def demo_toppling():
# slope face
strike = 60
dip = 55
# generalized friction angle of slip planes
friction = 25
fig, ax = st.subplots(ncols=4, projection='equal_angle_stereonet')
plt.sca(ax[0])
ax[0].grid(True)
ax[0].plane(strike, dip, 'k--', alpha=0.5, lw=5)
plt.title('Plot slope face\n')
plt.sca(ax[1])
ax[1].grid(True)
ax[1].plane(strike - strike, dip, 'k--', alpha=0.5, lw=5)
ax[1].set_azimuth_ticks([])
env.toppling_slipLimits(strike - strike, dip)
env.toppling_friction(strike - strike, dip, friction)
plt.title('Rotate, plot\n daylight and friction\nenvelopes\n')
jstr = np.random.randint(0, 361, 4) #np.random.random_integers(0,360,4)
jdip = np.random.randint(0, 91, 4)
plt.sca(ax[2])
ax[2].grid(True)
ax[2].plane(strike, dip, 'k--', alpha=0.5, lw=5)
env.toppling_slipLimits(strike, dip)
env.toppling_friction(strike, dip, friction)
ax[2].plane(jstr, jdip, c='k')
plt.title('Rotate back,\nplot discontinuity planes\n')
plt.sca(ax[3])
ax[3].grid(True)
ax[3].plane(strike, dip, 'k--', alpha=0.5, lw=5)
env.toppling_slipLimits(strike, dip)
env.toppling_friction(strike, dip, friction)
ax[3].plane(jstr, jdip, c='k')
ax[3].pole(jstr, jdip)
plt.title('Plot poles, evaluate results\n')
fig.suptitle('Toppling failure')
def topplingFailure(sstr, sdip, jfriction, jstr, jdip, to_plot=False):
"""
Evaluates toppling failure of joints vis-a-vis a slope face
with a given strike and dip, such that a joint's pole plots 1) within the
toppling slip limits, and 2) on the convex side of the toppling friction
envelope
Parameters
----------
sstr : int or float
The strike of the slope face in degrees, with dip direction indicated by
the azimuth (e.g. 315 vs. 135) specified following the "right hand
rule".
sdip : int or float
The dip of the slope face in degrees.
jfriction : int, float, or array of int or float
The friction angle of the joint plane in degrees.
jstr : int, float, or array of int or float
The strike of the joint plane in degrees, with dip direction indicated by
the azimuth (e.g. 315 vs. 135) specified following the "right hand
rule".
jdip : int, float, or array of int or float
The dip of the joint plane in degrees.
Returns
-------
topplingFail: boolean array of size = len(np.atleast_1d(jstr))
Indicates if corresponding joints will allow toppling failure.
"""
# ensure jstr, jdip, and jfriction are 1-d arrays
jstr, jdip = np.atleast_1d(jstr, jdip)
try:
len(jfriction)
uniformFriction = False
except:
jfriction = jfriction * (np.ones(len(jstr)))
uniformFriction = True
# determine daylight and friction envelopes
tsl_plunge, tsl_bearing, tsl_angle = env.toppling_slipLimits(
sstr, sdip, False)
tfe_strike, tfe_dip = env.toppling_friction(sstr, sdip, jfriction, False)
# convert joint plane (strike-dip) to pole (plunge-bearing)
jplunge, jbearing = st.pole2plunge_bearing(jstr, jdip)
# evaluate if joint poles are contained within slip limits (cones) and friction envelope (great circles)
inSlipLimit1 = np.empty(len(jstr))
inSlipLimit2 = np.empty(len(jstr))
convexFriction = np.empty(len(jstr))
for a in range(len(jstr)):
inSlipLimit1[a] = ~line_in_cone(tsl_plunge, tsl_bearing, tsl_angle,
jplunge[a], jbearing[a])
inSlipLimit2[a] = ~line_in_cone(tsl_plunge, tsl_bearing + 180,
tsl_angle, jplunge[a], jbearing[a])
convexFriction[a] = line_above_plane(tfe_strike[0], tfe_dip[a],
jplunge[a], jbearing[a])
topplingFail = ((inSlipLimit1 == True) & (inSlipLimit2 == True) &
(convexFriction == True))
# plotting results
if uniformFriction and to_plot:
env.setup_axes(sstr,
sdip,
jfriction[a],
failure='toppling',
to_plot=True)
plt.gca().pole(jstr[~topplingFail],
jdip[~topplingFail],
color='0.5',
marker='.')
plt.gca().pole(jstr[topplingFail],
jdip[topplingFail],
color='r',
marker='.')
return topplingFail