INTEC2

INTEC2

Description

Constitutive law of longitudinal and transversal flow in porous media for a interface element (FAIL2B or FAIN2B)

The model

This law is only used for non linear analysis of longitudinal seepage in porous media interface element.
The case of free surface seepage is also treated.
Transversal fluid transfer between the bodies depends upon the contact state.

Contact occurs (pression non zero) fluid transfer is computed according the transverse transmissivity $T_{t\_c}$.
Contact does not occur, fluid transfer is computed by convection with transverse transmissivity $T_{t\_nc}$.
In this case, the outside pressure is the following one:
- INDIC = 1 always the atmosphere pressure
- INDIC = 0 if the normal to the structure intersects one segment, this segment pressure is chosen; otherwise, the atmosphere pressure is used
- INDIC = 2 if the normal to the structure intersects one segment, this segment pressure is chosen; otherwise, no flux is computed (interest if 2 layers of contact element exist)

Files

Prepro: LINTEC.F
Lagamine: INTEC2.F

Availability

Plane stress state	YES
Plane strain state	YES
Axisymmetric state	YES
3D state	NO
Generalized plane state	YES

Input file

Parameters defining the type of constitutive law

Line 1 (2I5, 60A1)
IL	Law number
ITYPE	117
COMMENT	Any comment (up to 60 characters) that will be reproduced on the output listing

Integer parameters

Line 1 (4I5)
INDIC	= 0, 1, 2 to define the outside pressure used in case of no contact (see The model)
IKE	index of the longitudinal permeability formulation :
	= 0 → $k_l = k_{l0}$.
	= 1 → $k_l = f(d) = \frac{\left(D_0 + V\right)^{exp}}{12} = \frac{d^{exp}}{12}$.
ITR	index of transmissivity:
	= 0 if FAIL2 element;
	= 1 if FAIN2 element.
IDDL	DDL number (3 = water, 4 = air, 5 = temperature), only for the case NTANA=5 and FAIL2 element. If NTANA $\neq$ 5 or FAIN2 element, IDDL is always equal to 3 (Default value).

Real parameters

The longitudinal permeability $k$ is an intrinsic permeability $\left(\left[L^2\right]\right)$
($K_l$ is the permeability coefficient $(\left[LT^{-1}\right])$ \[ k_{f,intrinsic} = K_l \frac{\mu_f}{\rho_f g} \\ \left[ L^2 \right] = \left[ LT^{-1} \right] \frac{ \left[ ML^{-1}T^{-1}\right]}{\left[ML^{-3}\right]\left[LT^{-2}\right]} \]

Line 1 (7G10.0)
PERMEA	fault longitudinal intrinsic permeability (=$k_{l0}$)
RHO	specific mass of the fluid (=$\rho_f$)
POROS	fault porosity (=$n_0$)
EMMAG	storage coefficient (=$C_p$)
ALPHA	$\alpha$ * parameter used to
BETA	$\beta$ * define the curve $\theta = \theta(p)$
VISCO	fluid dynamic viscosity ($\mu_f=10^{-3}$=default value for water at 20°C)
Line 2 (6G10.0)
THCON	fault transverse transmissivity ($T_{t\_c}$) when contact occurs
CONVEC	fault transverse transmissivitty ($T_{t\_nc}$) when contact does not occur
PAMB	atmosphere pressure
D0	maximal fault closure in absolute value (correspond to D0 from INTME2 mechanical law) for formulation (IKE=1)
EXP	exponent (=$exp$) = 2 for cubic law
EPAIS	fault thickness (useful only if no Goodman's formulation in mechanical law)

The longitudinal permeability of the fault is computed according to IKE value :

IKE = 0 : $ k_{long} $ = PERMEA
IKE = 1 : $ k_{long} = (D0 + V)^{EXP} = d^{EXP} $
where $V$ is the fault closure computed by the mechanical law and $d = D0+V$ represents the actual fault opening.
In this case, the INTME2 mechanical parameters $(D0, \gamma, K_n\ \text{and}\ \sigma’)$ are linked with the hydraulic parameter $k_{long}$: \[ \begin{array}{l} V = D_0\left[ \sqrt[1-\gamma]{\left( \frac{(1-\gamma)}{D_0K_n}\sigma’ + 1\right)}-1\right] \\ d = \sqrt{12 k_{long}} \\ d-V = D_0 \end{array}\] The knowledge of four parameters is sufficient to determine the fifth parameter.

The evolution of the stored fluid volume ($\theta$) with the fluid pressure ($p$) is given by the following functions:

in case of seepage with free surface: \[ \theta = n_0 \left( \frac{1}{\pi} \arctan\left(\frac{p-\beta}{\alpha}\right) +\frac{1}{2}\right) + C_p^* \left(p-\beta\right)\] with $C_P^* = C_p$ below the free surface
and $C_P^* = 0$ above the free surface
in absence of free surface: \[n = n_0 + C_p\]

Stresses

Number of stresses

= 3 : if FAIL2 element
= 4 : if FAIN2D element

Meaning

SIG(1)	longitudinal flow in the interface element
SIG(2)	fluid flow stored as a consequence of the evolution of soil porosity
SIG(3)	1st transversal fluid flow in the interface element
SIG(4)	2nd transversal fluid flow in the interface element (only if FAIN2)

State variables

Number of state variables

List of state variables

Q(1)	for FAIN2 element: pore pressure inside the fault
Q(1)	for FAIL2 element: 0
Q(2)	intrinsic longitudinal permeability $(=k_{long})$
Q(3)	transverse transmissivity $(T_{t\_c}\ \text{or}\ T_{t\_nc})$

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