def resDamp(factProps, t1, t2, t3, t4, t5, tau_max, G_max, gamma, damp):
GQH_damp = GQH_damping(tau_max, G_max, t1, t2, t3, t4, t5, gamma)
GQH_GGmax = GQH_modulusreduction(tau_max, G_max, t1, t2, t3, t4, t5, gamma)
GQH_GGmax[np.where(GQH_GGmax > 1.0)] = 1.0
factor = factProps[0] - factProps[1] * (1.0 - GQH_GGmax)**factProps[2]
GQH_damp = factor * GQH_damp
return damp - GQH_damp
def plot_curve(t1,
t2,
t3,
t4,
t5,
p1,
p2,
p3,
D,
strength,
Gmax,
model,
p=101.3,
PI_Cu=0.0,
OCR_D50=1.0,
filename='test.png'):
ax_title = ""
if model == 'VuceticDobry':
GGmax, damp, gamma = VuceticDobry(PI_Cu)
ax_title = f"Vucetic-Dobry: PI = {PI_Cu}"
elif model == 'Darendeli':
GGmax, damp, gamma = Darendeli(p, PI_Cu, OCR_D50, Patm=101.3)
ax_title = f"Darendeli: p = {p:.2f}kPa, PI = {PI_Cu}, OCR = {OCR_D50}"
elif model == 'Menq':
GGmax, damp, gamma = Menq(p, PI_Cu, OCR_D50, Patm=101.3)
ax_title = f"Menq: p = {p:.2f}kPa, Cu = {PI_Cu}, D50 = {OCR_D50}"
elif model == 'Zhang':
GGmax, damp, gamma = Zhang2005(p, PI_Cu, age='Quaternary', Patm=101.3)
ax_title = f"Zhang2005: p = {p:.2f}kPa, Cu = {PI_Cu}, age='Quaternary'"
else:
raise (f"Material model {model} is not implemented!")
GQH_GGmax = GQH_modulusreduction(strength, Gmax, t1, t2, t3, t4, t5, gamma)
GQH_damp_org = GQH_damping(strength, Gmax, t1, t2, t3, t4, t5, gamma)
factor = p1 - p2 * (1.0 - GQH_GGmax)**p3
GQH_damp = D + factor * GQH_damp_org
fig = plt.figure(figsize=(7, 8), dpi=150, tight_layout=True)
ax1 = fig.add_subplot(2, 1, 1)
ax2 = fig.add_subplot(2, 1, 2)
ax3 = ax1.twinx()
ax1.semilogx(gamma * 100.0, GGmax, 'b-', lw=1.0, label='Empirical')
ax1.semilogx(gamma * 100.0, GQH_GGmax, 'r-', lw=2.0, label='GQH')
ax3.semilogx(gamma * 100.0, damp, 'b--', lw=1.0)
ax3.semilogx(gamma * 100.0, GQH_damp * 100.0, 'r--', lw=2.0)
ax1.set_xlim(0.0001, 10.0)
ax1.set_ylim(0.0, 1.0)
ax3.set_ylim(ymin=0.0)
ax1.set_xlabel(r'$\gamma$ (%)')
ax1.set_ylabel(r'$G/G_{max}$')
ax3.set_ylabel(r'$\xi$ (%)')
ax1.set_title(ax_title)
ax1.grid(which='both', lw=0.25, linestyle=':', color=(0.25, 0.25, 0.25))
ax2.plot(gamma * 100.0,
GGmax * Gmax * gamma,
'b-',
lw=1.0,
label='Empirical')
ax2.plot(gamma * 100.0,
GQH_GGmax * Gmax * gamma,
'r-',
lw=2.0,
label='GQH')
ax2.axhline(strength, color='k', linestyle='--', lw=1.0)
ax2.set_xlabel(r'$\gamma$ (%)')
ax2.set_ylabel(r'$\tau$ (kPa)')
ax2.set_xlim(0.0, 10.0)
ax2.set_ylim(ymin=0.0)
ax2.legend(loc="lower right")
ax2.grid(which='both', lw=0.25, linestyle=':', color=(0.25, 0.25, 0.25))
fig.savefig(filename)
plt.close(fig)
def calibrateGQH_Zhang2005_LS(p,
PI,
tau_max,
G_max,
age='Quaternary',
Patm=101.3):
# get the reference modulus reduction curve
GGmax2, damp2, gamma2 = Zhang2005(p, PI, age, Patm)
# set a cut-off strain for optimization
eps_cutoff = 100.0
index = np.where(gamma2 > eps_cutoff)
GGmax = np.delete(GGmax2, index)
gamma = np.delete(gamma2, index)
# calculate the theta_tau for the reference GGmax curve
gr = tau_max / G_max
Gam = (gamma / gr)
tt = (GGmax + GGmax * Gam - 1.0) / (GGmax**2.0 * Gam)
tt[np.where(tt > 1.0)] = 1.0
# initial guess
t10 = -1.0
t20 = -3.0
t30 = 1.0
t50 = 0.5
# perform the least squares analysis
initProp = [t10, t20, t30, t50]
# res = least_squares(GHQ_tt_res, initProp, args=(tt, tau_max, G_max, gamma), bounds=([-20.0, -20.0, 0.0001, 0.0],[20.0, 20.0, np.inf, 0.99]))
# t1 = res.x[0]
# t2 = res.x[1]
# t3 = res.x[2]
# t4 = 1.0
# t5 = res.x[3]
res = fmin_slsqp(errorGGmax,
initProp,
args=(tau_max, G_max, gamma2, GGmax2),
bounds=[(-20, 20), (-20, 20), (0, np.inf), (0.1, 0.99)],
ieqcons=[constraint1, constraint2, constraint3],
iprint=-1)
t1 = res[0]
t2 = res[1]
t3 = res[2]
t4 = 1.0
t5 = res[3]
# check the strength and the optimized values
GQH_GGmax = GQH_modulusreduction(tau_max, G_max, t1, t2, t3, t4, t5,
gamma2)
# app_strength = (G_max*GQH_GGmax*gamma2)[-1]
# if (app_strength < 0.95 * tau_max) or (t1 + t2 > 1.0):
# initProp = [t10, t20]
# res = least_squares(GHQ_tt_res95_1, initProp, args=(tt, tau_max, G_max, gamma, t3, t5), bounds=([-20.0, -20.0],[20.0, 20.0]))
# t1 = res.x[0]
# t2 = res.x[1]
# initProp = [t30, t50]
# res = least_squares(GHQ_tt_res95_2, initProp, args=(tt, tau_max, G_max, gamma, t1, t2), bounds=([0.0001, 0.0],[np.inf, 0.99]))
# t3 = res.x[0]
# t5 = res.x[1]
# optimize the damping parameters
initProps = [1.0, 0.0, 1.0]
res = least_squares(resDamp,
initProps,
args=(t1, t2, t3, t4, t5, tau_max, G_max, gamma2,
damp2 / 100.0),
bounds=([0.0, 0.0, 0.0], [np.inf, np.inf, np.inf]))
p1 = res.x[0]
p2 = res.x[1]
p3 = res.x[2]
# calculate the minimum damping and revise the parameters
GQH_damp_org = GQH_damping(tau_max, G_max, t1, t2, t3, t4, t5, gamma)
factor = p1 - p2 * (1.0 - GQH_GGmax)**p3
D = damp2[0] / 100.0 - factor[0] * GQH_damp_org[0]
res = least_squares(resDamp,
initProps,
args=(t1, t2, t3, t4, t5, tau_max, G_max, gamma2,
damp2 / 100.0 - D),
bounds=([0.0, 0.0, 0.0], [np.inf, np.inf, np.inf]))
p1 = res.x[0]
p2 = res.x[1]
p3 = res.x[2]
return t1, t2, t3, t4, t5, p1, p2, p3, D
def main():
PI = 50.0
G_max = 50000.0
tau_max = 100.0
# t1,t2,t3,t4,t5,p1,p2,p3,D = calibrateGQH_Darendeli(p,PI,OCR,tau_max,G_max, Patm=2117.0)
# GGmax, damp, gamma = VuceticDobry(PI)
# t1,t2,t3,t4,t5,p1,p2,p3,D = calibrateGQH_VuceticDobry_LS(PI,tau_max,G_max)
GGmax, damp, gamma = Zhang2005(200.0, PI, Patm=101.3)
t1, t2, t3, t4, t5, p1, p2, p3, D = calibrateGQH_Zhang2005_LS(200.0,
PI,
tau_max,
G_max,
Patm=101.3)
GQH_GGmax = GQH_modulusreduction(tau_max, G_max, t1, t2, t3, t4, t5, gamma)
GQH_damp_org = GQH_damping(tau_max, G_max, t1, t2, t3, t4, t5, gamma)
factor = p1 - p2 * (1.0 - GQH_GGmax)**p3
GQH_damp = D + factor * GQH_damp_org
print(" t1 = {0} \n t2 = {1} \n t3 = {2} \n t4 = {3} \n t5 = {4} \n p1 = {5} \n p2 = {6} \n p3 = {7} \n D = {8}".format( \
t1, t2, t3, t4, t5, p1, p2, p3, damp[0]-GQH_damp[0]))
plt.figure("GGmax")
plt.semilogx(gamma * 100.0, GGmax, label='Vucetic')
plt.semilogx(gamma * 100.0, GQH_GGmax, label='GQH')
plt.xlabel('gamma (%)')
plt.ylabel('G/Gmax')
plt.legend()
plt.grid(which='both')
plt.show(block=False)
plt.figure("Stress-Strain")
plt.plot(gamma * 100.0, GGmax * G_max * gamma, label='Vucetic')
plt.plot(gamma * 100.0, GQH_GGmax * G_max * gamma, label='GQH')
plt.plot(gamma * 100.0, 0.0 * gamma + tau_max, 'k--')
plt.plot(gamma * 100.0, 0.0 * gamma + (0.95 * tau_max), 'k--')
plt.xlabel('gamma (%)')
plt.ylabel('tau (psf)')
plt.legend()
plt.grid(which='both')
plt.show(block=False)
plt.figure("Damp")
plt.semilogx(gamma * 100.0, damp, label='Vucetic')
plt.semilogx(gamma * 100.0, GQH_damp_org * 100.0, label='GQH_original')
plt.semilogx(gamma * 100.0, GQH_damp * 100.0, label='GQH_corrected')
plt.ylabel('damping ratio (%)')
plt.xlabel('gamma (%)')
plt.legend()
plt.grid(which='both')
plt.show()
p = 650.0
PI = 0.0
OCR = 1.0
G_max = 130 / 32.2 * 1785.21**2.0
tau_max = 20000.0
GGmax, damp, gamma = Darendeli(p, PI, OCR, Patm=2117.0)
# t1,t2,t3,t4,t5,p1,p2,p3,D = calibrateGQH_Darendeli(p,PI,OCR,tau_max,G_max, Patm=2117.0)
t1, t2, t3, t4, t5, p1, p2, p3, D = calibrateGQH_Darendeli_LS(p,
PI,
OCR,
tau_max,
G_max,
Patm=2117.0)
GQH_GGmax = GQH_modulusreduction(tau_max, G_max, t1, t2, t3, t4, t5, gamma)
GQH_damp_org = GQH_damping(tau_max, G_max, t1, t2, t3, t4, t5, gamma)
factor = p1 - p2 * (1.0 - GQH_GGmax)**p3
GQH_damp = D + factor * GQH_damp_org
print(" t1 = {0} \n t2 = {1} \n t3 = {2} \n t4 = {3} \n t5 = {4} \n p1 = {5} \n p2 = {6} \n p3 = {7} \n D = {8}".format( \
t1, t2, t3, t4, t5, p1, p2, p3, damp[0]-GQH_damp[0]))
plt.figure("GGmax")
plt.semilogx(gamma * 100.0, GGmax, label='Darendeli')
plt.semilogx(gamma * 100.0, GQH_GGmax, label='GQH')
plt.xlabel('gamma (%)')
plt.ylabel('G/Gmax')
plt.legend()
plt.grid(which='both')
plt.show(block=False)
plt.figure("Stress-Strain")
plt.plot(gamma * 100.0, GGmax * G_max * gamma, label='Darendeli')
plt.plot(gamma * 100.0, GQH_GGmax * G_max * gamma, label='GQH')
plt.plot(gamma * 100.0, 0.0 * gamma + tau_max, 'k--')
plt.plot(gamma * 100.0, 0.0 * gamma + (0.95 * tau_max), 'k--')
plt.xlabel('gamma (%)')
plt.ylabel('tau (psf)')
plt.legend()
plt.grid(which='both')
plt.show(block=False)
plt.figure("Damp")
plt.semilogx(gamma * 100.0, damp, label='Darendeli')
plt.semilogx(gamma * 100.0, GQH_damp_org * 100.0, label='GQH_original')
plt.semilogx(gamma * 100.0, GQH_damp * 100.0, label='GQH_corrected')
plt.ylabel('damping ratio (%)')
plt.xlabel('gamma (%)')
plt.legend()
plt.grid(which='both')
plt.show()
p = 650.0
Cu = 2.0
D50 = 0.1
G_max = 130 / 32.2 * 1000.0**2.0
tau_max = 10000.0
GGmax, damp, gamma = Menq(p, Cu, D50, Patm=2117.0)
t1, t2, t3, t4, t5, p1, p2, p3, D = calibrateGQH_Menq_LS(p,
Cu,
D50,
tau_max,
G_max,
Patm=2117.0)
GQH_GGmax = GQH_modulusreduction(tau_max, G_max, t1, t2, t3, t4, t5, gamma)
GQH_damp_org = GQH_damping(tau_max, G_max, t1, t2, t3, t4, t5, gamma)
factor = p1 - p2 * (1.0 - GQH_GGmax)**p3
GQH_damp = D + factor * GQH_damp_org
print(" t1 = {0} \n t2 = {1} \n t3 = {2} \n t4 = {3} \n t5 = {4} \n p1 = {5} \n p2 = {6} \n p3 = {7} \n D = {8}".format( \
t1, t2, t3, t4, t5, p1, p2, p3, damp[0]-GQH_damp[0]))
plt.figure("GGmax")
plt.semilogx(gamma * 100.0, GGmax, label='Menq')
plt.semilogx(gamma * 100.0, GQH_GGmax, label='GQH')
plt.xlabel('gamma (%)')
plt.ylabel('G/Gmax')
plt.legend()
plt.grid(which='both')
plt.show(block=False)
plt.figure("Stress")
plt.plot(gamma * 100.0, GGmax * G_max * gamma, label='Menq')
plt.plot(gamma * 100.0, GQH_GGmax * G_max * gamma, label='GQH')
plt.plot(gamma * 100.0, 0.0 * gamma + tau_max, 'k--')
plt.plot(gamma * 100.0, 0.0 * gamma + (0.95 * tau_max), 'k--')
plt.xlabel('gamma (%)')
plt.ylabel('tau (psf)')
plt.legend()
plt.grid(which='both')
plt.show(block=False)
plt.figure("Damp")
plt.semilogx(gamma * 100.0, damp, label='Menq')
plt.semilogx(gamma * 100.0, GQH_damp_org * 100.0, label='GQH_original')
plt.semilogx(gamma * 100.0, GQH_damp * 100.0, label='GQH_corrected')
plt.ylabel('damping ratio (%)')
plt.xlabel('gamma (%)')
plt.legend()
plt.grid(which='both')
plt.show()
def errorDamp(factProps, t1, t2, t3, t4, t5, tau_max, G_max, gamma, damp):
GQH_damp = GQH_damping(tau_max, G_max, t1, t2, t3, t4, t5, gamma)
GQH_GGmax = GQH_modulusreduction(tau_max, G_max, t1, t2, t3, t4, t5, gamma)
factor = factProps[0] - factProps[1] * (1.0 - GQH_GGmax)**factProps[2]
GQH_damp = factProps[3] + factor * GQH_damp
return np.dot((damp - GQH_damp) / damp, (damp - GQH_damp) / damp)