Infiltration (hydrogeology)

Infiltration refers to the process of precipitation penetrating the soil ; it is an important part of the water cycle . Connection processes can be the formation of new groundwater and the formation of runoff . The amount of infiltration is measured in units of millimeters per second or, more conveniently, per minute .

The introduction of surface water into the subsoil via water management systems is called seepage , or in the case of polluted seepage water, also called trickling .

introduction

The infiltration is significantly influenced by two forces, gravity and capillarity or the matrix potential . Other decisive influencing factors are the temperature in the soil, the water saturation of the soil (pre-moisture), the degree of coverage (vegetation) and the intensity of precipitation. Sandy soils (63 µm - 2 mm grain size) with relatively large, well-connected pores and a large pore volume (30–45%) have the highest infiltration rates. Since a vegetation cover dampens the impact of raindrops, it effectively prevents the superficial silting up of pores and creates additional, well-water-conducting, coarse pores through your root network. It thus has a clearly positive influence on the infiltration properties of a soil (the highest infiltration rates can be recorded in forest soils).

Measurement

The potential infiltration is measured using a so-called infiltrometer. This is usually a ring with a defined cross-section, which is pierced into the ground and then filled with water up to a defined height.

Ring infiltrometer

Since the filled water volume is known via the filling height and the ring diameter, the potential infiltration (infiltration with maximum water availability) can be determined over the time that elapses until all the water has seeped out of the ring.

Double ring infiltrometer

By using double ring infiltrometers, an attempt is made to minimize lateral loss of seepage water, which would lead to higher infiltration rates when measured. With the double ring infiltrometer, only the inner volume is considered for measurement.

Out

${\displaystyle f(t)=-{\frac {dh(t)}{dt}}={\frac {Q(t)}{A}}}$

follows according to Darcy's law :

${\displaystyle k_{f}={\frac {l}{t}}={\frac {h(0)}{h(t)}}}$

With:

${\displaystyle k_{f}}$: Permeability coefficient [ ]; ${\displaystyle cms^{-1}}$

${\displaystyle l}$: Length of the flow path [ cm ];

${\displaystyle t}$: Time until the initial water level has dropped to the water level at time t ( ); ${\displaystyle h(0)}$ ${\displaystyle h(t)}$

${\displaystyle h(0)}$: Initial water level at time t = 0;

${\displaystyle h(t)}$: Final water level at time t

Estimate the actual infiltration

Estimation of the water balance

If all other parameters are known, the infiltration F can be calculated as the remainder of the water balance equation.

${\displaystyle F=B_{I}+P-T-ET-S-R-I_{A}-B_{O}\!\,}$

With:

Q : infiltration

${\displaystyle B_{I}}$: Edge inflow (underground or surface inflow into the system under consideration)

${\displaystyle B_{O}}$: Edge discharge (underground or above-ground discharge from the system)

P : precipitation

ET : evapotranspiration

S : memory

${\displaystyle I_{A}}$: short-term superficial retention (e.g. depression retention)

R : surface runoff

Depending on the assessment of the local conditions, this equation can also be simplified by individual terms.

Green Ampt infiltration model

The Green-Ampt infiltration model according to Green and Ampt offers an estimate of the actual infiltration taking into account various soil parameters, such as: suction tension, porosity, hydraulic conductivity and the soil-independent parameter time. The semi-physical formula approximates the infiltration process through a step profile with complete water saturation and the so-called transport zone. Only the water-saturated part of the soil is considered ( constant). The formula is derived from the Darcy-Weisbach equation , whereby the principle is based on the so-called gradient method. At the beginning there is a high suction tension ( matrix potential ), which becomes weaker over time. ${\displaystyle k_{f}}$

${\displaystyle \int _{0}^{F(t)}{1-\psi \,\Delta \theta \over F+\psi \,\Delta \theta }\,dF=\int _{0}^{t}K\,dt}$

With:

${\displaystyle \psi }$: Suction tension at the moisture front;

${\displaystyle \theta }$: Water content (pre-moisture);

${\displaystyle K}$: hydraulic conductivity;

${\displaystyle F}$: Accumulated volume of infiltrated water.

By integration, the equation can be solved either for the infiltration volume or for the initial infiltration rate.

${\displaystyle F(t)=Kt+\psi \,\Delta \theta \ln \left[1+{F(t) \over \psi \,\Delta \theta }\right]}$

${\displaystyle f(t)=K\left[{\psi \,\Delta \theta \over F(t)}+1\right]}$

Model after Horton

The initial infiltration value applies at the beginning of the infiltration process. With increasing duration, its effect is reduced and the final infiltration value is reached . The model describes an exponential decrease in the infiltration rate up to the final infiltration rate when the soil is saturated. ${\displaystyle f_{0}}$ ${\displaystyle f_{\infty }}$

${\displaystyle f(t)=f_{\infty }+(f_{0}-f_{\infty })\cdot e^{-k\cdot t}\!\,}$.

With:

${\displaystyle f_{0}}$: Initial infiltration rate ( ); ${\displaystyle t=0}$

${\displaystyle f(t)}$: Max. Infiltration rate at time t [ ]; ${\displaystyle mm*h^{-1}}$

${\displaystyle f_{\infty }}$: Max. Infiltration rate at saturation (t → ); ${\displaystyle \infty }$

${\displaystyle k}$: Constant of decline;

Similar to the Green and Ampt model, the Horton model also has a component that describes the decrease in the infiltration rate and one that takes into account the constant part. The infiltration rate never becomes 0, but approaches an end value that depends on the gravitational potential. This final value should theoretically be equal to the saturated hydraulic conductivity , which Green-Ampt uses explicitly for this purpose (for ). The model parameters for Horton are generally estimated; for bare, fine sandy clay or for grassy soil: ${\displaystyle k_{f}}$ ${\displaystyle f_{\infty }=k_{f}}$

parameter	volume	Grass floor
${\displaystyle f_{0}}$	210 mm / h	900 mm / h
${\displaystyle f_{\infty }}$	2 mm / h	290 mm / h
k	0.8 / min	2 / min

Other models

Other popular models are:

Model after Kostiakov

Empirical model

${\displaystyle f(t)=akt^{a-1}\!}$

With:

${\displaystyle a}$

${\displaystyle k}$ as empirical parameters.

literature

• Siegfried Dyck, Gerd Peschke: Fundamentals of hydrology. 3rd heavily edited edition. Verlag für Bauwesen, Berlin 1995, ISBN 3-345-00586-7 .