The solutions exist for confined, unconfined and confinedunconfined aquifers including homogeneous, multilayered or areallyheterogeneous aquifers. The solutions can include infiltration and account for different aquifer properties on the two sides of a drain. Constant head boundary is assumed at R distance from a drain. Additionally there is possibility of assigning Constant Flow boundary or NoFlow boundary for confined and unconfined conditions.
This dialog window assists in calculation of total inflow to a drain as well as inflows from each side. All parameters have to be assigned for the left and the right sides of a drain.
"Trench" tab of "Inflow to a trench" dialog box: unconfined homogeneous aquifer, confined multilayer aquifer and confined aquifer with Flow boundary
Explanatory table
"Aquifer" list

Selects the aquifer regime: "Confined", "Unconfined", "Confinedunconfined"

"ε1, m/day" and "ε2, m/day" text box

Recharge rate for the left (1) and the right (2) sides of an aquifer. This option is disabled for confinedunconfined aquifers

"m1, m/day" and "m2, m/day" text box

Thickness of aquifer (1) on the left and (2) the right side. This option is disabled for multilayered aquifers. The fields do not exist for homogeneous unconfined aquifers

"H1, m" and "H2, m" text box

Constant Hydraulic Heads (1) on the left and (2) the right boundaries. The values are calculated from the aquifer bottom and correspond to unimpacted piezometric levels in the aquifer far from a drain. These fields are disabled when the options "Boundary" or "Flow" are selected

"q1, m^2/day" and "q2, m^2/day" text box

Additional (regional) groundwater flow. The fields appear, when Constant Flow Boundary is selected (see option "Flow")

"Ho, m" text box

Hydraulic head (relatively to the aquifer bottom) inside a drain

"k1, m/day" and "k2, m/day" text box

Hydraulic conductivity (1) on the left and (2) the right sides of a drain. These fields are not applied to heterogeneous and multilayered aquifers, where hydraulic conductivities are assigned from a table (see below)

"R1, m" and "R2, m" text box

Radius of influence (or distance from a drain to Constant Head Boundary) for (1) the left and (2) the right sides. These fields are disabled for areallyheterogeneous aquifers, where they are automatically calculated as a sum of widths of each zone

"Boundary" option

Switches to NoFlow boundary at R distance from a drain. This option exists only for confined and unconfined homogeneous aquifers.

"Flow" option

Switches to constant flow q at R distance from a drain. This option exists only for confined and unconfined homogeneous aquifers.

"Q1, m^3/day" and "Q2, m^3/day" text box

Information field that displays calculated specific (i.e. divided by length of a drain, B) inflow to a drain from the left (1) and the right (2) sides.

"Q, m^3/day" text box

Information field that displays calculated specific total inflow to a drain (i.e. divided on the length of a drain (B)): Q = Q1 + Q2

"B, m" text box

Length of drain for inflow calculations

"Homogeneous", "Heterogeneous" and "Multilayered" list

Switches to areallyheterogeneous or multilayered conceptual schemes

"Table" button

Opens a new dialog window to enter parameters for areallyheterogeneous or multilayered aquifers (see explanations below). This window can be accessed, when "areallyheterogeneous" or "multylayerd" conceptual models are selected

"h" button

Switches to calculation of hydraulic head at a specific location. Location is indicated by the vertical black line that is moved by mouse cursor. This option exists only for homogeneous aquifers (select "homogeneous" from the list).

"x (max)" or "xp" button

Determines distance to the maximum hydraulic head (for confined and unconfined aquifers) or the location point where confined regime becomes unconfined (for confinedunconfined aquifers). Selection of this button will move the vertical black line to the maximum head location. Calculations are conducted for the side, where the line is currently located

"x1, m" or "x2, m" text box

Distance from the left (x1) or the righ (x2) side of a drain. Drain side changes with location of the vertical black line (see button "h"). When the mouse cursor is placed on this field, the context text displays distance from the opposite side

"h1, m" or "h2, m" text box

Information field that displays calculated hydraulic head at specified distances (text boxes "x1" or "x2") from a drain. If value is entered in this field, recharge rate is recalculated, that is required for the defined hydraulic head. The later option is accessible only for confined or unconfined homogeneous aquifers

When the button "table" is pressed, a dialog window appears allowing to enter a number of heterogeneity zones and their properties. Properties are entered separately for the left sides and the right sides of a drain. For areallyheterogeneous aquifers, a number of zones, hydraulic conductivities and widths of each zone have to be specified. For multilayered aquifers, inputs are required for hydraulic conductivity and thickness of each layer. the required inputs are illustrated by the sketch (see the figure below).
Dialog windows for input properties for areally heterogeneous and multylayered aquifers
After "OK" button is pressed, the dialog window is closed and values "R1" and "R2", "m1" and "m2" in window "Inflow to trench" are updated. Text boxes "m1" and "m2" contain the sum of thicknesses of individual layers.
Analytical solutions
Total inflow is calculated as the sum of the inflows from the left (I = 1) and the right (I = 2) side of the trench
Confined homogeneous aquifer

Inflow to the trench from one side:
Hydraulic head at the distance x from the trench:
Distance from the trench, at which the maximum hydraulic head is determined:
Determination of recharge rate with known hydraulic head hx at the distance x from the trench:

Confined homogeneous aquifer with NoFlow Boundary

Inflow to the trench from one side:
Hydraulic head at the distance x from the trench:
Distance from the trench, at which the maximum hydraulic head is determined:
Determination of recharge rate with known hydraulic head hx at the distance x from the trench:

Confined homogeneous aquifer with Constant Flow Boundary

Inflow to the trench from one side:
Hydraulic head at the distance x from the trench:
Distance from the trench, at which the maximum hydraulic head is determined:
Determination of recharge rate with known hydraulic head hx at the distance x from the trench:

Confined areallyheterogeneous aquifer

Inflow to the trench from one side: (n – number of heterogeneity zones):

Confined multylayered aquifer

Inflow to the trench from one side: (n – number of layers):


Unconfined homogeneous aquifer

Inflow to the trench from one side:
Hydraulic head at the distance x from the trench:
Distance from the trench, at which the maximum hydraulic head is determined:
Determination of recharge rate with known hydraulic head hx at the distance x from the trench:

Unconfined homogeneous aquifer with NoFlow Boundary

Inflow to the trench from one side:
Hydraulic head at the distance x from the trench:
Distance from the trench, at which the maximum hydraulic head is determined:
Determination of recharge rate with known hydraulic head hx at the distance x from the trench:

Unconfined homogeneous aquifer with Constant Flow Boundary

Inflow to the trench from one side:
Hydraulic head at the distance x from the trench:
Distance from the trench, at which the maximum hydraulic head is determined:
Determination of recharge rate with known hydraulic head hx at the distance x from the trench:

Unconfined areallyheterogeneous aquifer

Inflow to the trench from one side: (n – number of heterogeneity zones):

Unconfined multylayered aquifer

Inflow to the trench from one side:
m0 = 0,
n – number of saturated layers within the recharge zone,
n’ – number of saturated layers within the discharge zone


Confinedunconfined homogeneous aquifer

Inflow to the trench from one side:
Hydraulic head at the distance x from the trench with known distance xp (the point, where unconfined regime changes for uconfined regime:):
for a confined interval:
for an unconfined interval:
Distance from the trench to the point, where confined regime changes for unconfined regime:

Confinedunconfined areallyheterogeneous aquifer

Inflow to the trench from one side: (n – number of heterogeneity zones):

Confinedunconfined multylayered aquifer

Inflow to the trench from one side:
m0 = 0,
n – number of layers,
n’ – number of saturated layers within the discharge zone

