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εvol_c

Volumetric strain by isotropic unloading.

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εvol_d

Dilation volumetric strain or volumetric strain by contraction (positive) and dilatation (negative).

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εvol_dm

Maximum volumetric strain by contraction.

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εvol_dm0

Value of evol_dm at mean effective stress p’₀.

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σ(x)

Standard deviation of parameter x.

σ'

Normal effective stress.

[kN/m²]

σ’₁, σ’₂, σ’₃

Principal effective stresses.

[kN/m²]

σ’_h

Horizontal effective stress.

[kN/m²]

φ

Friction angle.

[°]

φ_mob

Mobilized friction angle.

[º]

ψ_5m

State parameter (Psi 5m), describes the state of the soil.

γ

Submerged unit weight of sand: γ = (1 – n) . (γ_s – γ_w)

[kN/m³]

γ_s

Unit weight of sand.

[kN/m³]

γ_w

Unit weight of water.

[kN/m³]