Geohydro functions

Deze module bevat verschillende geohydrologische methoden die worden gebruikt bij de veiligheidsbeoordeling van dijken. Achtergrondinformatie is te vinden in het ‘Technisch Rapport Waterspanningen bij dijken’ voor de Waterkeringen [3].

Functions

calc_lambda(kd, c)

Calculates leakage length

calc_W(lam, L)

Calculates effective leakage length by:

calc_r_BIT(w1, l2, w3)

Calculates response in stationary models at inner toe based on

calc_r_BUT(w1, l2, w3)

Calculates response in stationary models at outer toe based on

calc_respons2pot(h_ref, r_exit, h_riv)

Calculates potential from given response. See voor de Waterkeringen [3].

calc_pot2response(phi, h_ref, h_riv)

Calculates response from given potential. This is the reverse

calc_ang_frequency(T)

Calculates Angular frequency from period of a sinus wave.

calc_P_from_T(T)

Calculates duration P from period T.

calc_T_from_P(P)

Calculates storm period from storm duration P.

calc_lambda_cycl_from_stationary(LambdaStat, d, c_v, w)

Calculates cyclic lambda from stationary leakage length

calc_lambda_cycl(LambdaCycl_1, T2, T1)

Calculates cyclic lambda from one period to another.

calc_theta(b, lambda_w_vl)

Calculates theta, see figure b4.13 from 'Technisch Rapport

calc_f(b, lambda_w_vl)

Calculates f, see figure b4.13 from 'Technisch Rapport

calc_mean_pot_gradient(W1, W3, x_tp, mean_wl, phi_onv)

Approximation of hydraulic head under daily (mean) conditions.

Module Contents

calc_lambda(kd, c)

Calculates leakage length

\[\lambda = \sqrt{kDc}\]
Parameters:
  • kd (float) – transmissivity [m2/day]

  • c (float) – resistance of the topsoil [day]

Returns:

leakage length lambda [m]

Return type:

float

calc_W(lam, L)

Calculates effective leakage length by:

\[W = \lambda tanh(\frac{L}{\lambda})\]
Parameters:
  • lam (float) – leakage lengte [m]

  • L (float) – physical length [m]

Returns:

effective leakage length [m]

Return type:

float

calc_r_BIT(w1, l2, w3)

Calculates response in stationary models at inner toe based on given weights. See voor de Waterkeringen [3].

\[r_{BIT} = \frac{W_{3}}{W_{1} + L_{2} + W_{3}}\]
Parameters:
  • w1 (float) – weight of foreland [m]

  • l2 (float) – length of dike base [m]

  • w3 (float) – weight of hinterland [m]

Returns:

response at inner toe [0.0-1.0]

Return type:

float

calc_r_BUT(w1, l2, w3)

Calculates response in stationary models at outer toe based on given weights. See voor de Waterkeringen [3].

\[r_{BUT} = \frac{L_{2} + W_{3}}{W_{1} + L_{2} + W_{3}}\]
Parameters:
  • w1 (float) – weight of foreland [m]

  • l2 (float) – length of dike base [m]

  • w3 (float) – weight of hinterland [m]

Returns:

response at outer toe [0.0-1.0]

Return type:

float

calc_respons2pot(h_ref, r_exit, h_riv)

Calculates potential from given response. See voor de Waterkeringen [3].

\[\phi(x) = h_{ref} + r(x) (h_{river} - h_{ref})\]
Parameters:
  • h_ref (float) – potential in hinterland (polder)

  • r_exit (float) – response at given location [m]

  • h_riv (float) – water level at river

Returns:

potential at given location

Return type:

float

calc_pot2response(phi, h_ref, h_riv)

Calculates response from given potential. This is the reverse function of calc_respons2pot.

\[r(x) = \frac{\phi(x)-h_{ref}}{h_{river} -h_{ref}}\]
Parameters:
  • phi (float) – given potential [m+ref]

  • h_ref (float) – reference leve, e.g. potential in polder [m+ref]

  • h_riv (float) – water level at river, given potential [m+ref]

Returns:

response given reference level

Return type:

float

calc_ang_frequency(T)

Calculates Angular frequency from period of a sinus wave. See voor de Waterkeringen [3] for background information.

\[\omega = \frac{2 \pi}{T}\]
Parameters:

T (float) – period [s]

Returns:

angular frequency [rad/s]

Return type:

float

calc_P_from_T(T)

Calculates duration P from period T.

\[P = \frac{T}{2}\]

This is a helper function. Often a period T needs to be from a known storm surge P

Parameters:

T (float) – Storm period T [s]

Returns:

Storm duration P [s]

Return type:

float

calc_T_from_P(P)

Calculates storm period from storm duration P.

\[T = P * 2.0\]
Parameters:

P (float) – Storm duration P [s]

Returns:

Storm period T [s]

Return type:

float

calc_lambda_cycl_from_stationary(LambdaStat, d, c_v, w)

Calculates cyclic lambda from stationary leakage length

see en F.B.J. Barends [7]

\[ \begin{align}\begin{aligned}t_{h} = \frac{d^{2}}{c_{v}^{'}}\\\lambda_{\omega} = \frac{1.082 * \lambda_{s}} {\sqrt[4]{t_{h}^{'}\omega}}\end{aligned}\end{align} \]
Parameters:
  • LambdaStat (float) – stationary leakage length [m]

  • d (float) – thickness of impermeable cover layer [m]

  • c_v (float) – one dimensional consolidation coëfficiënt [m2/s]

  • w (float) – angular frequency [rad/s]

Returns:

cyclic lambda [m]

Return type:

float

calc_lambda_cycl(LambdaCycl_1, T2, T1)

Calculates cyclic lambda from one period to another. See voor de Waterkeringen [3].

\[\lambda_{\omega, T_{2}}^{'} = \lambda_{\omega, T_{1}}^{'} \sqrt[4]{\frac{T_{2}}{T_{1}}}\]

T1 and T2 are in same dimension (e.g. seconds, hours, days)

Parameters:
  • LambdaCycl_1 (float) – known cyclic lambda at given period T1

  • T2 (float) – period for which cyclic lambda needs te be calculated

  • T1 (float) – known period

Returns:

_description_

Return type:

float

calc_theta(b, lambda_w_vl)

Calculates theta, see figure b4.13 from ‘Technisch Rapport Waterspanningen bij dijken’ voor de Waterkeringen [3]. Approximation by 5th degree polynomials.

Parameters:
  • b (float) – with of river [m],

  • lambda_w_vl (float) – cyclic lambda of foreland [m]

Raises:

ValueError – Only for positive numbers

Returns:

theta from b4.13 voor de Waterkeringen [3]

Return type:

float

calc_f(b, lambda_w_vl)

Calculates f, see figure b4.13 from ‘Technisch Rapport Waterspanningen bij dijken’ voor de Waterkeringen [3]. Approximation by exponential function.

Parameters:
  • b (float) – with of river [m],

  • lambda_w_vl (float) – cyclic lambda of foreland [m]

Raises:

ValueError – Only for positive numbers

Returns:

f from b4.13 voor de Waterkeringen [3] b : with of river in m lambda_w_vl : cyclic lambda of foreland

Return type:

float

calc_mean_pot_gradient(W1, W3, x_tp, mean_wl, phi_onv)

Approximation of hydraulic head under daily (mean) conditions. Uses method from tipping point voor de Waterkeringen [3].

\[ \begin{align}\begin{aligned}\phi(x) = h_{ref} + r(x) (h_{rivier} - h_{ref})\\ r(x) = \frac{exp(\frac{- x_{tp}}{W_{3}})}{1+\frac{W_1}{W_3}}\end{aligned}\end{align} \]
Parameters:
  • W1 (float) – weight of foreland under daily conditions [m]

  • W3 (float) – weight of hinterland under daily conditions [m]

  • x_tp (float) – given location from tipping point [m]

  • mean_wl (float) – daily water level at river

  • phi_onv (float) – potential in hinterland (polder)

Returns:

hydraulic head at given distance from tipping point

Return type:

float