def hb_intersection(p0,
p1,
rtol=0.01,
maxit=100,
mi=20.0,
d=0.5,
gsi=85.0,
sigma_ci=200.0):
result = line(p0, p1)
if result is not None:
k = result[0]
b = result[1]
else:
x = 0
y = hoek_brown(x, x, mi=mi, d=d, gsi=gsi, sigma_ci=sigma_ci)
return x, y
if k != 1:
xy = b / (1 - k)
else:
xy = 0
s1min, s2min, s3min = hoek_brown_min_point(mi=mi,
d=d,
gsi=gsi,
sigma_ci=sigma_ci)
if xy < s3min:
return xy, xy
x = s3min
dx = xy - s3min
rdy = 1
i = 0
while rdy > rtol and i < maxit:
i += 1
x += dx
hb_y = hoek_brown(x, x, mi=mi, d=d, gsi=gsi, sigma_ci=sigma_ci)
pp_y = k * x + b
dy = hb_y - pp_y
if dy > 0:
x -= dx
dx *= 0.5
continue
length = dist([xy, xy], [pp_y, x])
rdy = abs(dy) / length
y = k * x + b
return x, y
def hb_normal(p,
cos_tol=0.001,
maxit=1000,
mi=20.0,
d=0.5,
gsi=85.0,
sigma_ci=200.0):
s1min, s2min, s3min = hoek_brown_min_point(mi=mi,
d=d,
gsi=gsi,
sigma_ci=sigma_ci)
x = s3min
y = s1min
i = 0
c = 1
delta_x = p[1] - s3min
kdx = 1e-6
hb1 = hoek_brown(p[0], p[0], mi=mi, d=d, gsi=gsi, sigma_ci=sigma_ci)
if p[1] <= s1min:
dx = kdx
dy = hoek_brown(
s3min + dx, s3min + dx, mi=mi, d=d, gsi=gsi, sigma_ci=sigma_ci) - y
p_hb = subs([x, y], p)
c = cos(p_hb, [dx, dy])
return [x, y], abs(c), i
elif hb1 == p[1]:
x = p[0]
y = p[1]
return [x, y], 0, i
while abs(c) > cos_tol and i < maxit:
i += 1
x += delta_x
y = hoek_brown(x, x, mi=mi, d=d, gsi=gsi, sigma_ci=sigma_ci)
dx = delta_x * kdx
dy = hoek_brown(x + dx, x + dx, mi=mi, d=d, gsi=gsi,
sigma_ci=sigma_ci) - y
p_hb = subs([x, y], p)
c = cos(p_hb, [dx, dy])
if c < 0:
x -= delta_x
delta_x *= 0.5
return [x, y], abs(c), i
def hoek_brown_min_point(mi=20, d=0.5, gsi=85, sigma_ci=200):
mb = mi * math.exp((gsi - 100) / (28 - 14 * d))
s = math.exp((gsi - 100) / (9 - 3 * d))
# a = 0.5 + (math.exp(-gsi / 15) - math.exp(-20 / 3)) / 6
sigma_3_min = -s * sigma_ci / mb
sigma_2_min = sigma_3_min
sigma_1_min = hoek_brown(sigma_2_min, sigma_3_min, mi=20, d=0.5, gsi=85,
sigma_ci=200)
if sigma_1_min >= sigma_2_min >= sigma_3_min:
sigma_1_min = max(sigma_2_min, sigma_3_min)
return sigma_1_min, sigma_2_min, sigma_3_min
min_d = 0 # 0
max_d = 1 # 1
min_gsi = 5 # 5
max_gsi = 100 # 100
mis = np.linspace(min_mi, max_mi, nc)
sigma_cis = np.linspace(min_sigma_ci, max_sigma_ci, nc)
ds = np.linspace(min_d, max_d, nc)
gsis = np.linspace(min_gsi, max_gsi, nc)
# X, Y
xs = [min_c, max_c]
ys = [min_c, max_c]
cmap = cm.get_cmap('Greys')
min_color = 0.3
hb_xs = np.linspace(min_c, max_c, n)
for i, mi in enumerate(mis):
hb_ys = [hoek_brown(x, x, mi=mi) for x in hb_xs]
plt.plot(hb_xs, hb_ys,
color=cmap(min_color + (1 - min_color) * (i / nc)), label=mi)
plt.xlim(min_c * 1.05, max_c * 1.05)
plt.ylim(min_c * 1.05, max_c * 1.05)
plt.legend(title='mi')
plot_axes(xs, ys)
plt.show()
plt.cla()
for i, sigma_ci in enumerate(sigma_cis):
hb_ys = [hoek_brown(x, x, sigma_ci=sigma_ci) for x in hb_xs]
plt.plot(hb_xs, hb_ys,
color=cmap(min_color + (1 - min_color) * (i / nc)),
label=sigma_ci)
plt.xlim(min_c * 1.05, max_c * 1.05)
plt.ylim(min_c * 1.05, max_c * 1.05)
from criteria import hoek_brown
import numpy as np
from norm import norm_sigma
from support import distance, angle
if __name__ == '__main__':
import matplotlib.pyplot as plt
min_x = -1000
max_x = 1000
n = 1001
hb_xs = np.linspace(min_x, max_x, n)
hb_ys = [hoek_brown(x, x) for x in hb_xs]
plt.plot(hb_xs, hb_ys)
sigma = [-500, -500, -700]
a = angle([1, 1, 0], [1, 0, 0])
sigma_max_1 = hoek_brown(sigma[1], sigma[2])
sigma_max = [sigma_max_1, sigma[1], sigma[2]]
d = distance(sigma, sigma_max)
sigma_n = norm_sigma(sigma)
plt.scatter(sigma[2], sigma[0], c='red')
plt.scatter(sigma_max[2], sigma_max[0], c='green')
plt.scatter(sigma_n[2], sigma_n[0], c='blue')
plt.plot([0, 0], [min_x, max_x], color='black', alpha=1, linewidth=0.5)
plt.plot([min_x, max_x], [0, 0], color='black', alpha=1, linewidth=0.5)
plt.xlim(min_x*1.05, max_x*1.05)
plt.ylim(min_x*1.05, max_x*1.05)
plt.show()
def norm_sigma(sigma, atol=0.01, maxit=100):
from criteria import hoek_brown
sigma[1] = sigma[2]
sigma_max_1 = hoek_brown(sigma[1], sigma[2])
sigma_max_3 = sigma[2]
sigma_max = [sigma_max_1, sigma[1], sigma[2]]
if sigma_max_1 < sigma[0]:
sigma_n = [hoek_brown(0, 0), 0.0, 0.0]
else:
sigma_n = sigma_max
d = distance(sigma, sigma_n)
dx = 1
pd = d
add = 100
cnt = 0
a = 1
while add > atol and cnt < maxit:
cnt += 1
# Move pos and neg
pos_sigma_n = [hoek_brown(sigma_n[1] + dx, sigma_n[2] + dx),
sigma_n[1] + dx, sigma_n[2] + dx]
neg_sigma_n = [hoek_brown(sigma_n[1] - dx, sigma_n[2] - dx),
sigma_n[1] - dx, sigma_n[2] - dx]
if pos_sigma_n[0] <= pos_sigma_n[2] or neg_sigma_n[0] <= neg_sigma_n[
2]:
# sigma_n = [0.0, 0.0, 0.0]
break
# New distances
pos_d = distance(sigma, pos_sigma_n)
neg_d = distance(sigma, neg_sigma_n)
if pos_d < neg_d:
sigma_n[1] += dx
sigma_n[2] += dx
sigma_n[0] = pos_sigma_n[0]
d = pos_d
elif pos_d > neg_d:
sigma_n[1] -= dx
sigma_n[2] -= dx
sigma_n[0] = neg_sigma_n[0]
d = neg_d
else:
break
k = 1
# cmap = cm.get_cmap('Set1')
# c = cmap(random.uniform(0, 1))
d_sigma_n = [
hoek_brown(sigma_n[1] + k * dx, sigma_n[2] + k * dx) - sigma_n[0],
k * dx, k * dx]
# plt.plot([sigma_n[2], sigma_n[2] + d_sigma_n[2]], [sigma_n[0], sigma_n[0] + d_sigma_n[0]], color=c)
ds = delta(sigma, sigma_n)
# plt.plot([sigma[2], sigma[2] + ds[2]], [sigma[0], sigma[0] + ds[0]], color=c)
a = angle(ds, d_sigma_n)
dsdydx = ds[0] / ds[1]
dsb = sigma[0] - dsdydx * sigma[1]
dsb2 = sigma_n[0] - dsdydx * sigma_n[1]
sigma_min_3 = dsb / (1 - dsdydx)
sigma_min_1 = sigma_min_3
# plt.plot([sigma[2], sigma[2] + ds[2]], [sigma[0], sigma[0] + ds[0]], color=c)
# plt.plot([sigma_n[2], sigma_min_3], [sigma_n[0], sigma_min_1])
add = abs(a - math.pi / 2)
pd = d
return sigma_n
# HB
mb = mi * math.exp((gsi - 100) / (28 - 14 * d))
s = math.exp((gsi - 100) / (9 - 3 * d))
a = 0.5 + (math.exp(-gsi / 15) - math.exp(-20 / 3)) / 6
min_c = -500
max_c = 500
n = 20001
xs = [min_c, max_c]
ys = [min_c, max_c]
hb1min, hb2min, hb3min = hoek_brown_min_point(mi=mi,
d=d,
gsi=gsi,
sigma_ci=sigma_ci)
hb_xs = np.linspace(hb3min, max_c, n)
hb_ys = [
hoek_brown(x, x, mi=mi, d=d, gsi=gsi, sigma_ci=sigma_ci)
for x in hb_xs
]
plt.plot(
hb_xs,
hb_ys,
color='black',
linewidth=2,
label=
'HB, mi={:.2f}, D={:.2f}, GSI={:.0f},\nσci={:.0f} МПа,mb={:.2f}, s={:.2f}, a={:.2f}'
.format(
mi,
d,
gsi,
sigma_ci,
mb,