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\chapter{Symbols}
This section provides a comprehensive compilation of used symbols throughout the book. As concepts and results are compiled from various disciplines (i.e. solid and fluid as well as porous media mechanics, geomechanics, geotechnics etc.) representing both theoretical and experimental work - a certain degree of redundancy is still necessary in this first book edition and will be homogenized further in subsequent work.
%\todo{OK: Symbols should be alphabetically listed also within each letter}
%\begin{longtable}[l]{|L{0.7in}|L{2.3in}|L{0.7in}|L{0.6in}|} \hline
\begin{longtable}[l]{L{0.4in}L{2.8in}L{0.9in}L{0.01in}}
%\begin{table}
%\begin{longtable}{cllc}
%\centering
\caption{Table of Symbols}
\label{tab:symbols}\\
%\begin{tabular}{cllc}
\hline
Symbol & Parameter & Unit & \\
\hline %--------------------------------------------------------------------------------------------------------------
\hline %--------------------------------------------------------------------------------------------------------------
\multicolumn{4}{l}{\textbf{Greek symbols}} \\
% --------------alpha----------------------
$\alpha$ & Biot coefficient & $\unit[]{-}$ & \\
$\alpha$ & Intergranular radius & $\unit[]{-}$ & \\
$\alpha$ & Thermal expansion coefficient & $\unit[]{K^{-1}}$ & \\
$\alpha$ & van Genuchten parameter & $\unit[]{m^{-1}}$ & \\
$\alpha_k$ & Kinetic isotope fractionation factor & $\unit[]{-}$ & \\
$\alpha_L$ & Longitudinal dispersion length & $\unit[]{m}$ & \\
%\rowcolor{red!50} % CAU Kiel
$\alpha_{Li}$ & Linear thermal expansion coefficient & $\unit[]{K^{-1}}$ & \\
$\alpha_{R}$ & Randomness factor & $\unit[]{-}$ & \\
$\alpha_{s}$ & Shrinkage and swelling coefficient & $\unit[]{-}$ & \\
$\alpha_T$ & Transversal dispersion length & $\unit[]{m}$ & \\
%\rowcolor{lightgray} % CAU Kiel
$\alpha_V$ & Volumetric thermal expansion coefficient & $\unit[]{K^{-1}}$ & \\
%-----------------beta---------------------
%\rowcolor{lightgray}
$\beta$ & Cubic thermal expansion coefficient & $\unit[]{K^{-1}}$ & \\
$\beta$ & fitting parameter & $\unit[]{-}$ & \\
$\beta_c$ & Burial constant & $\unit[]{-}$ & \\
$\beta^{\mathfrak{f}}$ & Fluid compressibility & $\unit[]{Pa^{-1}}$ & \\
%------------gamma------------------------
$\gamma$ & Activity coefficient for dissolved species & $\unit[]{-}$ & \\
%\rowcolor{red!50}
$\gamma$ & Dimensionless temperature & $\unit[]{-}$ & \\
$\gamma$ & Angle of inclination & $\unit[]{-}$ & \\
$\gamma_l$ & First-order degradation rate & $\unit[]{day^{-1}}$ & \\
$\Gamma$ & Domain boundary & $\unit[]{-}$ & \\
$\Gamma^{Fr}_-$ & Negative fracture surface domain & $\unit[]{m^2}$ & \\
$\Gamma^{Fr}_+$ & Positive fracture surface domain & $\unit[]{m^2}$ & \\
%-------------------delta------------------
$\delta$ & Dirac delta function & $\unit[]{-}$ & \\
$\delta$ & Fracture aperture & $\unit[]{m}$ & \\
$2\delta$ & Fracture width & $\unit[]{m}$ & \\
$\Delta$ & Half of aspect ratio & $\unit[]{-}$ & \\
$\Delta X$ & Change of quantity $X$ & $\unit[]{[X]}$ & \\
%------------------epsilon-----------------
$\epsilon$ & Error tolerance & $\unit[]{-}$ & \\
$\epsilon$ & Strain & $\unit[]{-}$ & \\
$\dot{\epsilon}$ & Strain rate & $\unit[]{s^{-1}}$ & \\
$\boldsymbol\epsilon$ & Strain tensor & $\unit[]{-}$ & \\
$\mbfs{\epsilon}_\mrm{el}$ & Elastic train tensor & $\unit[]{-}$ & \\
$\mbfs{\epsilon}_\mrm{pl}$ & Plastic train tensor & $\unit[]{-}$ & \\
%$\epsilon$ & Length scale & $\unit[]{m}$ & \\
%$\epsilon$ & Isotope enrichment factor & $\unit[]{-}$ & \\
%\rowcolor{lightgray} % CAU Kiel
$\epsilon_b$ & Element strain & $\unit[]{-}$ & \\
%\rowcolor{lightgray} % CAU Kiel
$\epsilon_{i,j,k,m}$ & Element strain alignment & $\unit[]{-}$ & \\
%\rowcolor{lightgray} % CAU Kiel
$\epsilon_f$ & Failure strain & $\unit[]{-}$ & \\
%\rowcolor{lightgray} % CAU Kiel
$\epsilon_\mrm{flex}$ & Flexural strain & $\unit[]{-}$ & \\
%\rowcolor{lightgray} % CAU Kiel
$\epsilon_p$ & Peak strain & $\unit[]{-}$ & \\
%\rowcolor{lightgray} % CAU Kiel
$\epsilon_{\mathbb{R}}$ & Continuum strain & $\unit[]{-}$ & \\
%\rowcolor{lightgray}
$\epsilon_v$ & Volume plastic strain & $\unit[]{-}$ & \\
%\rowcolor{lightgray} % CAU Kiel
$\epsilon_V$ & Volume strain & $\unit[]{-}$ & \\
%------------------varepsilon-----------------
%---------------zeta-----------
%--------------------eta--------
%\rowcolor{lightgray}
$\eta$ & Porosity & $\unit[]{-}$ & \\
$\eta^{\mathfrak{f}R}$ & Effective dynamic viscosity & $\unit[]{Pa \cdot s}$ & \\
%\rowcolor{cyan!50}
$\eta_\mathrm{M}$ & Maxwell viscosity & $\unit[]{Pa \cdot d}$ & \\
$\eta_\mathrm{K}$ & Kelvin viscosity & $\unit[]{Pa \cdot d}$ & \\
%-------------------------theta------------
$\theta^\ast$ & Apparent dip angle & $\unit[]{deg}$ & \\
$\theta^\ast_\mrm{max}$ & Maximum apparent dip angle & $\unit[]{deg}$ & \\
%-----------------iota------------------
%--------------kappa--------------------
$\kappa$ & Thermal conductivity & $\unit[]{W\cdot m^{-1}\,K^{-1}}$ & \\
%\rowcolor{lightgray} % CAU Kiel
$\kappa_{i,j}$ & Curvature strain & $\unit[]{-}$ & \\
%------------------lambda------------------
$\lambda$ & Lam\'e coefficients & $\unit[]{GPa}$ & \\
$\lambda$ & Plastic multiplier & $\unit[]{-}$ & \\
$\lambda$ & Thermal conductivity & $\unit[]{W\cdot m^{-1}\,K^{-1}}$ & \\
$\lambda_\mathsf{arith}$ & Arithmetic effective thermal conductivity & $\unit[]{W\cdot m^{-1}\,K^{-1}}$ & \\
$\lambda_b$ & Bulk thermal conductivity & $\unit[]{W\cdot m^{-1}\,K^{-1}}$ & \\
$\lambda_c$ & Virgin compression index & $\unit[]{-}$ & \\
$\lambda_\mathsf{eff}$ & Effective thermal conductivity & $\unit[]{W\cdot m^{-1}\,K^{-1}}$ & \\
%\rowcolor{cyan!50}
$\lambda_\mathsf{geom}$ & Geometric effective thermal conductivity & $\unit[]{W\cdot m^{-1}\,K^{-1}}$ & \\
$\lambda_\mathsf{harm}$ & Harmonic effective thermal conductivity & $\unit[]{W\cdot m^{-1}\,K^{-1}}$ & \\
$\lambda_p$ & Hardening parameter & $\unit[]{-}$ & \\
$\lambda_\mathsf{pm}$ & Thermal conductivity of porous medium & $\unit[]{W\cdot m^{-1}\,K^{-1}}$ & \\
$\lambda_s$ & Solid thermal conductivity & $\unit[]{W\cdot m^{-1}\,K^{-1}}$ & \\
%------------------my,mu---------------------
%\rowcolor{red!50}
$\mu$ & Lam\'{e} coefficient & $\unit[]{GPa}$ & \\
$\mu$ & Dynamic viscosity & $\unit[]{Pa\cdot s}$ & \\
$\mu_0$ & Reference dynamic viscosity & $\unit[]{Pa\cdot s}$ & \\
%-------------------ny,nu---------------------
$\nu$ & Poisson's ratio (Poisson number) & $\unit[]{-}$ & \\
%\rowcolor{pink!50} % CAU Kiel
$\nu_\text{dyn}$ & Dynamic Poisson's ratio & $\unit[]{-}$ & \\
%\rowcolor{lightgray} % CAU Kiel
$\nu_{f}^{k}$ & Kinematic fluid viscosity & $\unit[]{m^2\cdot s^{-1}}$ & \\
$\fourtens{{V}}_\mathrm{M}$ & Maxwell viscosity tensor & $\unit[]{Pa\cdot d}$ & \\
$\fourtens{{V}}_\mathrm{K}$ & Kelvin viscosity tensor & $\unit[]{Pa\cdot d}$ & \\
%--------------------xi---------------
%---------------omicron---------------------
%---------------------pi---------------
%------------------rho-----------------
%\arrayrulecolor{red}
\hline
$\rho$ & Electrical resistivity & $\unit[]{\Omega\cdot m}$ & \\
$\rho_{a}$ & Apparent electrical resistivity & $\unit[]{\Omega\cdot m}$ & \\
$\rho$ ($\varrho$) & Phase density & $\unit[]{kg\cdot m^{-3}}$ & \\
%\rowcolor{red!50} % CAU Kiel
$\rho^{\mathcal{f}}$ & Fluid density & $\unit[]{kg\cdot m^{-3}}$ & \\
%\rowcolor{red!50}
$\rho_{f}$ & Fluid density & $\unit[]{kg\cdot m^{-3}}$ & \\
$\rho^{\mathfrak{f}R}$ & Effective fluid density & $\unit[]{kg \cdot m^{-3}}$ & \\
$\rho_s$ & Density of solid & $\unit[]{kg\cdot m^{-3}}$ & \\
$\rho_w$ & Density of water & $\unit[]{kg\cdot m^{-3}}$ & \\
$\rho^s_d$ & Density of bentonite bulk & $\unit[]{kg\cdot m^{-3}}$ & \\
$\rho_0$ & Reference fluid density & $\unit[]{kg\cdot m^{-3}}$ & \\
%------------------varrho-----------------
$\varrho_\mrm{SR}$ & Real density of solid & $\unit[]{kg\cdot m^{-3}}$ & \\
$\varrho_\mrm{LR}$ & Real density of liquid & $\unit[]{kg\cdot m^{-3}}$ & \\
$\varrho_\mrm{IR}$ & Real density of ice & $\unit[]{kg\cdot m^{-3}}$ & \\
\hline
%\arrayrulecolor{black}
%---------------sigma---------------------
$\boldsymbol\sigma$ & Cauchy stress tensor & $\unit[]{Pa}$ & \\
$\sigma'$ & Effective stress & $\unit[]{Pa}$ & \\
$\sigma_a$ & Contact stress & $\unit[]{Pa}$ & \\
$\sigma_c$ & Critical stress & $\unit[]{Pa}$ & \\
$\sigma_c$ & Compressive strength & $\unit[]{Pa}$ & \\
$\sigma_\mathrm{con}$ & Confining stress & $\unit[]{Pa}$ & \\
%\rowcolor{lightgray} % CAU Kiel
$\sigma_\mathrm{dev}$ & Deviatoric stress & $\unit[]{Pa}$ & \\
$\sigma_\mathrm{eff}$ & Effective stress & $\unit[]{Pa}$ & \\
%\rowcolor{lightgray} % CAU Kiel
$\sigma_\mathrm{flex}$ & Flexural stress & $\unit[]{Pa}$ & \\
%\rowcolor{lightgray} % CAU Kiel
$\sigma_\mathrm{iso}$ & Isotropic stress & $\unit[]{Pa}$ & \\
$\sigma_\mathrm{loc}$ & Locally acting stress & $\unit[]{Pa}$ & \\
$\sigma_n$ & Normal stress & $\unit[]{Pa}$ & \\
%\rowcolor{lightgray} % CAU Kiel
$\sigma_{\mathbb{R}}$ & Continuum stress & $\unit[]{Pa}$ & \\
$\sigma^{sw}_\mathrm{max}$ & Tested maximum swelling stress & $\unit[]{Pa}$ & \\
%\rowcolor{lightgray} % CAU Kiel
$\sigma_\mathrm{sp}$ & Splitting stress & $\unit[]{Pa}$ & \\
$\sigma_t$ & Tensile strength & $\unit[]{Pa}$ & \\
$\sigma_{V}$ & von Mises equivalent stress & $\unit[]{Pa}$ & \\
%------------------tau-----------------
$\boldsymbol\tau$ & Shear stress tensor & $\unit[]{Pa}$ & \\
$\tau$ & Shear stress & $\unit[]{Pa}$ & \\
$\tau_p$ & Peak shear stress & $\unit[]{Pa}$ & \\
$\tau_r$ & Residual shear stress & $\unit[]{Pa}$ & \\
%--------------upsilon,ypsilon-----------
%------------------phi--------------------
$\phi$ & Porosity & $\unit[]{-}$ & \\
$\phi_{0}$ & Phase shift angle & $\unit[]{deg}$ & \\
$\phi$, ($\Phi$) & Friction angle & $\unit[]{deg}$ & \\
$\varphi_b$ & Basic friction angle & $\unit[]{deg}$ & \\
%---------------------chi------------------
$\chi$ & Bishop coefficient & $\unit[]{-}$ & \\
%--------------psi---------------------
$\psi$ & Dilatancy angle & $\unit[]{deg}$ & \\
$\psi$ & Strain energy density & $\unit[]{J\cdot m^{-3}}$ & \\
%\rowcolor{lightgray} % CAU Kiel
$\psi_\mathrm{total}$ & Total suction & $\unit[]{Pa}$ & \\
%-------------------omega------------------
$\omega$ & Intergranular thickness & $\unit[]{m}$ & \\
$\omega$ & Saturation index & $\unit[]{-}$ & \\
$\omega$ & Water content & $\unit[]{-}$ & \\
%
\hline
\multicolumn{4}{l}{\textbf{Roman symbols}} \\ %--------------------------------------------------------------------------------
\hline
%---a-A----------------
$a$ & Specific surface area & $\unit[]{m^2\cdot m^{-3}}$ & \\
$a$ & Grid constant & $\unit[]{m}$ & \\
%\rowcolor{lightgray} % CAU Kiel
$a_\mathrm{flex}$ & Flexural notch length & $\unit[]{m}$ & \\
%\rowcolor{lightgray} % CAU Kiel
$a_{h}$ & Hydraulic aperture & $\unit[]{m}$ & \\
$\dot{a}$ & Effective diameter of ion & $\unit[]{m}$ & \\
$a^{\sigma}$ & Activity of stressed solid & $\unit[]{-}$ & \\
$A$ & Surface area & $\unit[]{m^2}$ & \\
$A_0$ & Active surface area after Grasselli & $\unit[]{-}$ & \\
%\rowcolor{lightgray} % CAU Kiel
$A_{b}$ & Area of element & $\unit[]{m^2}$ & \\
\hline
%---b-B----------------
$b$ & Fracture aperture & $\unit[]{m}$ & \\
$\mbf{b}$ & Body force vector & $\unit[]{N}$ & \\
$b_0$ & Initial fracture aperture & $\unit[]{m}$ & \\
$b_h$ & Fracture hydraulic aperture & $\unit[]{m}$ & \\
$b_m$ & Fracture mechanical aperture & $\unit[]{m}$ & \\
$B_\mathrm{flex}$ & Flexural sample thickness & $\unit[]{m}$ & \\
\hline
%---c-C----------------
$c$ & Cohesion & $\unit[]{-}$ & \\
$c$ & Normalized concentration & $\unit[]{-}$ & \\
$c$ & Specific heat capacity of a cell & $\unit[]{J\cdot K^{-1}}$ & \\
$c_f$ & Specific fluid heat capacity & $\unit[]{J\cdot kg^{-1}\cdot K^{-1}}$ & \\
$c_{\mathcal{f}}$ & Speed of sound & $\unit[]{m\cdot s^{-1}}$ & \\
$c_p$ & Heat capacity & $\unit[]{J\cdot kg^{-1}\cdot K^{-1}}$ & \\
%
$C$ & Concentration & $\unit[]{kg\cdot m^{-3}}$ & \\
$C$ & Roughness after Grasselli & $\unit[]{-}$ & \\
$C_{eq}^h$ & Solubility under hydrostatic pressure & $\unit[]{mol\cdot m^{-3}}$ & \\
$C_i$ & Intergranular concentration & $\unit[]{mol\cdot m^{-3}}$ & \\
$C_{i,j,k,m}$ & Element stiffness matrix & $\unit[]{Pa}$ & \\
$C_p$ & Pore-space concentration & $\unit[]{mol\cdot m^{-3}}$ & \\
$Cp$ & Heat capacity & $\unit[]{J\cdot kg^{-1}\cdot K^{-1}}$ & \\
Cr & Courant number & $\unit[]{-}$ & \\
$C_{\mathbb{R}}$ & Continuum stiffness & $\unit[]{Pa}$ & \\
$\mathds{C}$ & Elasticity tensor & $\unit[]{Pa}$ & \\
\hline
%---d-D----------------
$d$ & Order parameter & $\unit[]{-}$ & \\
$d_{i,j}$ & Curvature stiffness & $\unit[]{Pa}$ & \\
$D$ & Diffusivity coefficient & $\unit[]{m^2\cdot s^{-1}}$ & \\
$D_\mathrm{cyl}$ & Diameter of cylindrical sample & $\unit[]{m}$ & \\
$D_f$ & Intergranular diffusion coefficient & $\unit[]{m^2\cdot s^{-1}}$ & \\
\hline
%---e-E----------------
$e$ & Void ratio & $\unit[]{-}$ & \\
$e_{0}$ & Initial void ratio & $\unit[]{-}$ & \\
$E$ & Young's modulus & $\unit[]{Pa}$ & \\
$E$ & Energy total & $\unit[]{J}$ & \\
$E_{b}$ & Element Young's modulus & $\unit[]{Pa}$ & \\
%\rowcolor{pink!50}
$E_\mathrm{dyn}$ & Dynamic Young's modulus & $\unit[]{Pa}$ & \\
$E_\mathrm{flex}$ & Flexural Young's modulus & $\unit[]{Pa}$ & \\
\hline
%---f-F----------------
$f_\mathrm{flex}$ & Flexural force & $\unit[]{N}$ & \\
$f_{p}$ & Peak axial load & $\unit[]{N}$ & \\
$f_\mathrm{sp}$ & Splitting force & $\unit[]{N}$ & \\
$f_{x}$ & Axial force & $\unit[]{N}$ & \\
$f_{y}$ & Shear force & $\unit[]{N}$ & \\
%
$F_{b}$ & Element forces & $\unit[]{N}$ & \\
$F_n$ & Normal force & $\unit[]{N}$ & \\
$F_\mathrm{shear}$ & Shear-off force & $\unit[]{N}$ & \\
$F_\mathrm{slide}$ & Sliding force & $\unit[]{N}$ & \\
\hline
%---g-G----------------
$g$ & Gravitational coefficient & $\unit[]{m\cdot s^{-2}}$ & \\
$g$ & Plastic potential & $\unit[]{J}$ & \\
$\mathbf g$ & Gravity vector & $\unit[]{m\cdot s^{-2}}$ & \\
$\mathbf{g}$ & Gravitational acceleration & $\unit[]{m\cdot s^{-2}}$ & \\
$g_c$ & Fracture toughness & $\unit[]{N\cdot m^{-1}}$ & \\
%
$G$ & Gibbs energy & $\unit[]{J}$ & \\
$G$ & Gibbs energy & $\unit[]{J\cdot mol^{-1}}$ & \\
$G$ & Shear modulus & $\unit[]{Pa}$ & \\
$G_{b}$ & Element shear modulus & $\unit[]{Pa}$ & \\
$G_{c}$ & Fracture toughness & $\unit[]{Pa \cdot m}$ & \\
%\rowcolor{pink!50} % CAU Kiel
$G_\mathrm{dyn}$ & Dynamic shear modulus & $\unit[]{Pa}$ & \\
$G_\mathrm{F}$ & Plastic potential & $\unit[]{J}$ & \\
$G_\mathrm{M}$ & Maxwell shear modulus & $\unit[]{-}$ & \\
$G_\mathrm{K}$ & Kelvin shear modulus & $\unit[]{-}$ & \\
$G_{s}$ & Specific gravity & $\unit[]{kg \cdot m^{-3}}$ & \\
\hline
%---h-H----------------
$H$ & Fault height & $\unit[]{m}$ & \\
$H_{\text{PW}}$ & Pipe water level & $\unit[]{m}$ & \\
$h$ & Hardening parameter & $\unit[]{-}$ & \\
$h$ & Height of sample & $\unit[]{m}$ & \\
%\rowcolor{lightgray} % CAU Kiel
$h_b$ & Thermal conductance & $\unit[]{W \cdot K^{-1}}$ & \\
$h_c$ & Thickness of colmation layer & $\unit[]{m}$ & \\
$h_f$ & Freshwater hydraulic head & $\unit[]{m}$ & \\
$h_s$ & Saltwater hydraulic head & $\unit[]{m}$ & \\
$\triangle h_\mrm{I}$ & Specific enthalpy of fusion & $\unit[]{J}$ & \\
\hline
%---i-I----------------
$I$ & Ionic strength & $\unit[]{-}$ & \\
$\boldsymbol{I}$ & Identity tensor & $\unit[]{-}$ & \\
$I(L)$ & intensity values of X-rays & $\unit[]{-}$ & \\
$I_1$ & First principal invariant of the stress tensor $\unit[]{Pa}$ & \\
$I_{b}$ & Element moment of inertia & $\unit[]{kg.m^2}$ & \\
%$I_r$ & Friction slope & $\unit[]{-}$ & \\
%$I_s$ & Bottom slope & $\unit[]{-}$ & \\
\hline
%---j-J----------------
$\textbf{J}_f$ & Fluid mass flux & $\unit[]{kg\cdot m^{-3}\cdot s{-1}}$ & \\
$J_2$ & Second principal invariant of deviatoric stress tensor & $\unit[]{Pa^2}$ & \\
$J_3$ & Third principal invariant of deviatoric stress tensor & $\unit[]{Pa^3}$ & \\
$JCS$ & Joint wall compressive strength & $\unit[]{Pa}$ & \\
$JRC$ & Joint roughness coefficient & $\unit[]{-}$ & \\
\hline
%---k-K----------------
$k$ & Residual stiffness parameter & $\unit[]{-}$ & \\
$\mathbf k$ & Permeability tensor & $\unit[]{m^2}$ & \\
%\rowcolor{red!50} % CAU Kiel
$k_b$ & Thermal conductivity & $\unit[]{W \cdot K^{-1} \cdot m^{-1}}$ & \\
$k_c$ & Swelling/recompression index & $\unit[]{-}$ & \\
%\rowcolor{lightgray} % CAU Kiel
$k_h$ & Hydraulic conductivity & $\unit[]{m^1.s^{-1}}$ & \\
%\rowcolor{cyan!50}
$k^\mathfrak{s}_{Fr}$ & Local fracture permeability & $\unit[]{m^2}$ & \\
%\rowcolor{cyan!50}
$k^\mathfrak{s}_{Fr,t}$ & Local transversal fracture permeability & $\unit[]{m^2}$ & \\
$k_\text{perp}$ & Permeability perpendicular to the bedding plane & $\unit[]{m^2}$ & \\
$k_\text{parallel}$ & Permeability parallel to the bedding plane & $\unit[]{m^2}$ & \\
$k_\text{rel}$ & Relative permeability & $\unit[]{-}$ & \\
$k^+$ & Dissolution rate constant & $\unit[]{mol\cdot m^-2\cdot s^{-1}}$ & \\
$k^{\circ{}}$ & Reaction rate constant & $\unit[]{mol\cdot m^-2\cdot s^{-1}}$ & \\
%
%\rowcolor{red!50} % CAU Kiel
$K_\text{eff}$ & Effective thermal conductivity & $\unit[]{W\cdot K^{-1}\cdot m^{-1}}$ & \\
$K_\mathrm{eq}$ & Equilibrium constant & $\unit[]{-}$ & \\
%\rowcolor{red!50}
$K_{f}$ & Fluids bulk modulus & $\unit[]{Pa}$ & \\
$K^\mathfrak{f}$ & Fluid bulk modulus & $\unit[]{Pa}$ & \\
$K^\mathcal{f}$ & Fluid bulk modulus & $\unit[]{Pa}$ & \\
$K_I$ & Fracture toughness & $\unit[]{Pa \cdot m^{0.5}}$ & \\
$K_{I}$ & Stress intensity factor & $\unit[]{Pa \cdot m^{0.5}}$ & \\
%\rowcolor{red!50} % CAU Kiel
$K_{Ic}$ & Fracture toughness & $\unit[]{Pa \cdot m^{0.5}}$ & \\
$K_\mathrm{M}$ & Maxwell bulk modulus & $\unit[]{-}$ & \\
$K_\mathrm{n}$ & Normal stiffness & $\unit[]{Pa \cdot m^{-1}}$ & \\
$K_\mathrm{s}$ & Shear stiffness & $\unit[]{Pa \cdot m^{-1}}$ & \\
$K_s$ & Saturated hydraulic conductivity & $\unit[]{m\cdot d^{-1}}$ & \\
$K_{s}$ & Solids bulk modulus & $\unit[]{Pa}$ & \\
\hline
%---l-L----------------
$\ell$ & Regularization length & $\unit[]{m}$ & \\
$\ell_c$ & Internal length of continuum & $\unit[]{m}$ & \\
$L_{b}$ & Element length & $\unit[]{m}$ & \\
$L_b^\prime$ & Element contact length & $\unit[]{m}$ & \\
$L_\mathrm{cyl}$ & Length of cylindrical sample & $\unit[]{m}$ & \\
\hline
%---m-M----------------
$m$ & Mass & $\unit[]{kg}$ & \\
$m$ & Fitting parameter & $\unit[]{-}$ & \\
$m$ & Van Genuchten parameter & $\unit[]{-}$ & \\
$M$ & Kinetic coefficient & $\unit[]{mm^2\cdot N^{-1}\cdot s^{-1}}$ & \\
$M$ & Slope of critical state line & $\unit[]{-}$ & \\
$M_{b}$ & Element moment & $\unit[]{N.m}$ & \\
$M_w$ & Molecular mass of water vapor & $\unit[18.016]{g\cdot mol^{-1}}$ & \\
\hline
%---n-N----------------
$n$ & Porosity & $\unit[]{m^3\cdot m^{-3}}$ & \\
$n$ & van Genuchten parameter & $\unit[]{-}$ & \\
$n_{i,j,k,m}$ & Element alignment & $\unit[]{-}$ & \\
$\mathbf{n}$ & Normal of fracture surface & $\unit[]{-}$ & \\
$\mathbf{n}^+$ & Normal of positive fracture surface & $\unit[]{-}$ & \\
$\mathbf{n}^-$ & Normal of negative fracture surface & $\unit[]{-}$ & \\
$N_{b}$ & Element's total number of bonds & $\unit[]{-}$ & \\
$N_{c}$ & Number of Voronoi cells in the boundary & $\unit[]{-}$ & \\
%---o-O----------------
\hline
%---p-P----------------
$p, P$ & Pressure [$\unit[]{Pa}$] & $\unit[]{kg\cdot s^{-1}\cdot m^{-1}}$ & \\
$p_s$ & Mean stress & $\unit[]{Pa}$ & \\
$p_\mathrm{scn}$ & Isotropic pre-consolidation pressure & $\unit[]{Pa}$ & \\
$p^+$ & Fluid pressure at positive fracture surface & $\unit[]{Pa}$ & \\
$p^-$ & Fluid pressure at negative fracture surface & $\unit[]{Pa}$ & \\
%
$P$ & Load & $\unit[]{Pa}$ & \\
$P_c$ & Capillary pressure & $\unit[]{Pa}$ & \\
$P_d$ & air entry pressure & $\unit[]{Pa}$ & \\
$P_\mathfrak{f}$ & Averaged fluid pressure & $\unit[]{Pa}$ & \\
$P_{vap}$ & Vapor pressure & $\unit[]{Pa}$ & \\
Pe & P\'{e}clet number & $\unit[]{-}$ & \\
\hline
%---q-Q----------------
$q$ & Source/sink term & $\unit[]{-}$ & \\
$q$ & Shear stress & $\unit[]{Pa}$ & \\
$q$ & Heat source & $\unit[]{W}$ & \\
$q$ & Darcy velocity & $\unit[]{m\cdot s^{-1}}$ & \\
$\mathbf q$ & Darcy velocity vector & $\unit[]{m\cdot s^{-1}}$ & \\
$\dot{q}$ & Heat density & $\unit[]{W\cdot kg^{-1}}$ & \\
$q_\text{ave}$ & Average Heat flux & $\unit[]{W\cdot m^{-2}}$ & \\
%\rowcolor{red!50} % CAU Kiel
$q_{b}$ & Heat flow & $\unit[]{W}$ & \\
$q_\text{cell}^b$ & Heat flow from boundary Voronoi cells & $\unit[]{W}$ & \\
$q_\text{lk}$ & Leak-off & $\unit[]{Pa\cdot s^{-1}}$ & \\
$q_\mathsf{T}$ & Heat flux through unit area & $\unit[]{W\cdot m^{-2}}$ & \\
$Q$ & Ion activity product & $\unit[]{-}$ & \\
$Q_{\text{leak}}$ & Leakage flow & $\unit[]{m^3\cdot s^{-1}}$ & \\
$Q_{\omega}$ & Source/sink term & $\unit[]{kg\cdot m^{-3}\cdot s{-1}}$ & \\
$Q_{f}$ & Source/sink term & $\unit[]{kg\cdot m^{-3}\cdot s{-1}}$ & \\
\hline
%---r-R----------------
$R$ & Universal gas constant ($\unit[8.31432]{}$) & $\unit[]{J\cdot mol^{-1}\cdot K^{-1}}$ & \\
$R$ & Transformation matrix & $\unit[]{-}$ & \\
$R_c$ & Contact area ratio & $\unit[]{-}$ & \\
$R_{h}^b$ & Hydraulic resistance & $\unit[]{s^{-1}}$ & \\
$(R)^{\prime}$ & First stiffness coefficient & $\unit[]{Pa}$ & \\
$(R)^{\prime\prime}$ & Second stiffness coefficient & $\unit[]{Pa}$ & \\
$\mathrm{Ra}$ & Rayleigh number & $\unit{-}$ & \\
$\mathrm{Ra}_\mathrm{crit}$ & Critical Rayleigh number & $\unit{-}$ & \\
\hline
%---s-S----------------
$s$ & Soil suction & $\unit[]{kPa}$ & \\
$S$ & Saturation & $\unit[]{-}$ & \\
$S$ & Storage & $\unit[]{Pa^{-1}}$ & \\
$S_e$ & Effective saturation & $\unit[]{-}$ & \\
$S_\text{eff}$ & Effective saturation & $\unit[]{-}$ & \\
$S_\text{flex}$ & Flexural sample span & $\unit[]{m}$ & \\
$S_\text{max}$ & Maximum water saturation & $\unit[]{-}$ & \\
$Sr$ & Saturation degree & $\unit[]{-}$ & \\
$S_r$ & Residual saturation & $\unit[]{-}$ & \\
$S_r$ & Residual water saturation & $\unit[]{-}$ & \\
$SA$ & Reactive surface area & $\unit[]{m^2}$ & \\
\hline
%---t-T----------------
$t$ & Time & $\unit[]{s}$ & \\
$\mathbf{t}$ & Traction force vector & $\unit[]{N}$ & \\
$\mathbf{t}_c$ & Traction force vector at interface & $\unit[]{N}$ & \\
$T$ & Temperature & $\unit[]{K}$ & \\
$T$ & Period & $\unit[]{d}$ & \\
$T_{tot}$ & total simulation time & $\unit[]{d}$ & \\
$T_c$ & Top temperature (cold) & $\unit[]{K}$ & \\
$T_h$ & Bottom temperature (hot) & $\unit[]{K}$ & \\
$T_\text{iso}$ & Isotropic thermal loading & $\unit[]{K}$ & \\
$T_\mathrm{init}$ & Initial temperature & $\unit[]{K}$ & \\
$T_v$ & Approximation temperature & $\unit[]{K}$ & \\
\hline
%---u-U----------------
$u$ & Displacement & $\unit[]{m}$ & \\
$\mathbf u$ & Displacement vector & $\unit[]{m}$ & \\
$u_{b}$ & Element displacement & $\unit[]{m}$ & \\
$u_n$ & Normal displacement & $\unit[]{m}$ & \\
$u_s$ & Shear displacement & $\unit[]{m}$ & \\
$U_a^b$ & Axial strain energy & $\unit[]{N\cdot m}$ & \\
$U_\text{cell}$ & Cell strain energy & $\unit[]{N\cdot m}$ & \\
$U_m^b$ & Moment strain energy & $\unit[]{N\cdot m}$ & \\
$U_{\mathbb{R}}$ & Continuum strain energy & $\unit[]{N\cdot m}$ & \\
$U_s^b$ & Shear strain energy & $\unit[]{N\cdot m}$ & \\
$U_t^b$ & Total stored strain energy & $\unit[]{N\cdot m}$ & \\
\hline
%---v-V----------------
%\rowcolor{lightgray} % CAU Kiel
$v$ & Volume of a Voronoi cell & $\unit[]{m^3}$ & \\
$\mathbf v$ & Velocity vector & $\unit[]{m\cdot s^{-1}}$ & \\
$v_p, v_s$ & Ultrasonic velocities (p-s wave related) & $\unit[]{m\cdot s^{-1}}$ & \\
%
$V$ & Volume & $\unit[]{m^3}$ & \\
$V_\text{cav}$ & Volume of the cavity & $\unit[]{m^3}$ & \\
$V_m$ & Molar volume & $\unit[]{m^3\cdot mol^{-1}}$ & \\
$V_\text{mol}$ & Molecular volume & $\unit[]{m^3}$ & \\
$V_{\mathbb{R}}$ & Continuum volume & $\unit[]{m^3}$ & \\
$V_u$ & Cell volume & $\unit[]{m^3}$ & \\
\hline
%---w-W----------------
$w$ & Margules parameter & $\unit[]{J\cdot mol^{-1}}$ & \\
$w_a$ & Test function of auxiliary element & $\unit[]{-}$ & \\
$\mathbf{w}_\mathfrak{f}$ & Relative fluid velocity & $\unit[]{m \cdot s^{-1}}$ & \\
$\mathbf{w}^-_\mathfrak{f}$ & Relative fluid velocity positive fracture surface & $\unit[]{m \cdot s^{-1}}$ & \\
$\mathbf{w}^+_\mathfrak{f}$ & Relative fluid velocity negative fracture surface& $\unit[]{m \cdot s^{-1}}$ & \\
$\mathbf{w}^l_\mathfrak{f}$ & Relative longitudinal fluid velocity & $\unit[]{m \cdot s^{-1}}$ & \\
$\mathbf{w}^t_\mathfrak{f}$ & Relative transversal fluid velocity & $\unit[]{m \cdot s^{-1}}$ & \\
%
$W$ & SPH kernel function & $\unit[]{}$ & \\
$\mathbf{W}_\mathfrak{f}$ & Averaged relative fluid velocity & $\unit[]{m\cdot s^{-1}}$ & \\
$W_\text{flex}$ & Flexural sample width & $\unit[]{m}$ & \\
\hline
%---x-X----------------
%\rowcolor{lightgray} % CAU Kiel
$\mathbf{x}$ & Position vector & $\unit[]{m}$ & \\
$\hat{x}_\text{cell}$ & Relative coordinates & $\unit[]{m}$ & \\
$X$ & Molar fraction & $\unit[]{-}$ & \\
%---y-Y----------------
\hline
%---z-Z----------------
$Z$ & Ionic charge & $\unit[]{-}$ & \\
\hline
\hline
\multicolumn{4}{l}{\textbf{Indices}} \\ %--------------------------------------------------------------------------------------
$_{||}$ & Co-linear direction & & \\
$_{\bot}$ & Orthogonal direction & & \\
%\rowcolor{cyan!50}
$+$ & Positive fracture surface & & \\
%\rowcolor{cyan!50}
$-$ & Negative fracture surface & & \\
%$_\mrm{\parallel}$ & Parallel to the plane of isotropy & & \\
%$_\mrm{\bot}$ & Normal to the plane of isotropy & & \\
$e$ & Efficient value & & \\
$f$ & Fluid phase & & \\
$f$ & Fracture & & \\
$l$ & Longitudinal fracture direction & & \\
$R$ & Effective Value & & \\
$s$ & Solid phase & & \\
$t$ & Transversal fracture direction & & \\
$w$ & Water & & \\
$0$ & Reference value & & \\
\hline
\hline
\multicolumn{4}{l}{\textbf{Operators}} \\ %------------------------------------------------------------------------------------
div, $\nabla\cdot$ & Divergence operator & & \\
grad, $\nabla$ & Nabla, gradient operator & & \\
tr & Trace & & \\
\hline
%\end{tabular}
\end{longtable}
%
%\todo{MW: with a unit of m/s, the second \textbf{k} (Permeability tensor) should be called ``hydraulic conductivity tensor''.}
%