def _calc_Tm(alp, t, mag_vs_time):
"""calculate the Tm expression at a given time
Parameters
----------
alp : float
eigenvalue, note that this will be squared
t : float
time value
mag_vs_time: PolyLine
magnitude vs time
Returns
-------
Tm: float
time dependant function
"""
loadmag = mag_vs_time.y
loadtim = mag_vs_time.x
(
ramps_less_than_t,
constants_less_than_t,
steps_less_than_t,
ramps_containing_t,
constants_containing_t,
) = pwise.segment_containing_also_segments_less_than_xi(loadtim, loadmag, t, steps_or_equal_to=True)
exp = math.exp
Tm = 0
cv = 1 # I copied the Tm function from SchiffmanAndStein1970
i = 0 # only one time value
for k in steps_less_than_t[i]:
sig1 = loadmag[k]
sig2 = loadmag[k + 1]
Tm += (sig2 - sig1) * exp(-cv * alp ** 2 * (t - loadtim[k]))
for k in ramps_containing_t[i]:
sig1 = loadmag[k]
sig2 = loadmag[k + 1]
t1 = loadtim[k]
t2 = loadtim[k + 1]
# Tm += (-sig1 + sig2)/(alp**2*cv*(-t1 + t2)) - (-sig1 + sig2)*exp(-alp**2*cv*t)*exp(alp**2*cv*t1)/(alp**2*cv*(-t1 + t2))
Tm += (-sig1 + sig2) / (alp ** 2 * cv * (-t1 + t2)) - (-sig1 + sig2) * exp(-alp ** 2 * cv * (t - t1)) / (
alp ** 2 * cv * (-t1 + t2)
)
for k in ramps_less_than_t[i]:
sig1 = loadmag[k]
sig2 = loadmag[k + 1]
t1 = loadtim[k]
t2 = loadtim[k + 1]
# Tm += -(-sig1 + sig2)*exp(-alp**2*cv*t)*exp(alp**2*cv*t1)/(alp**2*cv*(-t1 + t2)) + (-sig1 + sig2)*exp(-alp**2*cv*t)*exp(alp**2*cv*t2)/(alp**2*cv*(-t1 + t2))
Tm += -(-sig1 + sig2) * exp(-alp ** 2 * cv * (t - t1)) / (alp ** 2 * cv * (-t1 + t2)) + (
-sig1 + sig2
) * exp(-alp ** 2 * cv * (t - t2)) / (alp ** 2 * cv * (-t1 + t2))
return Tm
def _calc_Tm(alp, t, mag_vs_time):
"""calculate the Tm expression at a given time
Parameters
----------
alp : float
eigenvalue, note that this will be squared
t : float
time value
mag_vs_time: PolyLine
magnitude vs time
Returns
-------
Tm: float
time dependant function
"""
loadmag = mag_vs_time.y
loadtim = mag_vs_time.x
(ramps_less_than_t, constants_less_than_t, steps_less_than_t,
ramps_containing_t, constants_containing_t) = (
pwise.segment_containing_also_segments_less_than_xi(
loadtim, loadmag, t, steps_or_equal_to=True))
exp = math.exp
Tm = 0
cv = 1 # I copied the Tm function from SchiffmanAndStein1970
i = 0 #only one time value
for k in steps_less_than_t[i]:
sig1 = loadmag[k]
sig2 = loadmag[k + 1]
Tm += (sig2 - sig1) * exp(-cv * alp**2 * (t - loadtim[k]))
for k in ramps_containing_t[i]:
sig1 = loadmag[k]
sig2 = loadmag[k + 1]
t1 = loadtim[k]
t2 = loadtim[k + 1]
# Tm += (-sig1 + sig2)/(alp**2*cv*(-t1 + t2)) - (-sig1 + sig2)*exp(-alp**2*cv*t)*exp(alp**2*cv*t1)/(alp**2*cv*(-t1 + t2))
Tm += (-sig1 + sig2) / (alp**2 * cv *
(-t1 + t2)) - (-sig1 + sig2) * exp(
-alp**2 * cv *
(t - t1)) / (alp**2 * cv * (-t1 + t2))
for k in ramps_less_than_t[i]:
sig1 = loadmag[k]
sig2 = loadmag[k + 1]
t1 = loadtim[k]
t2 = loadtim[k + 1]
# Tm += -(-sig1 + sig2)*exp(-alp**2*cv*t)*exp(alp**2*cv*t1)/(alp**2*cv*(-t1 + t2)) + (-sig1 + sig2)*exp(-alp**2*cv*t)*exp(alp**2*cv*t2)/(alp**2*cv*(-t1 + t2))
Tm += -(-sig1 + sig2) * exp(-alp**2 * cv * (t - t1)) / (
alp**2 * cv *
(-t1 + t2)) + (-sig1 + sig2) * exp(-alp**2 * cv *
(t - t2)) / (alp**2 * cv *
(-t1 + t2))
return Tm
def _calc_Tm(self, cv, beta, t):
"""calculate the Tm expression at a given time
Parameters
----------
cv : float
coefficient of vertical consolidation for layer
beta : float
eigenvalue for layer
t : float
time value
Returns
-------
Tm: float
time dependant function
"""
loadmag = self.surcharge_vs_time.y
loadtim = self.surcharge_vs_time.x
(ramps_less_than_t, constants_less_than_t, steps_less_than_t,
ramps_containing_t, constants_containing_t
) = pwise.segment_containing_also_segments_less_than_xi(
loadtim, loadmag, t, steps_or_equal_to=True)
exp = math.exp
Tm = 0
i = 0 #only one time value
for k in steps_less_than_t[i]:
sig1 = loadmag[k]
sig2 = loadmag[k + 1]
Tm += (sig2 - sig1) * exp(-cv * beta**2 * (t - loadtim[k]))
for k in ramps_containing_t[i]:
sig1 = loadmag[k]
sig2 = loadmag[k + 1]
t1 = loadtim[k]
t2 = loadtim[k + 1]
# Tm += (-sig1 + sig2)/(beta**2*cv*(-t1 + t2)) - (-sig1 + sig2)*exp(-beta**2*cv*t)*exp(beta**2*cv*t1)/(beta**2*cv*(-t1 + t2))
Tm += (-sig1 + sig2) / (beta**2 * cv *
(-t1 + t2)) - (-sig1 + sig2) * exp(
-beta**2 * cv *
(t - t1)) / (beta**2 * cv * (-t1 + t2))
for k in ramps_less_than_t[i]:
sig1 = loadmag[k]
sig2 = loadmag[k + 1]
t1 = loadtim[k]
t2 = loadtim[k + 1]
# Tm += -(-sig1 + sig2)*exp(-beta**2*cv*t)*exp(beta**2*cv*t1)/(beta**2*cv*(-t1 + t2)) + (-sig1 + sig2)*exp(-beta**2*cv*t)*exp(beta**2*cv*t2)/(beta**2*cv*(-t1 + t2))
Tm += -(-sig1 + sig2) * exp(-beta**2 * cv * (t - t1)) / (
beta**2 * cv *
(-t1 + t2)) + (-sig1 + sig2) * exp(-beta**2 * cv *
(t - t2)) / (beta**2 * cv *
(-t1 + t2))
return Tm
def _calc_Tm(self, cv, beta, t):
"""calculate the Tm expression at a given time
Parameters
----------
cv : float
coefficient of vertical consolidation for layer
beta : float
eigenvalue for layer
t : float
time value
Returns
-------
Tm: float
time dependant function
"""
loadmag = self.surcharge_vs_time.y
loadtim = self.surcharge_vs_time.x
(ramps_less_than_t, constants_less_than_t, steps_less_than_t,
ramps_containing_t, constants_containing_t) = pwise.segment_containing_also_segments_less_than_xi(loadtim, loadmag, t, steps_or_equal_to = True)
exp = math.exp
Tm=0
i=0 #only one time value
for k in steps_less_than_t[i]:
sig1 = loadmag[k]
sig2 = loadmag[k+1]
Tm += (sig2-sig1)*exp(-cv * beta**2 * (t-loadtim[k]))
for k in ramps_containing_t[i]:
sig1 = loadmag[k]
sig2 = loadmag[k+1]
t1 = loadtim[k]
t2 = loadtim[k+1]
# Tm += (-sig1 + sig2)/(beta**2*cv*(-t1 + t2)) - (-sig1 + sig2)*exp(-beta**2*cv*t)*exp(beta**2*cv*t1)/(beta**2*cv*(-t1 + t2))
Tm += (-sig1 + sig2)/(beta**2*cv*(-t1 + t2)) - (-sig1 + sig2)*exp(-beta**2*cv*(t-t1))/(beta**2*cv*(-t1 + t2))
for k in ramps_less_than_t[i]:
sig1 = loadmag[k]
sig2 = loadmag[k+1]
t1 = loadtim[k]
t2 = loadtim[k+1]
# Tm += -(-sig1 + sig2)*exp(-beta**2*cv*t)*exp(beta**2*cv*t1)/(beta**2*cv*(-t1 + t2)) + (-sig1 + sig2)*exp(-beta**2*cv*t)*exp(beta**2*cv*t2)/(beta**2*cv*(-t1 + t2))
Tm += -(-sig1 + sig2)*exp(-beta**2*cv*(t-t1))/(beta**2*cv*(-t1 + t2)) + (-sig1 + sig2)*exp(-beta**2*cv*(t-t2))/(beta**2*cv*(-t1 + t2))
return Tm
