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boreholeStress.py
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boreholeStress.py
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import numpy as np
from numpy import sin, cos, tan
import matplotlib.pyplot as plt
import math
plt.rcParams["font.family"] = "Helvetica"
def degToRad(ang, reverse = False):
res = (np.pi/180)*ang
if reverse == True:
res = ang * 180 / np.pi
return res
def boreholeStress(s1, s2, s3, pp, alpha, beta, gamma, delta, phi, v,to,thetacoh,TS, viz = True):
thetacoh = thetacoh
Ss = np.eye(3)
Ss[0][0] = s1
Ss[1][1] = s2
Ss[2][2] = s3
Pp = pp
Rs = np.zeros((3,3))
alp = degToRad(alpha)
bet = degToRad(beta)
gam = degToRad(gamma)
Rs[0][0] = cos(alp)*cos(bet)
Rs[0][1] = sin(alp)*cos(bet)
Rs[0][2] = -1 * sin(bet)
Rs[1][0] = cos(alp)*sin(bet)*sin(gam) - sin(alp)*cos(gam)
Rs[1][1] = sin(alp)*sin(bet)*sin(gam) + cos(alp)*cos(gam)
Rs[1][2] = cos(bet)*sin(gam)
Rs[2][0] = cos(alp)*sin(bet)*cos(gam) + sin(alp)*sin(gam)
Rs[2][1] = sin(alp)*sin(bet)*cos(gam) - cos(alp)*sin(gam)
Rs[2][2] = cos(bet)*cos(gam)
Rb = np.zeros((3,3))
de = degToRad(delta)
phi = degToRad(phi)
Rb[0][0] = -cos(de)*cos(phi)
Rb[0][1] = -sin(de)*cos(phi)
Rb[0][2] = sin(phi)
Rb[1][0] = sin(de)
Rb[1][1] = -cos(de)
Rb[1][2] = 0
Rb[2][0] = cos(de)*sin(phi)
Rb[2][1] = sin(de)*sin(phi)
Rb[2][2] = cos(phi)
S = Rb @ Rs.transpose() @ Ss @ Rs @ Rb.transpose()
Seff = S.copy()
Seff[0][0] = Seff[0][0] - Pp
Seff[1][1] = Seff[1][1] - Pp
Seff[2][2] = Seff[2][2] - Pp
###
v = v
theta = np.linspace(0,2*np.pi)
i = pp - (pp*.5)
thetacoh = degToRad(thetacoh)
diffvalues=[]
ivalues = []
solution = False
while i < pp*3:
Sigmas=[0]
dp = i - pp
Szz = Seff[2][2] - 2*v*(Seff[0][0] - Seff[1][1])*cos(2*theta) - 4*v*Seff[0][1]*sin(2*theta)
Stt = Seff[0][0] + Seff[1][1] - 2*(Seff[0][0] - Seff[1][1])*cos(2*theta) - 4*Seff[0][1]*sin(2*theta) - dp
Stz = 2*(Seff[1][2]*cos(theta) - Seff[0][2]*sin(theta))
Srr = np.abs(dp)
Stmax = 0.5*(Szz + Stt + ((Szz - Stt)**2 + 4*(Stz)**2)**0.5)
Stmin = 0.5*(Szz + Stt - ((Szz - Stt)**2 + 4*(Stz)**2)**0.5)
Srr = np.repeat(dp, len(Stmin))
StmaxNorm = Stmax
StminNorm = Stmin
SrrNorm = Srr
Stmaxmax = np.amax(StmaxNorm)
Stminmin = np.amax(StminNorm)
Srrmin = np.amin(Srr)
Sigmas.append(Srrmin)
Sigmas.append(Stmaxmax)
Sigmas.append(Stminmin)
Sigmas.pop(0)
Sigmassort = np.sort(Sigmas,axis=None)
sider1 = to*np.cos(thetacoh)
sider2 = .5*np.sin(thetacoh)*(Sigmassort[2]+Sigmassort[0])
sider = sider1+sider2
sideleft = .5*(Sigmassort[2]-Sigmassort[0])
sider = np.round(sider,6)
sideleft = np.round(sideleft,6)
diff = np.abs(sider-sideleft)
if diff <= .3:
Pmin = i
solution = True
break
else:
diffvalues.append(diff)
ivalues.append(i)
i+=.2
if solution==False:
minvalspot = diffvalues.index(np.amin(diffvalues))
Pmin = ivalues[minvalspot]
solution = False
diffvalues = []
jvalues=[]
j = Pmin + (Pmin*.25)
while j < Pmin*3:
Sigmas=[0]
dp = j - pp
Szz = Seff[2][2] - 2*v*(Seff[0][0] - Seff[1][1])*cos(2*theta) - 4*v*Seff[0][1]*sin(2*theta)
Stt = Seff[0][0] + Seff[1][1] - 2*(Seff[0][0] - Seff[1][1])*cos(2*theta) - 4*Seff[0][1]*sin(2*theta) - dp
Stz = 2*(Seff[1][2]*cos(theta) - Seff[0][2]*sin(theta))
Srr = dp
Stmax = 0.5*(Szz + Stt + ((Szz - Stt)**2 + 4*(Stz)**2)**0.5)
Stmin = 0.5*(Szz + Stt - ((Szz - Stt)**2 + 4*(Stz)**2)**0.5)
Srr = np.repeat(dp, len(Stmin))
StmaxNorm = Stmax
StminNorm = Stmin
SrrNorm = np.abs(Srr)
Stmaxmax = np.amin(StmaxNorm)
Stminmin = np.amin(StminNorm)
Srrmin = np.amin(Srr)
Sigmas.append(np.abs(Srrmin))
Sigmas.append(np.abs(Stmaxmax))
Sigmas.append(np.abs(Stminmin))
Sigmas.pop(0)
Sigmassort = np.sort(Sigmas,axis=None)
sider1 = 3*Sigmassort[0]
sider2 = -1*Sigmassort[2] + TS - pp
sider = sider1 + sider2
sider = np.abs(np.round(sider,6))
j = np.round(j,6)
diff = np.abs(j-sider)
if j >= sider:
Pmax = j
solution = True
break
else:
diffvalues.append(diff)
jvalues.append(j)
j+=.01
if solution == False:
minvalspot = diffvalues.index(np.amin(diffvalues))
Pmax = jvalues[minvalspot]
###
if viz == True:
plt.plot(degToRad(theta[:51], reverse = True), StmaxNorm[:51],
label = "$\sigma_{t \ max}$", color = "red")
plt.plot(degToRad(theta[:51], reverse = True), StminNorm[:51],
label = "$\sigma_{t \ min}$", color = "blue")
plt.plot(degToRad(theta[:51], reverse = True), SrrNorm[:51],
label = "$\sigma_{rr}$", color = "green")
plt.xlabel("borehole angle ($\degree$)")
plt.ylabel("Effective stress (normalized with $\sigma_1$)")
plt.legend()
plt.tight_layout()
plt.show()
resultDict = {"Szz":Szz,
"stt":Stt,
"Stz":Stz,
"Srr":dp,
"Stmax":Stmax,
"Stmin":Stmin
}
return Pmin,Pmax
def MohrCoulombSlope(mu):
"""
Parameters
----------
mu : float
frcition coeff.
Returns
-------
res : float
the slope in MC failure criterion.
"""
res = ((mu**2 + 1)**0.5 + mu)**2
return res
def getMaxStrength(s1,s3,slope):
"""
Parameters
----------
s1 : float
maximum effective stress.
s3 : float
minimum effective stress.
slope : object
function to calculate the slope in MC criterion
Returns
-------
res : float
max strength allowable with given stress configs.
"""
res = s1 - slope*s3
return res
''''
while j < pp*3:
Sigmas=[0]
dp = j - pp
Szz = Seff[2][2] - 2*v*(Seff[0][0] - Seff[1][1])*cos(2*theta) - 4*v*Seff[0][1]*sin(2*theta)
Stt = Seff[0][0] + Seff[1][1] - 2*(Seff[0][0] - Seff[1][1])*cos(2*theta) - 4*Seff[0][1]*sin(2*theta) - dp
Stz = 2*(Seff[1][2]*cos(theta) - Seff[0][2]*sin(theta))
Srr = dp
Stmax = 0.5*(Szz + Stt + ((Szz - Stt)**2 + 4*(Stz)**2)**0.5)
Stmin = 0.5*(Szz + Stt - ((Szz - Stt)**2 + 4*(Stz)**2)**0.5)
Srr = np.repeat(dp, len(Stmin))
StmaxNorm = Stmax
StminNorm = Stmin
SrrNorm = np.abs(Srr)
Stmaxmax = np.amin(StmaxNorm)
Stminmin = np.amin(StminNorm)
Srrmin = np.amin(Srr)
Sigmas.append(np.abs(Srrmin))
Sigmas.append(np.abs(Stmaxmax))
Sigmas.append(np.abs(Stminmin))
Sigmas.pop(0)
Sigmassort = np.sort(Sigmas,axis=None)
sider1 = 3*Sigmassort[0]
sider2 = -1*Sigmassort[2] + TS - pp
sider = sider1 + sider2
sider = np.abs(np.round(sider,4))
j = np.round(j,4)
diff = np.abs(j-sider)
if diff<.5:
Pmax = j
print(Pmax)
break
else:
j+=.1
'''