Permeability in interfaces

PLAXIS 2D 2017 and PLAXIS 3D 2017 have has several new features. One of them is permeability in interfaces. In previous versions, interface elements could be either impermeable or fully permeable in groundwater flow, consolidation and fully coupled flow-deformation analyses. This allows for blocking the flow through walls, plates or tunnel linings since plates by themselves are fully permeable in PLAXIS. However, several applications may require semi-permeable interfaces that allow for some water to pass the structure. Moreover, interfaces may also contribute to groundwater flow in the interface longitudinal (parallel) direction. In this way, they act as ‘drains’ with a certain drainage capacity.

Hydraulic properties of interfaces

The hydraulic conductivity or resistance of interfaces is not only defined by permeability, but also by the ‘thickness’ of the structure or the soil-structure interaction zone. However, this ‘thickness’ is not always a well-defined quantity. Therefore, the hydraulic properties of interfaces are defined by two quantities that have a well-defined meaning:

• Hydraulic resistance: to define the hydraulic conductivity across the interface or structure
• Drainage conductivity: to define the hydraulic conductivity in the interface longitudinal direction

Figure 1. Interface permeability parameters: left hydraulic conductivity across
the interface (d/k) for flow normal to the interface, right: hydraulic conductivity
in the interface longitudinal direction (d·k) for flow parallel to the interface.

Considering a semi-permeable wall with a thickness d and permeability k, the hydraulic resistance is defined by d/k, expressed in the unit of time. Considering Darcy’s law, q = k dφ/dl, where k is the cross permeability and dφ/dl is the gradient of the groundwater head across the wall, which is the difference between the groundwater head left and right of the wall over the wall thickness (Δφ/d). Hence, for a given hydraulic resistance d/k, the specific discharge q = k Δφ/d = Δφ/ (d/k). In order to determine d/k, one needs to measure the average discharge q through a wall (per unit of area) for a given head difference Δφ, so d/k = Δφ / q

Considering a semi-permeable gap with a thickness d and permeability k between two impermeable media, the drainage conductivity is defined by the product of d and k (d·k), expressed in the unit of volume per unit of time per unit of width in the out-of-plane direction. This quantity defines the total amount of water that is transported through the gap (drain) per unit of time per unit width. Considering Darcy’s law, as listed above, the gradient is now defined by the difference in groundwater head over the length of the gap (in longitudinal direction) divided by the gap length, such that q = k Δφ / L. The total amount of water Q is q times the thickness d times the unit width b, where b = 1 length unit for a plane strain application, so Q/b = d k Δφ / L. In order to determine d·k, one needs to measure the total discharge Q/b through the gap (per unit of width in the out-of-plane direction) for a given head difference Δφ and a given length of the gap L, such that d·k = Q/b * L / Δφ.

Note that, neither for the hydraulic resistance nor for the drainage conductivity, the actual thickness d and permeability k really matter.