2^nd Generation

Row

Column

Node

Appendix references

Concept

Depends on/

Related to

Contribution

2

1

ASTM_2,1

[5]

Intrinsic

Permeability

PP_1,1

Hydraulic conductivity (K) depends on intrinsic permeability (k_intr), according to the implicit function:

$\begin{array}{l}K=\left(v_z\right)\ast f(\left(\frac{v_z}{q}\right),\left(\frac{\rho \ast v_z^2}{\psi }\right),\left(\frac{1}{Ri}\right),\left(\frac{1}{Re}\right),\left(\frac{H^2}{A_{inf}}\right),\left(\frac{\rho }{{\rho }_s}\right),\left(\frac{H^2}{k_{intr}}\right),\\ \left(\frac{H}{v_z\ast t}\right),\left(\frac{v_z\ast H}{D}\right),\left(\frac{\rho \ast v_z^2\ast H}{\sigma }\right),\Phi ,\theta ,S_e,n,i)\end{array}$

The terms, definitions and dimensions of $\left(K,v_z,q,\rho ,\psi ,Ri,Re,H,A_{inf},{\rho }_s,k_{intr},t,D,\sigma ,\Phi ,\theta ,S_e,n,i\right)$ are presented in detail in the below terminology (Table A8) of the Appendix. For clarification purposes, (q) refers to infiltration rate, (Φ) is the total porosity, (θ) is the liquid content/soil-water content, (n) is pore size distribution index. Rayleigh’s method of indices was deployed along with the echelon matrix procedure as an additional confirmation method.

2

2

ASTM_2,2

[8]

Hydraulic

conductivity

PP_1,2

Soil sorptivity (S) depends on hydraulic conductivity (K), according to the implicit function:

$\begin{array}{l}S=\left(\frac{z}{t^{0.5}}\right)\ast f(\left(\frac{z}{q\ast t}\right),\left(Sh\right),\left(Re\right),\left(\frac{\gamma }{\psi \ast z}\right),\left(Ri\right),\left(\frac{t\ast \gamma }{\mu \ast z}\right),\left(\frac{z}{v_z\ast t}\right),\\ \left(\frac{t^2\ast \gamma }{{\rho }_s\ast z^3}\right),\left(\frac{z^2}{k_{intr}}\right),\left(Sc\right),\left(\frac{z}{H}\right),\left(\frac{z}{h_c}\right),\Phi ,\theta ,n)\end{array}$

Where the terms, definitions and dimensions of $\left(S,z,t,q,Sh,Re,\gamma ,\psi ,Ri,\mu ,v_z,{\rho }_s,k_{intr},Sc,H,h_c,\Phi ,\theta ,n\right)$ are presented in detail in the below terminology (Table A8) of the Appendix. For clarification purposes, (q) refers to infiltration rate, (Φ) is the total porosity, (θ) is the liquid content/soil-water content, (n) is pore size distribution index. Rayleigh’s method of indices was deployed along with the echelon matrix procedure as an additional confirmation method.

2

3

ASTM_2,3

[3]

Hydraulic

Diffusivity

ASTM_1,3

Soil sorptivity (S) depends on hydraulic diffusivity (D), according to the implicit function:

$\begin{array}{l}S=\left(\frac{z}{t^{0.5}}\right)\ast f(\left(Sh\right),\left(\frac{M}{\rho \ast z^3}\right),\left(\frac{M}{\psi \ast t^2\ast z}\right),\left(\frac{z}{g\ast t^2}\right),\left(\frac{\mu \ast t\ast z}{M}\right),\\ \left(\frac{M}{{\rho }_s\ast z^3}\right),\left(\frac{z^2}{k_{intr}}\right),\left(Sc\right),\left(\frac{M}{t^2\ast \gamma }\right))\end{array}$

Where the terms, definitions and dimensions of $\left(S,z,t,Sh,M,\rho ,\psi ,g,\mu ,{\rho }_s,k_{intr},Sc,\gamma \right)$ are presented in detail in the terminology (Table A8) of the Appendix. For clarification purposes, (M) refers to the initial liquid mass. Rayleigh’s method of indices was deployed along with the echelon matrix procedure as an additional confirmation method.

2

4

PP_2,4

[20]

Effective liquid saturation

ASTM_1,4

Hydraulic conductivity (Κ) depends on effective saturation or degree of saturation (S_e), according to Van Genuchten-Mualem model [20], (equation 15c, page 23) initially introduced by van Genuchten, 1980 and Mualem, 1976:

$K\left(\theta \right)=K_s\ast S_e^l\ast {\left[1-{\left(1-S_e^{\left(\frac{1}{m}\right)}\right)}^m\right]}^2$

where the terms, definitions and dimensions of $\left(K\left(\theta \right),K_s,S_e,m\right)$ are presented in detail in the terminology (Table A8) of the Appendix (where $m=1-\frac{1}{n}$ ).