# -*- coding: utf-8 -*-
"""
Routines to calculate pore pressure
"""
from __future__ import (absolute_import, division, print_function,
unicode_literals)
__author__ = "yuhao"
import numpy as np
[docs]def bowers(v, obp, u, start_idx, a, b, vmax, end_idx=None):
"""
Compute pressure using Bowers equation.
Parameters
----------
v : 1-d ndarray
velocity array whose unit is m/s.
obp : 1-d ndarray
Overburden pressure whose unit is Pa.
v0 : float, optional
the velocity of unconsolidated regolith whose unit is m/s.
a : float, optional
coefficient a
b : float, optional
coefficient b
Notes
-----
.. math:: P = S - \\left[\\frac{(V-V_{0})}{a}\\right]^{\\frac{1}{b}}
[3]_
.. [3] Bowers, G. L. (1994). Pore pressure estimation from velocity data:
accounting from overpressure mechanisms besides undercompaction:
Proceedings of the IADC/SPE drilling conference, Dallas, 1994,
(IADC/SPE), 1994, pp 515–530. In International Journal of Rock
Mechanics and Mining Sciences & Geomechanics Abstracts (Vol. 31,
p. 276). Pergamon.
"""
sigma_max = ((vmax-1524)/a)**(1/b)
ves = ((v - 1524) / a)**(1.0 / b)
ves_fe = sigma_max*(((v-1524)/a)**(1/b)/sigma_max)**u
ves[start_idx: end_idx] = ves_fe[start_idx: end_idx]
return obp - ves
[docs]def bowers_varu(v, obp, u, start_idx, a, b, vmax, buf=20,
end_idx=None, end_buffer=10):
"""
Bowers Method with buffer zone above unloading zone
Parameters
----------
v : 1-d ndarray
velocity array whose unit is m/s.
obp : 1-d ndarray
Overburden pressure whose unit is Pa.
u : float
coefficient u
start_idx : int
index of start of fluid expansion
a : float, optional
coefficient a
b : float, optional
coefficient b
vmax : float
buf : int, optional
len of buffer interval, buf should be smaller than start_idx
end_idx : int
end of fluid expasion
end_buffer : int
len of end buffer interval
"""
u_array = np.ones(v.shape)
u_array[start_idx: end_idx] = u
# start buffer
u_buffer = np.linspace(1, u, buf)
u_array[start_idx-buf+1: start_idx + 1] = u_buffer
# end buffer
if end_idx is not None:
u_array[end_idx: end_idx + end_buffer] = np.linspace(u, 1, end_buffer)
sigma_max = ((vmax-1524)/a)**(1/b)
ves = sigma_max*(((v-1524)/a)**(1/b)/sigma_max)**u_array
return obp - ves
[docs]def virgin_curve(sigma, a, b):
"Virgin curve in Bowers' method."
v0 = 1524
return v0 + a * sigma**b
[docs]def invert_virgin(v, a, b):
"invert of virgin curve."
v0 = 1524
return ((v-v0)/a)**(1/b)
[docs]def unloading_curve(sigma, a, b, u, v_max):
"Unloading curve in Bowers's method."
sigma_max = ((v_max-1524)/a)**(1/b)
independent = sigma_max*(sigma/sigma_max)**(1/u)
return virgin_curve(independent, a, b)
[docs]def invert_unloading(v, a, b, u, v_max):
"invert of Unloading curve in Bowers's method."
sigma_max = invert_virgin(v_max, a, b)
sigma_vc = invert_virgin(v, a, b)
return sigma_max * (sigma_vc/sigma_max)**u
[docs]def power_bowers(sigma_vc_ratio, u):
return sigma_vc_ratio**u
