def run():
osi = o3.OpenSeesInstance(ndm=1, ndf=1)
mat = o3.uniaxial_material.Elastic(osi, 3000.0)
n1 = o3.node.Node(osi, 0.0)
n2 = o3.node.Node(osi, 72.0)
o3.Fix1DOF(osi, n1, o3.cc.FIXED)
o3.element.Truss(osi, [n1, n2], 10.0, mat)
ts0 = o3.time_series.Linear(osi)
o3.pattern.Plain(osi, ts0)
o3.Load(osi, n1, [10])
o3.constraints.Transformation(osi)
o3.test_check.NormDispIncr(osi, tol=1.0e-6, max_iter=10)
o3.numberer.RCM(osi)
o3.system.ProfileSPD(osi)
o3.algorithm.NewtonLineSearch(osi, 0.75)
o3.integrator.Newmark(osi, 0.5, 0.25)
o3.analysis.VariableTransient(osi)
o3.analyze(osi, 5, 0.0001, 0.00001, 0.001, 10)
time = o3.get_time(osi)
print(f'time: ', o3.get_time(osi))
approx_vtime = 0.0001 + 0.001 # One step at target, then one step at maximum
assert 0.99 < time / approx_vtime < 1.01, (time, approx_vtime)
o3.set_time(osi, 0.0)
# Can still run a non-variable analysis - since analyze function has multiple dispatch.
o3.analyze(osi, 5, 0.0001)
time = o3.get_time(osi)
print(f'time: ', o3.get_time(osi))
approx_vtime = 0.0001 * 5 # variable transient is not active so time should be dt * 5
# If variable transient is not active then time would be 0.0005
assert 0.99 < time / approx_vtime < 1.01, (time, approx_vtime)
def site_response(sp,
asig,
freqs=(0.5, 10),
xi=0.03,
analysis_dt=0.001,
dy=0.5,
analysis_time=None,
outs=None,
rec_dt=None):
"""
Run seismic analysis of a soil profile - example based on:
http://opensees.berkeley.edu/wiki/index.php/Site_Response_Analysis_of_a_Layered_Soil_Column_(Total_Stress_Analysis)
Parameters
----------
sp: sfsimodels.SoilProfile object
A soil profile
asig: eqsig.AccSignal object
An acceleration signal
Returns
-------
"""
if analysis_time is None:
analysis_time = asig.time[-1]
if outs is None:
outs = {
'ACCX': [0]
} # Export the horizontal acceleration at the surface
if rec_dt is None:
rec_dt = analysis_dt
osi = o3.OpenSeesInstance(ndm=2, ndf=2, state=3)
assert isinstance(sp, sm.SoilProfile)
sp.gen_split(props=['shear_vel', 'unit_mass'], target=dy)
thicknesses = sp.split["thickness"]
n_node_rows = len(thicknesses) + 1
node_depths = np.cumsum(sp.split["thickness"])
node_depths = np.insert(node_depths, 0, 0)
ele_depths = (node_depths[1:] + node_depths[:-1]) / 2
unit_masses = sp.split["unit_mass"] / 1e3
grav = 9.81
omega_1 = 2 * np.pi * freqs[0]
omega_2 = 2 * np.pi * freqs[1]
a0 = 2 * xi * omega_1 * omega_2 / (omega_1 + omega_2)
a1 = 2 * xi / (omega_1 + omega_2)
k0 = 0.5
pois = k0 / (1 + k0)
newmark_gamma = 0.5
newmark_beta = 0.25
ele_width = min(thicknesses)
total_soil_nodes = len(thicknesses) * 2 + 2
# Define nodes and set boundary conditions for simple shear deformation
# Start at top and build down?
sn = [[o3.node.Node(osi, 0, 0), o3.node.Node(osi, ele_width, 0)]]
for i in range(1, n_node_rows):
# Establish left and right nodes
sn.append([
o3.node.Node(osi, 0, -node_depths[i]),
o3.node.Node(osi, ele_width, -node_depths[i])
])
# set x and y dofs equal for left and right nodes
o3.EqualDOF(osi, sn[i][0], sn[i][1], [o3.cc.X, o3.cc.Y])
sn = np.array(sn)
# Fix base nodes
o3.Fix2DOF(osi, sn[-1][0], o3.cc.FREE, o3.cc.FIXED)
o3.Fix2DOF(osi, sn[-1][1], o3.cc.FREE, o3.cc.FIXED)
# Define dashpot nodes
dashpot_node_l = o3.node.Node(osi, 0, -node_depths[-1])
dashpot_node_2 = o3.node.Node(osi, 0, -node_depths[-1])
o3.Fix2DOF(osi, dashpot_node_l, o3.cc.FIXED, o3.cc.FIXED)
o3.Fix2DOF(osi, dashpot_node_2, o3.cc.FREE, o3.cc.FIXED)
# define equal DOF for dashpot and soil base nodes
o3.EqualDOF(osi, sn[-1][0], sn[-1][1], [o3.cc.X])
o3.EqualDOF(osi, sn[-1][0], dashpot_node_2, [o3.cc.X])
# define materials
ele_thick = 1.0 # m
soil_mats = []
strains = np.logspace(-6, -0.5, 16)
ref_strain = 0.005
rats = 1. / (1 + (strains / ref_strain)**0.91)
prev_args = []
prev_kwargs = {}
prev_sl_type = None
eles = []
tau_inds = []
total_stress_inds = 0
strs_inds = []
total_strain_inds = 0
for i in range(len(thicknesses)):
y_depth = ele_depths[i]
sl_id = sp.get_layer_index_by_depth(y_depth)
sl = sp.layer(sl_id)
app2mod = {}
if y_depth > sp.gwl:
umass = sl.unit_sat_mass / 1e3
else:
umass = sl.unit_dry_mass / 1e3
# Define material
if sl.type == 'pm4sand':
sl_class = o3.nd_material.PM4Sand
overrides = {'nu': pois, 'p_atm': 101, 'unit_moist_mass': umass}
app2mod = sl.app2mod
elif sl.type == 'sdmodel':
sl_class = o3.nd_material.StressDensity
overrides = {'nu': pois, 'p_atm': 101, 'unit_moist_mass': umass}
app2mod = sl.app2mod
elif sl.type == 'pimy':
sl_class = o3.nd_material.PressureIndependMultiYield
overrides = {
'nu': pois,
'p_atm': 101,
'rho': umass,
'nd': 2.0,
'g_mod_ref': sl.g_mod / 1e3,
'bulk_mod_ref': sl.bulk_mod / 1e3,
'cohesion': sl.cohesion / 1e3,
'd': 0.0,
# 'no_yield_surf': 20
}
tau_inds.append(total_stress_inds + 3) # 4th
total_stress_inds += 5
strs_inds.append(total_strain_inds + 2) # 3rd
total_strain_inds += 3
else:
sl_class = o3.nd_material.ElasticIsotropic
sl.e_mod = 2 * sl.g_mod * (1 - sl.poissons_ratio) / 1e3
app2mod['rho'] = 'unit_moist_mass'
overrides = {'nu': sl.poissons_ratio, 'unit_moist_mass': umass}
# opw.extensions.to_py_file(osi)
args, kwargs = o3.extensions.get_o3_kwargs_from_obj(
sl, sl_class, custom=app2mod, overrides=overrides)
changed = 0
if sl.type != prev_sl_type or len(args) != len(prev_args) or len(
kwargs) != len(prev_kwargs):
changed = 1
else:
for j, arg in enumerate(args):
if not np.isclose(arg, prev_args[j]):
changed = 1
for pm in kwargs:
if pm not in prev_kwargs or not np.isclose(
kwargs[pm], prev_kwargs[pm]):
changed = 1
if changed:
mat = sl_class(osi, *args, **kwargs)
prev_sl_type = sl.type
prev_args = copy.deepcopy(args)
prev_kwargs = copy.deepcopy(kwargs)
soil_mats.append(mat)
# def element
nodes = [sn[i + 1][0], sn[i + 1][1], sn[i][1],
sn[i][0]] # anti-clockwise
# ele = o3.element.Quad(osi, nodes, ele_thick, o3.cc.PLANE_STRAIN, mat, b2=grav * unit_masses[i])
ele = o3.element.SSPquad(osi,
nodes,
mat,
'PlaneStrain',
ele_thick,
0.0,
b2=grav * unit_masses[i])
eles.append(ele)
# define material and element for viscous dampers
base_sl = sp.layer(sp.n_layers)
c_base = ele_width * base_sl.unit_dry_mass / 1e3 * sp.get_shear_vel_at_depth(
sp.height)
dashpot_mat = o3.uniaxial_material.Viscous(osi, c_base, alpha=1.)
o3.element.ZeroLength(osi, [dashpot_node_l, dashpot_node_2],
mats=[dashpot_mat],
dirs=[o3.cc.DOF2D_X])
# Static analysis
o3.constraints.Transformation(osi)
o3.test_check.NormDispIncr(osi, tol=1.0e-4, max_iter=30, p_flag=0)
o3.algorithm.Newton(osi)
o3.numberer.RCM(osi)
o3.system.ProfileSPD(osi)
o3.integrator.Newmark(osi, newmark_gamma, newmark_beta)
o3.analysis.Transient(osi)
o3.analyze(osi, 40, 1.)
for i in range(len(soil_mats)):
if isinstance(soil_mats[i], o3.nd_material.PM4Sand) or isinstance(
soil_mats[i], o3.nd_material.PressureIndependMultiYield):
o3.update_material_stage(osi, soil_mats[i], 1)
o3.analyze(osi, 50, 0.5)
# reset time and analysis
o3.set_time(osi, 0.0)
o3.wipe_analysis(osi)
# o3.recorder.NodeToFile(osi, 'sample_out.txt', node=nd["R0L"], dofs=[o3.cc.X], res_type='accel')
na = o3.recorder.NodeToArrayCache(osi,
node=sn[0][0],
dofs=[o3.cc.X],
res_type='accel')
otypes = ['ACCX', 'TAU', 'STRS']
ods = {}
for otype in outs:
if otype == 'ACCX':
ods['ACCX'] = []
if isinstance(outs['ACCX'], str) and outs['ACCX'] == 'all':
ods['ACCX'] = o3.recorder.NodesToArrayCache(osi,
nodes=sn[:, 0],
dofs=[o3.cc.X],
res_type='accel',
dt=rec_dt)
else:
for i in range(len(outs['ACCX'])):
ind = np.argmin(abs(node_depths - outs['ACCX'][i]))
ods['ACCX'].append(
o3.recorder.NodeToArrayCache(osi,
node=sn[ind][0],
dofs=[o3.cc.X],
res_type='accel',
dt=rec_dt))
if otype == 'TAU':
ods['TAU'] = []
if isinstance(outs['TAU'], str) and outs['TAU'] == 'all':
ods['TAU'] = o3.recorder.ElementsToArrayCache(
osi, eles=eles, arg_vals=['stress'], dt=rec_dt)
else:
for i in range(len(outs['TAU'])):
ind = np.argmin(abs(ele_depths - outs['TAU'][i]))
ods['TAU'].append(
o3.recorder.ElementToArrayCache(osi,
ele=eles[ind],
arg_vals=['stress'],
dt=rec_dt))
if otype == 'STRS':
ods['STRS'] = []
if isinstance(outs['STRS'], str) and outs['STRS'] == 'all':
ods['STRS'] = o3.recorder.ElementsToArrayCache(
osi, eles=eles, arg_vals=['strain'], dt=rec_dt)
else:
for i in range(len(outs['STRS'])):
ind = np.argmin(abs(ele_depths - outs['STRS'][i]))
ods['STRS'].append(
o3.recorder.ElementToArrayCache(osi,
ele=eles[ind],
arg_vals=['strain'],
dt=rec_dt))
# Define the dynamic analysis
ts_obj = o3.time_series.Path(osi,
dt=asig.dt,
values=asig.velocity * -1,
factor=c_base)
o3.pattern.Plain(osi, ts_obj)
o3.Load(osi, sn[-1][0], [1., 0.])
# Run the dynamic analysis
o3.algorithm.Newton(osi)
o3.system.SparseGeneral(osi)
o3.numberer.RCM(osi)
o3.constraints.Transformation(osi)
o3.integrator.Newmark(osi, newmark_gamma, newmark_beta)
o3.rayleigh.Rayleigh(osi, a0, a1, 0, 0)
o3.analysis.Transient(osi)
o3.test_check.EnergyIncr(osi, tol=1.0e-7, max_iter=10)
o3.extensions.to_py_file(osi)
while opy.getTime() < analysis_time:
print(opy.getTime())
if o3.analyze(osi, 1, analysis_dt):
print('failed')
break
opy.wipe()
out_dict = {}
for otype in ods:
if isinstance(ods[otype], list):
out_dict[otype] = []
for i in range(len(ods[otype])):
a = ods[otype][i].collect()
out_dict[otype].append(
a[3::4]) # TODO: not working for generic case
out_dict[otype] = np.array(out_dict[otype])
else:
if otype == 'TAU':
a = ods[otype].collect()
out_dict[otype] = a[:, tau_inds].T * 1e3
elif otype == 'STRS':
a = ods[otype].collect()
out_dict[otype] = a[:, strs_inds].T
else:
out_dict[otype] = ods[otype].collect().T
out_dict['time'] = np.arange(0, len(out_dict[otype][0])) * rec_dt
return out_dict
def site_response(sp,
asig,
freqs=(0.5, 10),
xi=0.03,
analysis_dt=0.001,
dy=0.5,
analysis_time=None,
outs=None,
rec_dt=None,
use_explicit=0):
"""
Run seismic analysis of a soil profile that has a compliant base
Parameters
----------
sp: sfsimodels.SoilProfile object
A soil profile
asig: eqsig.AccSignal object
An acceleration signal
Returns
-------
"""
if analysis_time is None:
analysis_time = asig.time[-1]
if outs is None:
outs = {
'ACCX': [0]
} # Export the horizontal acceleration at the surface
if rec_dt is None:
rec_dt = analysis_dt
osi = o3.OpenSeesInstance(ndm=2, ndf=2, state=3)
assert isinstance(sp, sm.SoilProfile)
sp.gen_split(props=['shear_vel', 'unit_mass'], target=dy)
thicknesses = sp.split["thickness"]
n_node_rows = len(thicknesses) + 1
node_depths = np.cumsum(sp.split["thickness"])
node_depths = np.insert(node_depths, 0, 0)
ele_depths = (node_depths[1:] + node_depths[:-1]) / 2
unit_masses = sp.split["unit_mass"] / 1e3
grav = 9.81
omega_1 = 2 * np.pi * freqs[0]
omega_2 = 2 * np.pi * freqs[1]
a0 = 2 * xi * omega_1 * omega_2 / (omega_1 + omega_2)
a1 = 2 * xi / (omega_1 + omega_2)
k0 = 0.5
pois = k0 / (1 + k0)
newmark_gamma = 0.5
newmark_beta = 0.25
ele_width = min(thicknesses)
# Define nodes and set boundary conditions for simple shear deformation
# Start at top and build down?
sn = [[o3.node.Node(osi, 0, 0), o3.node.Node(osi, ele_width, 0)]]
for i in range(1, n_node_rows):
# Establish left and right nodes
sn.append([
o3.node.Node(osi, 0, -node_depths[i]),
o3.node.Node(osi, ele_width, -node_depths[i])
])
# set x and y dofs equal for left and right nodes
o3.EqualDOF(osi, sn[i][0], sn[i][1], [o3.cc.X, o3.cc.Y])
# Fix base nodes
o3.Fix2DOF(osi, sn[-1][0], o3.cc.FREE, o3.cc.FIXED)
o3.Fix2DOF(osi, sn[-1][1], o3.cc.FREE, o3.cc.FIXED)
# Define dashpot nodes
dashpot_node_l = o3.node.Node(osi, 0, -node_depths[-1])
dashpot_node_2 = o3.node.Node(osi, 0, -node_depths[-1])
o3.Fix2DOF(osi, dashpot_node_l, o3.cc.FIXED, o3.cc.FIXED)
o3.Fix2DOF(osi, dashpot_node_2, o3.cc.FREE, o3.cc.FIXED)
# define equal DOF for dashpot and soil base nodes
o3.EqualDOF(osi, sn[-1][0], sn[-1][1], [o3.cc.X])
o3.EqualDOF(osi, sn[-1][0], dashpot_node_2, [o3.cc.X])
# define materials
ele_thick = 1.0 # m
soil_mats = []
prev_args = []
prev_kwargs = {}
prev_sl_type = None
eles = []
for i in range(len(thicknesses)):
y_depth = ele_depths[i]
sl_id = sp.get_layer_index_by_depth(y_depth)
sl = sp.layer(sl_id)
app2mod = {}
if y_depth > sp.gwl:
umass = sl.unit_sat_mass / 1e3
else:
umass = sl.unit_dry_mass / 1e3
# Define material
sl_class = o3.nd_material.ElasticIsotropic
sl.e_mod = 2 * sl.g_mod * (1 + sl.poissons_ratio) / 1e3
app2mod['rho'] = 'unit_moist_mass'
overrides = {'nu': sl.poissons_ratio, 'unit_moist_mass': umass}
args, kwargs = o3.extensions.get_o3_kwargs_from_obj(
sl, sl_class, custom=app2mod, overrides=overrides)
changed = 0
if sl.type != prev_sl_type or len(args) != len(prev_args) or len(
kwargs) != len(prev_kwargs):
changed = 1
else:
for j, arg in enumerate(args):
if not np.isclose(arg, prev_args[j]):
changed = 1
for pm in kwargs:
if pm not in prev_kwargs or not np.isclose(
kwargs[pm], prev_kwargs[pm]):
changed = 1
if changed:
mat = sl_class(osi, *args, **kwargs)
prev_sl_type = sl.type
prev_args = copy.deepcopy(args)
prev_kwargs = copy.deepcopy(kwargs)
soil_mats.append(mat)
# def element
nodes = [sn[i + 1][0], sn[i + 1][1], sn[i][1],
sn[i][0]] # anti-clockwise
eles.append(
o3.element.SSPquad(osi, nodes, mat, o3.cc.PLANE_STRAIN, ele_thick,
0.0, -grav))
# eles.append(o3.element.Quad(osi, nodes, mat=mat, otype=o3.cc.PLANE_STRAIN, thick=ele_thick, pressure=0.0, rho=unit_masses[i], b2=grav))
# define material and element for viscous dampers
base_sl = sp.layer(sp.n_layers)
c_base = ele_width * base_sl.unit_dry_mass / 1e3 * sp.get_shear_vel_at_depth(
sp.height)
dashpot_mat = o3.uniaxial_material.Viscous(osi, c_base, alpha=1.)
o3.element.ZeroLength(osi, [dashpot_node_l, dashpot_node_2],
mats=[dashpot_mat],
dirs=[o3.cc.DOF2D_X])
# Static analysis
o3.constraints.Transformation(osi)
o3.test_check.NormDispIncr(osi, tol=1.0e-4, max_iter=30, p_flag=0)
o3.algorithm.Newton(osi)
o3.numberer.RCM(osi)
o3.system.ProfileSPD(osi)
o3.integrator.Newmark(osi, newmark_gamma, newmark_beta)
o3.analysis.Transient(osi)
o3.analyze(osi, 40, 1.)
for i in range(len(soil_mats)):
if isinstance(soil_mats[i], o3.nd_material.PM4Sand) or isinstance(
soil_mats[i], o3.nd_material.PressureIndependMultiYield):
o3.update_material_stage(osi, soil_mats[i], 1)
o3.analyze(osi, 50, 0.5)
# reset time and analysis
o3.set_time(osi, 0.0)
o3.wipe_analysis(osi)
ods = {}
for otype in outs:
if otype == 'ACCX':
ods['ACCX'] = []
if isinstance(outs['ACCX'], str) and outs['ACCX'] == 'all':
ods['ACCX'] = o3.recorder.NodesToArrayCache(osi,
nodes=sn[:][0],
dofs=[o3.cc.X],
res_type='accel',
dt=rec_dt)
else:
for i in range(len(outs['ACCX'])):
ind = np.argmin(abs(node_depths - outs['ACCX'][i]))
ods['ACCX'].append(
o3.recorder.NodeToArrayCache(osi,
node=sn[ind][0],
dofs=[o3.cc.X],
res_type='accel',
dt=rec_dt))
if otype == 'TAU':
ods['TAU'] = []
if isinstance(outs['TAU'], str) and outs['TAU'] == 'all':
ods['TAU'] = o3.recorder.ElementsToArrayCache(
osi, eles=eles, arg_vals=['stress'], dt=rec_dt)
else:
for i in range(len(outs['TAU'])):
ind = np.argmin(abs(ele_depths - outs['TAU'][i]))
ods['TAU'].append(
o3.recorder.ElementToArrayCache(osi,
ele=eles[ind],
arg_vals=['stress'],
dt=rec_dt))
if otype == 'STRS':
ods['STRS'] = []
if isinstance(outs['STRS'], str) and outs['STRS'] == 'all':
ods['STRS'] = o3.recorder.ElementsToArrayCache(
osi, eles=eles, arg_vals=['strain'], dt=rec_dt)
else:
for i in range(len(outs['STRS'])):
ind = np.argmin(abs(ele_depths - outs['STRS'][i]))
ods['STRS'].append(
o3.recorder.ElementToArrayCache(osi,
ele=eles[ind],
arg_vals=['strain'],
dt=rec_dt))
# Define the dynamic analysis
ts_obj = o3.time_series.Path(osi,
dt=asig.dt,
values=asig.velocity * 1,
factor=c_base)
o3.pattern.Plain(osi, ts_obj)
o3.Load(osi, sn[-1][0], [1., 0.])
# Run the dynamic analysis
if use_explicit:
o3.system.FullGeneral(osi)
# o3.algorithm.Newton(osi)
o3.algorithm.Linear(osi)
# o3.integrator.ExplicitDifference(osi)
# o3.integrator.CentralDifference(osi)
o3.integrator.NewmarkExplicit(osi, newmark_gamma) # also works
else:
o3.system.SparseGeneral(osi)
o3.algorithm.Newton(osi)
o3.integrator.Newmark(osi, newmark_gamma, newmark_beta)
o3.numberer.RCM(osi)
o3.constraints.Transformation(osi)
n = 2
modal_damp = 0
omegas = np.array(o3.get_eigen(osi, n=n))**0.5
response_periods = 2 * np.pi / omegas
print('response_periods: ', response_periods)
if not modal_damp:
o3.rayleigh.Rayleigh(osi, a0, a1, 0, 0)
else:
o3.ModalDamping(osi, [xi, xi])
o3.analysis.Transient(osi)
o3.test_check.NormDispIncr(osi, tol=1.0e-6, max_iter=10)
while o3.get_time(osi) < analysis_time:
print(o3.get_time(osi))
if o3.analyze(osi, 1, analysis_dt):
print('failed')
break
o3.wipe(osi)
out_dict = {}
for otype in ods:
if isinstance(ods[otype], list):
out_dict[otype] = []
for i in range(len(ods[otype])):
out_dict[otype].append(ods[otype][i].collect())
out_dict[otype] = np.array(out_dict[otype])
else:
out_dict[otype] = ods[otype].collect().T
out_dict['time'] = np.arange(0, analysis_time, rec_dt)
return out_dict
def site_response(sp, asig, linear=0):
"""
Run seismic analysis of a soil profile - example based on:
http://opensees.berkeley.edu/wiki/index.php/Site_Response_Analysis_of_a_Layered_Soil_Column_(Total_Stress_Analysis)
:param sp: sfsimodels.SoilProfile object
A soil profile
:param asig: eqsig.AccSignal object
An acceleration signal
:return:
"""
osi = o3.OpenSeesInstance(ndm=2, ndf=2, state=3)
assert isinstance(sp, sm.SoilProfile)
sp.gen_split(props=['shear_vel', 'unit_mass', 'cohesion', 'phi', 'bulk_mod', 'poissons_ratio', 'strain_peak'])
thicknesses = sp.split["thickness"]
n_node_rows = len(thicknesses) + 1
node_depths = np.cumsum(sp.split["thickness"])
node_depths = np.insert(node_depths, 0, 0)
ele_depths = (node_depths[1:] + node_depths[:-1]) / 2
shear_vels = sp.split["shear_vel"]
unit_masses = sp.split["unit_mass"] / 1e3
g_mods = unit_masses * shear_vels ** 2
poissons_ratio = sp.split['poissons_ratio']
youngs_mods = 2 * g_mods * (1 - poissons_ratio)
bulk_mods = youngs_mods / (3 * (1 - 2 * poissons_ratio))
bulk_mods = sp.split['bulk_mod'] / 1e3
ref_pressure = 80.0
cohesions = sp.split['cohesion'] / 1e3
phis = sp.split['phi']
strain_peaks = sp.split['strain_peak']
grav = 9.81
damping = 0.03
omega_1 = 2 * np.pi * 0.5
omega_2 = 2 * np.pi * 10
a0 = 2 * damping * omega_1 * omega_2 / (omega_1 + omega_2)
a1 = 2 * damping / (omega_1 + omega_2)
newmark_gamma = 0.5
newmark_beta = 0.25
ele_width = min(thicknesses)
total_soil_nodes = len(thicknesses) * 2 + 2
# Define nodes and set boundary conditions for simple shear deformation
# Start at top and build down?
nd = OrderedDict()
nd["R0L"] = o3.node.Node(osi, 0, 0) # row 0 left
nd["R0R"] = o3.node.Node(osi, ele_width, 0)
for i in range(1, n_node_rows):
# Establish left and right nodes
nd[f"R{i}L"] = o3.node.Node(osi, 0, -node_depths[i])
nd[f"R{i}R"] = o3.node.Node(osi, ele_width, -node_depths[i])
# set x and y dofs equal for left and right nodes
o3.EqualDOF(osi, nd[f"R{i}L"], nd[f"R{i}R"], [o3.cc.X, o3.cc.Y])
# Fix base nodes
o3.Fix2DOF(osi, nd[f"R{n_node_rows - 1}L"], o3.cc.FREE, o3.cc.FIXED)
o3.Fix2DOF(osi, nd[f"R{n_node_rows - 1}R"], o3.cc.FREE, o3.cc.FIXED)
# Define dashpot nodes
dashpot_node_l = o3.node.Node(osi, 0, -node_depths[-1])
dashpot_node_2 = o3.node.Node(osi, 0, -node_depths[-1])
o3.Fix2DOF(osi, dashpot_node_l, o3.cc.FIXED, o3.cc.FIXED)
o3.Fix2DOF(osi, dashpot_node_2, o3.cc.FREE, o3.cc.FIXED)
# define equal DOF for dashpot and soil base nodes
o3.EqualDOF(osi, nd[f"R{n_node_rows - 1}L"], nd[f"R{n_node_rows - 1}R"], [o3.cc.X])
o3.EqualDOF(osi, nd[f"R{n_node_rows - 1}L"], dashpot_node_2, [o3.cc.X])
# define materials
ele_thick = 1.0 # m
soil_mats = []
strains = np.logspace(-6, -0.5, 16)
ref_strain = 0.005
rats = 1. / (1 + (strains / ref_strain) ** 0.91)
eles = []
for i in range(len(thicknesses)):
if not linear:
mat = o3.nd_material.PressureIndependMultiYield(osi, 2, unit_masses[i], g_mods[i],
bulk_mods[i], cohesions[i], strain_peaks[i],
phis[i], d=0.0, n_surf=16,
strains=strains, ratios=rats)
else:
mat = o3.nd_material.ElasticIsotropic(osi, youngs_mods[i], poissons_ratio[i], rho=unit_masses[i])
soil_mats.append(mat)
# def element
nodes = [nd[f"R{i + 1}L"], nd[f"R{i + 1}R"], nd[f"R{i}R"], nd[f"R{i}L"]]
ele = o3.element.Quad(osi, nodes, ele_thick, o3.cc.PLANE_STRAIN, mat, b2=grav * unit_masses[i])
eles.append(ele)
# define material and element for viscous dampers
c_base = ele_width * unit_masses[-1] * shear_vels[-1]
dashpot_mat = o3.uniaxial_material.Viscous(osi, c_base, alpha=1.)
o3.element.ZeroLength(osi, [dashpot_node_l, dashpot_node_2], mats=[dashpot_mat], dirs=[o3.cc.DOF2D_X])
# Static analysis
o3.constraints.Transformation(osi)
o3.test_check.NormDispIncr(osi, tol=1.0e-4, max_iter=30, p_flag=0)
o3.algorithm.Newton(osi)
o3.numberer.RCM(osi)
o3.system.ProfileSPD(osi)
o3.integrator.Newmark(osi, newmark_gamma, newmark_beta)
o3.analysis.Transient(osi)
o3.analyze(osi, 40, 1.)
# for i in range(len(soil_mats)):
# o3.update_material_stage(osi, soil_mats[i], 1)
o3.analyze(osi, 50, 0.5)
# reset time and analysis
o3.set_time(osi, 0.0)
o3.wipe_analysis(osi)
na = o3.recorder.NodeToArrayCache(osi, node=nd["R0L"], dofs=[o3.cc.X], res_type='accel')
es = o3.recorder.ElementsToArrayCache(osi, eles=eles, arg_vals=['stress'])
# Define the dynamic analysis
ts_obj = o3.time_series.Path(osi, dt=asig.dt, values=asig.velocity * -1, factor=c_base)
o3.pattern.Plain(osi, ts_obj)
o3.Load(osi, nd["R{0}L".format(n_node_rows - 1)], [1., 0.])
# Run the dynamic analysis
o3.algorithm.Newton(osi)
o3.system.SparseGeneral(osi)
o3.numberer.RCM(osi)
o3.constraints.Transformation(osi)
o3.integrator.Newmark(osi, newmark_gamma, newmark_beta)
o3.rayleigh.Rayleigh(osi, a0, a1, 0, 0)
o3.analysis.Transient(osi)
o3.test_check.EnergyIncr(osi, tol=1.0e-10, max_iter=10)
analysis_time = asig.time[-1]
analysis_dt = 0.01
# o3.extensions.to_py_file(osi)
while o3.get_time(osi) < analysis_time:
o3.analyze(osi, 1, analysis_dt)
o3.wipe(osi)
outputs = {
"time": np.arange(0, analysis_time, analysis_dt),
"rel_disp": [],
"rel_accel": na.collect(),
'ele_stresses': es.collect()
}
return outputs
def site_response(sp, asig, freqs=(0.5, 10), xi=0.03, dy=0.5, analysis_time=None, outs=None,
rec_dt=None, etype='implicit', forder=1.0):
"""
Run seismic analysis of a soil profile
Parameters
----------
sp: sfsimodels.SoilProfile object
A soil profile
asig: eqsig.AccSignal object
An acceleration signal
Returns
-------
"""
if analysis_time is None:
analysis_time = asig.time[-1]
if outs is None:
outs = {'ACCX': [0]} # Export the horizontal acceleration at the surface
osi = o3.OpenSeesInstance(ndm=2, ndf=2, state=3)
assert isinstance(sp, sm.SoilProfile)
sp.gen_split(props=['shear_vel', 'unit_mass', 'g_mod', 'poissons_ratio'], target=dy)
thicknesses = sp.split["thickness"]
n_node_rows = len(thicknesses) + 1
node_depths = np.cumsum(sp.split["thickness"])
node_depths = np.insert(node_depths, 0, 0)
ele_depths = (node_depths[1:] + node_depths[:-1]) / 2
rho = sp.split['unit_mass']
g_mod = sp.split['g_mod']
poi = sp.split['poissons_ratio']
lam = 2 * g_mod * poi / (1 - 2 * poi)
mu = g_mod
v_dil = np.sqrt((lam + 2 * mu) / rho)
ele_h = sp.split['thickness']
dts = ele_h / v_dil
min_dt = min(dts)
print('min_dt: ', min_dt)
grav = 9.81
ele_width = min(thicknesses)
# Define nodes and set boundary conditions for simple shear deformation
# Start at top and build down?
sn = [[o3.node.Node(osi, 0, 0), o3.node.Node(osi, ele_width, 0)]]
for i in range(1, n_node_rows):
# Establish left and right nodes
sn.append([o3.node.Node(osi, 0, -node_depths[i]),
o3.node.Node(osi, ele_width, -node_depths[i])])
# set x and y dofs equal for left and right nodes
o3.EqualDOF(osi, sn[i][0], sn[i][1], [o3.cc.X, o3.cc.Y])
# Fix base nodes
o3.Fix2DOF(osi, sn[-1][0], o3.cc.FIXED, o3.cc.FIXED)
o3.Fix2DOF(osi, sn[-1][1], o3.cc.FIXED, o3.cc.FIXED)
# define materials
ele_thick = 1.0 # m
soil_mats = []
eles = []
prev_id = -1
for i in range(len(thicknesses)):
y_depth = ele_depths[i]
sl_id = sp.get_layer_index_by_depth(y_depth)
sl = sp.layer(sl_id)
mat = sl.o3_mat
if sl_id != prev_id:
mat.build(osi)
soil_mats.append(mat)
prev_id = sl_id
# def element
nodes = [sn[i+1][0], sn[i+1][1], sn[i][1], sn[i][0]] # anti-clockwise
eles.append(o3.element.SSPquad(osi, nodes, mat, o3.cc.PLANE_STRAIN, ele_thick, 0.0, -grav))
for i, soil_mat in enumerate(soil_mats):
if hasattr(soil_mat, 'update_to_linear'):
print('Update model to linear')
soil_mat.update_to_linear()
# Gravity analysis
o3.constraints.Transformation(osi)
o3.test_check.NormDispIncr(osi, tol=1.0e-5, max_iter=30, p_flag=0)
o3.algorithm.Newton(osi)
o3.numberer.RCM(osi)
o3.system.ProfileSPD(osi)
o3.integrator.Newmark(osi, 5./6, 4./9) # include numerical damping
o3.analysis.Transient(osi)
o3.analyze(osi, 40, 1.)
for i, soil_mat in enumerate(soil_mats):
if hasattr(soil_mat, 'update_to_nonlinear'):
print('Update model to nonlinear')
soil_mat.update_to_nonlinear()
if o3.analyze(osi, 50, 0.5):
print('Model failed')
return
print('finished nonlinear gravity analysis')
# reset time and analysis
o3.set_time(osi, 0.0)
o3.wipe_analysis(osi)
n = 10
# omegas = np.array(o3.get_eigen(osi, solver='fullGenLapack', n=n)) ** 0.5 # DO NOT USE fullGenLapack
omegas = np.array(o3.get_eigen(osi, n=n)) ** 0.5
periods = 2 * np.pi / omegas
print('response_periods: ', periods)
o3.constraints.Transformation(osi)
o3.test_check.NormDispIncr(osi, tol=1.0e-6, max_iter=10)
o3.numberer.RCM(osi)
if etype == 'implicit':
o3.system.ProfileSPD(osi)
o3.algorithm.NewtonLineSearch(osi, 0.75)
o3.integrator.Newmark(osi, 0.5, 0.25)
dt = 0.001
else:
o3.algorithm.Linear(osi)
if etype == 'newmark_explicit':
o3.system.ProfileSPD(osi)
o3.integrator.NewmarkExplicit(osi, gamma=0.5)
explicit_dt = min_dt / 1
elif etype == 'central_difference':
o3.system.ProfileSPD(osi)
o3.integrator.CentralDifference(osi)
explicit_dt = min_dt / 8
elif etype == 'explicit_difference':
o3.system.Diagonal(osi)
o3.integrator.ExplicitDifference(osi)
explicit_dt = min_dt / 2 # need reduced time step due to Rayleigh damping
else:
raise ValueError(etype)
ndp = np.ceil(np.log10(explicit_dt))
if 0.5 * 10 ** ndp < explicit_dt:
dt = 0.5 * 10 ** ndp
elif 0.2 * 10 ** ndp < explicit_dt:
dt = 0.2 * 10 ** ndp
elif 0.1 * 10 ** ndp < explicit_dt:
dt = 0.1 * 10 ** ndp
else:
raise ValueError(explicit_dt, 0.1 * 10 ** ndp)
print('explicit_dt: ', explicit_dt, dt)
use_modal_damping = 0
if not use_modal_damping:
omega_1 = 2 * np.pi * freqs[0]
omega_2 = 2 * np.pi * freqs[1]
a0 = 2 * xi * omega_1 * omega_2 / (omega_1 + omega_2)
a1 = 2 * xi / (omega_1 + omega_2)
o3.rayleigh.Rayleigh(osi, a0, 0, a1, 0)
else:
o3.ModalDamping(osi, [xi])
o3.analysis.Transient(osi)
o3.test_check.NormDispIncr(osi, tol=1.0e-7, max_iter=10)
rec_dt = 0.001
ods = {}
for otype in outs:
if otype == 'ACCX':
ods['ACCX'] = []
if isinstance(outs['ACCX'], str) and outs['ACCX'] == 'all':
ods['ACCX'] = o3.recorder.NodesToArrayCache(osi, nodes=sn[:][0], dofs=[o3.cc.X], res_type='accel', dt=rec_dt)
else:
for i in range(len(outs['ACCX'])):
ind = np.argmin(abs(node_depths - outs['ACCX'][i]))
ods['ACCX'].append(o3.recorder.NodeToArrayCache(osi, node=sn[ind][0], dofs=[o3.cc.X], res_type='accel', dt=rec_dt))
if otype == 'TAU':
ods['TAU'] = []
if isinstance(outs['TAU'], str) and outs['TAU'] == 'all':
ods['TAU'] = o3.recorder.ElementsToArrayCache(osi, eles=eles, arg_vals=['stress'], dt=rec_dt)
else:
for i in range(len(outs['TAU'])):
ind = np.argmin(abs(ele_depths - outs['TAU'][i]))
ods['TAU'].append(o3.recorder.ElementToArrayCache(osi, ele=eles[ind], arg_vals=['stress'], dt=rec_dt))
if otype == 'STRS':
ods['STRS'] = []
if isinstance(outs['STRS'], str) and outs['STRS'] == 'all':
ods['STRS'] = o3.recorder.ElementsToArrayCache(osi, eles=eles, arg_vals=['strain'], dt=rec_dt)
else:
for i in range(len(outs['STRS'])):
ind = np.argmin(abs(ele_depths - outs['STRS'][i]))
ods['STRS'].append(o3.recorder.ElementToArrayCache(osi, ele=eles[ind], arg_vals=['strain'], dt=rec_dt))
ods['time'] = o3.recorder.TimeToArrayCache(osi, dt=rec_dt)
acc_series = o3.time_series.Path(osi, dt=asig.dt, values=asig.values)
o3.pattern.UniformExcitation(osi, dir=o3.cc.X, accel_series=acc_series)
# Run the dynamic analysis
inc = 1
if etype != 'implicit':
inc = 10
o3.record(osi)
while o3.get_time(osi) < analysis_time:
print(o3.get_time(osi))
if o3.analyze(osi, inc, dt):
print('failed')
break
o3.wipe(osi)
out_dict = {}
for otype in ods:
if isinstance(ods[otype], list):
out_dict[otype] = []
for i in range(len(ods[otype])):
out_dict[otype].append(ods[otype][i].collect())
out_dict[otype] = np.array(out_dict[otype])
else:
out_dict[otype] = ods[otype].collect().T
return out_dict
def site_response(sp,
asig,
freqs=(0.5, 10),
xi=0.03,
dtype='rayleigh',
analysis_dt=0.001,
dy=0.5,
analysis_time=None,
outs=None,
rec_dt=None):
"""
Run seismic analysis of a soil profile
Parameters
----------
sp: sfsimodels.SoilProfile object
A soil profile
asig: eqsig.AccSignal object
An acceleration signal
Returns
-------
"""
if analysis_time is None:
analysis_time = asig.time[-1]
if outs is None:
outs = {
'ACCX': [0]
} # Export the horizontal acceleration at the surface
if rec_dt is None:
rec_dt = analysis_dt
osi = o3.OpenSeesInstance(ndm=2, ndf=2, state=3)
assert isinstance(sp, sm.SoilProfile)
sp.gen_split(props=['shear_vel', 'unit_mass'], target=dy)
thicknesses = sp.split["thickness"]
n_node_rows = len(thicknesses) + 1
node_depths = np.cumsum(sp.split["thickness"])
node_depths = np.insert(node_depths, 0, 0)
ele_depths = (node_depths[1:] + node_depths[:-1]) / 2
grav = 9.81
k0 = 0.5
pois = k0 / (1 + k0)
newmark_gamma = 0.5
newmark_beta = 0.25
ele_width = min(thicknesses)
# Define nodes and set boundary conditions for simple shear deformation
# Start at top and build down?
sn = [[o3.node.Node(osi, 0, 0), o3.node.Node(osi, ele_width, 0)]]
for i in range(1, n_node_rows):
# Establish left and right nodes
sn.append([
o3.node.Node(osi, 0, -node_depths[i]),
o3.node.Node(osi, ele_width, -node_depths[i])
])
# set x and y dofs equal for left and right nodes
o3.EqualDOF(osi, sn[i][0], sn[i][1], [o3.cc.X, o3.cc.Y])
# Fix base nodes
o3.Fix2DOF(osi, sn[-1][0], o3.cc.FIXED, o3.cc.FIXED)
o3.Fix2DOF(osi, sn[-1][1], o3.cc.FIXED, o3.cc.FIXED)
# define materials
ele_thick = 1.0 # m
soil_mats = []
prev_pms = [0, 0, 0]
eles = []
for i in range(len(thicknesses)):
y_depth = ele_depths[i]
sl_id = sp.get_layer_index_by_depth(y_depth)
sl = sp.layer(sl_id)
# Define material
e_mod = 2 * sl.g_mod * (1 + sl.poissons_ratio)
umass = sl.unit_dry_mass
nu = sl.poissons_ratio
pms = [e_mod, nu, umass]
changed = 0
for pp in range(len(pms)):
if not np.isclose(pms[pp], prev_pms[pp]):
changed = 1
if changed:
mat = o3.nd_material.ElasticIsotropic(osi,
e_mod=e_mod,
nu=nu,
rho=umass)
soil_mats.append(mat)
# def element
nodes = [sn[i + 1][0], sn[i + 1][1], sn[i][1],
sn[i][0]] # anti-clockwise
eles.append(
o3.element.SSPquad(osi, nodes, mat, o3.cc.PLANE_STRAIN, ele_thick,
0.0, grav * umass))
# Static analysis
o3.constraints.Transformation(osi)
o3.test_check.NormDispIncr(osi, tol=1.0e-5, max_iter=30, p_flag=0)
o3.algorithm.Newton(osi)
o3.numberer.RCM(osi)
o3.system.ProfileSPD(osi)
o3.integrator.Newmark(osi, 5. / 6, 4. / 9) # include numerical damping
o3.analysis.Transient(osi)
o3.analyze(osi, 40, 1.)
# reset time and analysis
o3.set_time(osi, 0.0)
o3.wipe_analysis(osi)
ods = {}
for otype in outs:
if otype == 'ACCX':
ods['ACCX'] = []
if isinstance(outs['ACCX'], str) and outs['ACCX'] == 'all':
ods['ACCX'] = o3.recorder.NodesToArrayCache(osi,
nodes=sn[:][0],
dofs=[o3.cc.X],
res_type='accel',
dt=rec_dt)
else:
for i in range(len(outs['ACCX'])):
ind = np.argmin(abs(node_depths - outs['ACCX'][i]))
ods['ACCX'].append(
o3.recorder.NodeToArrayCache(osi,
node=sn[ind][0],
dofs=[o3.cc.X],
res_type='accel',
dt=rec_dt))
# Run the dynamic analysis
o3.algorithm.Newton(osi)
o3.system.SparseGeneral(osi)
o3.numberer.RCM(osi)
o3.constraints.Transformation(osi)
o3.integrator.Newmark(osi, newmark_gamma, newmark_beta)
if dtype == 'rayleigh':
omega_1 = 2 * np.pi * freqs[0]
omega_2 = 2 * np.pi * freqs[1]
a0 = 2 * xi * omega_1 * omega_2 / (omega_1 + omega_2)
a1 = 2 * xi / (omega_1 + omega_2)
o3.rayleigh.Rayleigh(osi, a0, a1, 0, 0)
else:
n = 20
omegas = np.array(o3.get_eigen(osi, n=n))**0.5
o3.ModalDamping(osi, [xi])
o3.analysis.Transient(osi)
o3.test_check.NormDispIncr(osi, tol=1.0e-7, max_iter=10)
# Define the dynamic analysis
acc_series = o3.time_series.Path(osi, dt=asig.dt, values=asig.values)
o3.pattern.UniformExcitation(osi, dir=o3.cc.X, accel_series=acc_series)
while o3.get_time(osi) < analysis_time:
print(o3.get_time(osi))
if o3.analyze(osi, 1, analysis_dt):
print('failed')
break
o3.wipe(osi)
out_dict = {}
for otype in ods:
if isinstance(ods[otype], list):
out_dict[otype] = []
for i in range(len(ods[otype])):
out_dict[otype].append(ods[otype][i].collect())
out_dict[otype] = np.array(out_dict[otype])
else:
out_dict[otype] = ods[otype].collect().T
out_dict['time'] = np.arange(0, analysis_time, rec_dt)
return out_dict
def site_response(sp, dy=0.5, forder=1.0e3, static=0):
"""
Run gravity analysis of a soil profile
Parameters
----------
sp: sfsimodels.SoilProfile object
A soil profile
Returns
-------
"""
osi = o3.OpenSeesInstance(ndm=2, ndf=2, state=3)
assert isinstance(sp, sm.SoilProfile)
sp.gen_split(props=['shear_vel', 'unit_mass', 'g_mod', 'poissons_ratio'],
target=dy)
thicknesses = sp.split["thickness"]
n_node_rows = len(thicknesses) + 1
node_depths = np.cumsum(sp.split["thickness"])
node_depths = np.insert(node_depths, 0, 0)
ele_depths = (node_depths[1:] + node_depths[:-1]) / 2
rho = sp.split['unit_mass']
g_mod = sp.split['g_mod']
poi = sp.split['poissons_ratio']
lam = 2 * g_mod * poi / (1 - 2 * poi)
mu = g_mod
v_dil = np.sqrt((lam + 2 * mu) / rho)
ele_h = sp.split['thickness']
dts = ele_h / v_dil
min_dt = min(dts)
print('min_dt: ', min_dt)
grav = 9.81
ele_width = min(thicknesses)
# Define nodes and set boundary conditions for simple shear deformation
# Start at top and build down?
sn = [[o3.node.Node(osi, 0, 0), o3.node.Node(osi, ele_width, 0)]]
for i in range(1, n_node_rows):
# Establish left and right nodes
sn.append([
o3.node.Node(osi, 0, -node_depths[i]),
o3.node.Node(osi, ele_width, -node_depths[i])
])
# set x and y dofs equal for left and right nodes
o3.EqualDOF(osi, sn[i][0], sn[i][1], [o3.cc.X, o3.cc.Y])
# Fix base nodes
o3.Fix2DOF(osi, sn[-1][0], o3.cc.FIXED, o3.cc.FIXED)
o3.Fix2DOF(osi, sn[-1][1], o3.cc.FIXED, o3.cc.FIXED)
# define materials
ele_thick = 1.0 # m
soil_mats = []
prev_args = []
prev_kwargs = {}
prev_sl_type = None
eles = []
for i in range(len(thicknesses)):
y_depth = ele_depths[i]
sl_id = sp.get_layer_index_by_depth(y_depth)
sl = sp.layer(sl_id)
app2mod = {}
if y_depth > sp.gwl:
umass = sl.unit_sat_mass / forder
else:
umass = sl.unit_dry_mass / forder
# Define material
sl_class = o3.nd_material.ElasticIsotropic
sl.e_mod = 2 * sl.g_mod * (1 + sl.poissons_ratio) / forder
app2mod['rho'] = 'unit_moist_mass'
overrides = {'nu': sl.poissons_ratio, 'unit_moist_mass': umass}
args, kwargs = o3.extensions.get_o3_kwargs_from_obj(
sl, sl_class, custom=app2mod, overrides=overrides)
changed = 0
if sl.type != prev_sl_type or len(args) != len(prev_args) or len(
kwargs) != len(prev_kwargs):
changed = 1
else:
for j, arg in enumerate(args):
if not np.isclose(arg, prev_args[j]):
changed = 1
for pm in kwargs:
if pm not in prev_kwargs or not np.isclose(
kwargs[pm], prev_kwargs[pm]):
changed = 1
if changed:
mat = sl_class(osi, *args, **kwargs)
prev_sl_type = sl.type
prev_args = copy.deepcopy(args)
prev_kwargs = copy.deepcopy(kwargs)
soil_mats.append(mat)
# def element
nodes = [sn[i + 1][0], sn[i + 1][1], sn[i][1],
sn[i][0]] # anti-clockwise
eles.append(
o3.element.SSPquad(osi, nodes, mat, o3.cc.PLANE_STRAIN, ele_thick,
0.0, -grav))
# Gravity analysis
if not static:
o3.constraints.Transformation(osi)
o3.test_check.NormDispIncr(osi, tol=1.0e-5, max_iter=30, p_flag=0)
o3.algorithm.Newton(osi)
o3.numberer.RCM(osi)
o3.system.ProfileSPD(osi)
o3.integrator.Newmark(osi, 5. / 6, 4. / 9) # include numerical damping
o3.analysis.Transient(osi)
o3.analyze(osi, 40, 1.)
# reset time and analysis
o3.set_time(osi, 0.0)
o3.wipe_analysis(osi)
else:
o3.domain_change(osi)
o3.constraints.Transformation(osi)
o3.test_check.NormDispIncr(osi, tol=1.0e-6, max_iter=10, p_flag=0)
o3.algorithm.Newton(osi)
o3.numberer.apply_rcm(osi)
o3.system.Mumps(osi)
o3.integrator.LoadControl(osi, 0.1)
o3.analysis.Static(osi)
o3.analyze(osi, 10)
ys = []
for nn in range(len(sn)):
nd = sn[nn][0]
ys.append(o3.get_node_disp(osi, nd, dof=o3.cc.Y))
return np.array(ys)
def get_inelastic_response(fb,
roof_drift_ratio=0.05,
elastic=False,
w_sfsi=False,
out_folder=''):
"""
Run seismic analysis of a nonlinear FrameBuilding
Units: Pa, N, m, s
Parameters
----------
fb: sfsimodels.Frame2DBuilding object
xi
Returns
-------
"""
osi = o3.OpenSeesInstance(ndm=2, state=3)
q_floor = 7.0e3 # Pa
trib_width = fb.floor_length
trib_mass_per_length = q_floor * trib_width / 9.8
# Establish nodes and set mass based on trib area
# Nodes named as: C<column-number>-S<storey-number>, first column starts at C1-S0 = ground level left
nd = OrderedDict()
col_xs = np.cumsum(fb.bay_lengths)
col_xs = np.insert(col_xs, 0, 0)
n_cols = len(col_xs)
sto_ys = fb.heights
sto_ys = np.insert(sto_ys, 0, 0)
for cc in range(1, n_cols + 1):
for ss in range(fb.n_storeys + 1):
nd[f"C{cc}-S{ss}"] = o3.node.Node(osi, col_xs[cc - 1], sto_ys[ss])
if ss != 0:
if cc == 1:
node_mass = trib_mass_per_length * fb.bay_lengths[0] / 2
elif cc == n_cols:
node_mass = trib_mass_per_length * fb.bay_lengths[-1] / 2
else:
node_mass = trib_mass_per_length * (
fb.bay_lengths[cc - 2] + fb.bay_lengths[cc - 1] / 2)
o3.set_node_mass(osi, nd[f"C{cc}-S{ss}"], node_mass, 0., 0.)
# Set all nodes on a storey to have the same displacement
for ss in range(0, fb.n_storeys + 1):
for cc in range(2, n_cols + 1):
o3.set_equal_dof(osi, nd[f"C1-S{ss}"], nd[f"C{cc}-S{ss}"], o3.cc.X)
# Fix all base nodes
for cc in range(1, n_cols + 1):
o3.Fix3DOF(osi, nd[f"C{cc}-S0"], o3.cc.FIXED, o3.cc.FIXED, o3.cc.FIXED)
# Define material
e_conc = 30.0e9 # kPa
i_beams = 0.4 * fb.beam_widths * fb.beam_depths**3 / 12
i_columns = 0.5 * fb.column_widths * fb.column_depths**3 / 12
a_beams = fb.beam_widths * fb.beam_depths
a_columns = fb.column_widths * fb.column_depths
ei_beams = e_conc * i_beams
ei_columns = e_conc * i_columns
eps_yield = 300.0e6 / 200e9
phi_y_col = calc_yield_curvature(fb.column_depths, eps_yield)
phi_y_beam = calc_yield_curvature(fb.beam_depths, eps_yield)
# Define beams and columns
# Columns named as: C<column-number>-S<storey-number>, first column starts at C1-S0 = ground floor left
# Beams named as: B<bay-number>-S<storey-number>, first beam starts at B1-S1 = first storey left (foundation at S0)
md = OrderedDict() # material dict
sd = OrderedDict() # section dict
ed = OrderedDict() # element dict
for ss in range(fb.n_storeys):
# set columns
lp_i = 0.4
lp_j = 0.4 # plastic hinge length
col_transf = o3.geom_transf.Linear2D(
osi, ) # d_i=[0.0, lp_i], d_j=[0.0, -lp_j]
for cc in range(1, fb.n_cols + 1):
ele_str = f"C{cc}-S{ss}S{ss + 1}"
if elastic:
top_sect = o3.section.Elastic2D(osi, e_conc,
a_columns[ss][cc - 1],
i_columns[ss][cc - 1])
bot_sect = o3.section.Elastic2D(osi, e_conc,
a_columns[ss][cc - 1],
i_columns[ss][cc - 1])
else:
m_cap = ei_columns[ss][cc - 1] * phi_y_col[ss][cc - 1]
mat = o3.uniaxial_material.ElasticBilin(
osi, ei_columns[ss][cc - 1], 0.05 * ei_columns[ss][cc - 1],
1 * phi_y_col[ss][cc - 1])
mat_axial = o3.uniaxial_material.Elastic(
osi, e_conc * a_columns[ss][cc - 1])
top_sect = o3.section.Aggregator(osi,
mats=[[mat_axial, o3.cc.P],
[mat, o3.cc.M_Z]])
bot_sect = o3.section.Aggregator(osi,
mats=[[mat_axial, o3.cc.P],
[mat, o3.cc.M_Z]])
centre_sect = o3.section.Elastic2D(osi, e_conc,
a_columns[ss][cc - 1],
i_columns[ss][cc - 1])
sd[ele_str + "T"] = top_sect
sd[ele_str + "B"] = bot_sect
sd[ele_str + "C"] = centre_sect
integ = o3.beam_integration.HingeMidpoint(osi, bot_sect, lp_i,
top_sect, lp_j,
centre_sect)
bot_node = nd[f"C{cc}-S{ss}"]
top_node = nd[f"C{cc}-S{ss + 1}"]
ed[ele_str] = o3.element.ForceBeamColumn(osi, [bot_node, top_node],
col_transf, integ)
print('mc: ', ei_columns[ss][cc - 1] * phi_y_col[ss][cc - 1])
# Set beams
lp_i = 0.4
lp_j = 0.4
beam_transf = o3.geom_transf.Linear2D(osi, )
for bb in range(1, fb.n_bays + 1):
ele_str = f"C{bb}C{bb + 1}-S{ss + 1}"
print('mb: ', ei_beams[ss][bb - 1] * phi_y_beam[ss][bb - 1])
print('phi_b: ', phi_y_beam[ss][bb - 1])
if elastic:
left_sect = o3.section.Elastic2D(osi, e_conc,
a_beams[ss][bb - 1],
i_beams[ss][bb - 1])
right_sect = o3.section.Elastic2D(osi, e_conc,
a_beams[ss][bb - 1],
i_beams[ss][bb - 1])
else:
m_cap = ei_beams[ss][bb - 1] * phi_y_beam[ss][bb - 1]
# mat_flex = o3.uniaxial_material.ElasticBilin(osi, ei_beams[ss][bb - 1], 0.05 * ei_beams[ss][bb - 1], phi_y_beam[ss][bb - 1])
mat_flex = o3.uniaxial_material.Steel01(osi,
m_cap,
e0=ei_beams[ss][bb -
1],
b=0.05)
mat_axial = o3.uniaxial_material.Elastic(
osi, e_conc * a_beams[ss][bb - 1])
left_sect = o3.section.Aggregator(osi,
mats=[[mat_axial, o3.cc.P],
[mat_flex, o3.cc.M_Z],
[mat_flex, o3.cc.M_Y]])
right_sect = o3.section.Aggregator(osi,
mats=[[mat_axial, o3.cc.P],
[mat_flex, o3.cc.M_Z],
[mat_flex,
o3.cc.M_Y]])
centre_sect = o3.section.Elastic2D(osi, e_conc,
a_beams[ss][bb - 1],
i_beams[ss][bb - 1])
integ = o3.beam_integration.HingeMidpoint(osi, left_sect, lp_i,
right_sect, lp_j,
centre_sect)
left_node = nd[f"C{bb}-S{ss + 1}"]
right_node = nd[f"C{bb + 1}-S{ss + 1}"]
ed[ele_str] = o3.element.ForceBeamColumn(osi,
[left_node, right_node],
beam_transf, integ)
# Apply gravity loads
gravity = 9.8 * 1e-2
# If true then load applied along beam
g_beams = 0 # TODO: when this is true and analysis is inelastic then failure
ts_po = o3.time_series.Linear(osi, factor=1)
o3.pattern.Plain(osi, ts_po)
for ss in range(1, fb.n_storeys + 1):
print('ss:', ss)
if g_beams:
for bb in range(1, fb.n_bays + 1):
ele_str = f"C{bb}C{bb + 1}-S{ss}"
o3.EleLoad2DUniform(osi, ed[ele_str],
-trib_mass_per_length * gravity)
else:
for cc in range(1, fb.n_cols + 1):
if cc == 1 or cc == n_cols:
node_mass = trib_mass_per_length * fb.bay_lengths[0] / 2
elif cc == n_cols:
node_mass = trib_mass_per_length * fb.bay_lengths[-1] / 2
else:
node_mass = trib_mass_per_length * (
fb.bay_lengths[cc - 2] + fb.bay_lengths[cc - 1] / 2)
# This works
o3.Load(osi, nd[f"C{cc}-S{ss}"], [0, -node_mass * gravity, 0])
tol = 1.0e-3
o3.constraints.Plain(osi)
o3.numberer.RCM(osi)
o3.system.BandGeneral(osi)
o3.test_check.NormDispIncr(osi, tol, 10)
o3.algorithm.Newton(osi)
n_steps_gravity = 10
d_gravity = 1. / n_steps_gravity
o3.integrator.LoadControl(osi, d_gravity, num_iter=10)
o3.analysis.Static(osi)
o3.analyze(osi, n_steps_gravity)
o3.gen_reactions(osi)
print('b1_int: ', o3.get_ele_response(osi, ed['C1C2-S1'], 'force'))
print('c1_int: ', o3.get_ele_response(osi, ed['C1-S0S1'], 'force'))
# o3.extensions.to_py_file(osi, 'po.py')
o3.load_constant(osi, time=0.0)
# Define the analysis
# set damping based on first eigen mode
angular_freq = o3.get_eigen(osi, solver='fullGenLapack', n=1)[0]**0.5
if isinstance(angular_freq, complex):
raise ValueError(
"Angular frequency is complex, issue with stiffness or mass")
print('angular_freq: ', angular_freq)
response_period = 2 * np.pi / angular_freq
print('response period: ', response_period)
# Run the analysis
o3r = o3.results.Results2D()
o3r.cache_path = out_folder
o3r.dynamic = True
o3r.pseudo_dt = 0.001 # since analysis is actually static
o3.set_time(osi, 0.0)
o3r.start_recorders(osi)
# o3res.coords = o3.get_all_node_coords(osi)
# o3res.ele2node_tags = o3.get_all_ele_node_tags_as_dict(osi)
d_inc = 0.0001
o3.numberer.RCM(osi)
o3.system.BandGeneral(osi)
# o3.test_check.NormUnbalance(osi, 2, max_iter=10, p_flag=2)
# o3.test_check.FixedNumIter(osi, max_iter=10)
o3.test_check.NormDispIncr(osi, 0.002, 10, p_flag=0)
o3.algorithm.Newton(osi)
o3.integrator.DisplacementControl(osi, nd[f"C1-S{fb.n_storeys}"], o3.cc.X,
d_inc)
o3.analysis.Static(osi)
d_max = 0.05 * fb.max_height # TODO: set to 5%
print('d_max: ', d_max)
# n_steps = int(d_max / d_inc)
print("Analysis starting")
print('int_disp: ',
o3.get_node_disp(osi, nd[f"C1-S{fb.n_storeys}"], o3.cc.X))
# opy.recorder('Element', '-file', 'ele_out.txt', '-time', '-ele', 1, 'force')
tt = 0
outputs = {
'h_disp': [],
'vb': [],
'REACT-C1C2-S1': [],
'REACT-C1-S0S1': [],
}
hd = 0
n_max = 2
n_cycs = 0
xs = fb.heights / fb.max_height # TODO: more sophisticated displacement profile
ts_po = o3.time_series.Linear(osi, factor=1)
o3.pattern.Plain(osi, ts_po)
for i, xp in enumerate(xs):
o3.Load(osi, nd[f"C1-S{i + 1}"], [xp, 0.0, 0])
# o3.analyze(osi, 2)
# n_max = 0
time = [0]
while n_cycs < n_max:
print('n_cycles: ', n_cycs)
for i in range(2):
if i == 0:
o3.integrator.DisplacementControl(osi,
nd[f"C1-S{fb.n_storeys}"],
o3.cc.X, d_inc)
else:
o3.integrator.DisplacementControl(osi,
nd[f"C1-S{fb.n_storeys}"],
o3.cc.X, -d_inc)
while hd * (-1)**i < d_max:
ok = o3.analyze(osi, 10)
time.append(time[len(time) - 1] + 1)
hd = o3.get_node_disp(osi, nd[f"C1-S{fb.n_storeys}"], o3.cc.X)
outputs['h_disp'].append(hd)
o3.gen_reactions(osi)
vb = 0
for cc in range(1, fb.n_cols + 1):
vb += o3.get_node_reaction(osi, nd[f"C{cc}-S0"], o3.cc.X)
outputs['vb'].append(-vb)
outputs['REACT-C1C2-S1'].append(
o3.get_ele_response(osi, ed['C1C2-S1'], 'force'))
outputs['REACT-C1-S0S1'].append(
o3.get_ele_response(osi, ed['C1-S0S1'], 'force'))
n_cycs += 1
o3.wipe(osi)
o3r.save_to_cache()
for item in outputs:
outputs[item] = np.array(outputs[item])
print('complete')
return outputs
def site_response(sp,
asig,
freqs=(0.5, 10),
xi=0.03,
analysis_dt=0.001,
dy=0.5,
analysis_time=None,
outs=None,
rec_dt=None,
forder=1.0e3):
"""
Run seismic analysis of a soil profile
Parameters
----------
sp: sfsimodels.SoilProfile object
A soil profile
asig: eqsig.AccSignal object
An acceleration signal
Returns
-------
"""
if analysis_time is None:
analysis_time = asig.time[-1]
if outs is None:
outs = {
'ACCX': [0]
} # Export the horizontal acceleration at the surface
if rec_dt is None:
rec_dt = analysis_dt
osi = o3.OpenSeesInstance(ndm=2, ndf=2, state=3)
assert isinstance(sp, sm.SoilProfile)
sp.gen_split(props=['shear_vel', 'unit_mass'], target=dy)
thicknesses = sp.split["thickness"]
n_node_rows = len(thicknesses) + 1
node_depths = np.cumsum(sp.split["thickness"])
node_depths = np.insert(node_depths, 0, 0)
ele_depths = (node_depths[1:] + node_depths[:-1]) / 2
grav = 9.81
omega_1 = 2 * np.pi * freqs[0]
omega_2 = 2 * np.pi * freqs[1]
a0 = 2 * xi * omega_1 * omega_2 / (omega_1 + omega_2)
a1 = 2 * xi / (omega_1 + omega_2)
k0 = 0.5
pois = k0 / (1 + k0)
newmark_gamma = 0.5
newmark_beta = 0.25
ele_width = min(thicknesses)
# Define nodes and set boundary conditions for simple shear deformation
# Start at top and build down?
sn = [[o3.node.Node(osi, 0, 0), o3.node.Node(osi, ele_width, 0)]]
for i in range(1, n_node_rows):
# Establish left and right nodes
sn.append([
o3.node.Node(osi, 0, -node_depths[i]),
o3.node.Node(osi, ele_width, -node_depths[i])
])
if i != n_node_rows - 1:
# set x and y dofs equal for left and right nodes
o3.EqualDOF(osi, sn[i][0], sn[i][1], [o3.cc.X, o3.cc.Y])
# Fix base nodes
o3.Fix2DOF(osi, sn[-1][0], o3.cc.FREE, o3.cc.FIXED)
o3.Fix2DOF(osi, sn[-1][1], o3.cc.FREE, o3.cc.FIXED)
o3.EqualDOF(osi, sn[-1][0], sn[-1][1], [o3.cc.X])
# Define dashpot nodes
dashpot_node_1 = o3.node.Node(osi, 0, -node_depths[-1])
dashpot_node_2 = sn[-1][0]
o3.Fix2DOF(osi, dashpot_node_1, o3.cc.FIXED, o3.cc.FIXED)
# define materials
ele_thick = 1.0 # m
soil_mats = []
prev_args = []
prev_kwargs = {}
prev_sl_type = None
eles = []
for i in range(len(thicknesses)):
y_depth = ele_depths[i]
sl_id = sp.get_layer_index_by_depth(y_depth)
sl = sp.layer(sl_id)
app2mod = {}
if y_depth > sp.gwl:
umass = sl.unit_sat_mass / forder
else:
umass = sl.unit_dry_mass / forder
p_atm = 101e3 / forder
# Define material
if sl.o3_type == 'pm4sand':
sl_class = o3.nd_material.PM4Sand
overrides = {'nu': pois, 'p_atm': p_atm, 'unit_moist_mass': umass}
app2mod = sl.app2mod
elif sl.o3_type == 'sdmodel':
sl_class = o3.nd_material.StressDensity
overrides = {'nu': pois, 'p_atm': p_atm, 'unit_moist_mass': umass}
app2mod = sl.app2mod
elif sl.o3_type == 'pimy':
sl_class = o3.nd_material.PressureIndependMultiYield
overrides = {
'nu': pois,
'p_atm': p_atm,
'rho': umass,
'nd': 2.0,
'g_mod_ref': sl.g_mod / forder,
'bulk_mod_ref': sl.bulk_mod / forder,
'peak_strain': 0.05,
'cohesion': sl.cohesion / forder,
'phi': sl.phi,
'p_ref': 101e3 / forder,
'd': 0.0,
'n_surf': 25
}
else:
sl_class = o3.nd_material.ElasticIsotropic
sl.e_mod = 2 * sl.g_mod * (1 + sl.poissons_ratio) / forder
app2mod['rho'] = 'unit_moist_mass'
overrides = {'nu': sl.poissons_ratio, 'unit_moist_mass': umass}
args, kwargs = o3.extensions.get_o3_kwargs_from_obj(
sl, sl_class, custom=app2mod, overrides=overrides)
changed = 0
if sl.type != prev_sl_type or len(args) != len(prev_args) or len(
kwargs) != len(prev_kwargs):
changed = 1
else:
for j, arg in enumerate(args):
if not np.isclose(arg, prev_args[j]):
changed = 1
for pm in kwargs:
if pm not in prev_kwargs or not np.isclose(
kwargs[pm], prev_kwargs[pm]):
changed = 1
if changed:
mat = sl_class(osi, *args, **kwargs)
prev_sl_type = sl.type
prev_args = copy.deepcopy(args)
prev_kwargs = copy.deepcopy(kwargs)
soil_mats.append(mat)
# def element
nodes = [sn[i + 1][0], sn[i + 1][1], sn[i][1],
sn[i][0]] # anti-clockwise
eles.append(
o3.element.SSPquad(osi, nodes, mat, o3.cc.PLANE_STRAIN, ele_thick,
0.0, -grav))
# Static analysis
o3.constraints.Transformation(osi)
o3.test_check.NormDispIncr(osi, tol=1.0e-5, max_iter=30, p_flag=0)
o3.algorithm.Newton(osi)
o3.numberer.RCM(osi)
o3.system.ProfileSPD(osi)
o3.integrator.Newmark(osi, 5. / 6, 4. / 9) # include numerical damping
o3.analysis.Transient(osi)
o3.analyze(osi, 40, 1.)
for i, soil_mat in enumerate(soil_mats):
if hasattr(soil_mat, 'update_to_nonlinear'):
print('Update model to nonlinear')
soil_mat.update_to_nonlinear()
o3.analyze(osi, 50, 0.5)
o3.extensions.to_py_file(osi, 'ofile_sra_pimy_og.py')
# reset time and analysis
o3.set_time(osi, 0.0)
o3.wipe_analysis(osi)
# define material and element for viscous dampers
base_sl = sp.layer(sp.n_layers)
c_base = ele_width * base_sl.unit_dry_mass / forder * sp.get_shear_vel_at_depth(
sp.height)
dashpot_mat = o3.uniaxial_material.Viscous(osi, c_base, alpha=1.)
o3.element.ZeroLength(osi, [dashpot_node_1, dashpot_node_2],
mats=[dashpot_mat],
dirs=[o3.cc.DOF2D_X])
ods = {}
for otype in outs:
if otype == 'ACCX':
ods['ACCX'] = []
if isinstance(outs['ACCX'], str) and outs['ACCX'] == 'all':
ods['ACCX'] = o3.recorder.NodesToArrayCache(osi,
nodes=sn[:][0],
dofs=[o3.cc.X],
res_type='accel',
dt=rec_dt)
else:
for i in range(len(outs['ACCX'])):
ind = np.argmin(abs(node_depths - outs['ACCX'][i]))
ods['ACCX'].append(
o3.recorder.NodeToArrayCache(osi,
node=sn[ind][0],
dofs=[o3.cc.X],
res_type='accel',
dt=rec_dt))
if otype == 'TAU':
ods['TAU'] = []
if isinstance(outs['TAU'], str) and outs['TAU'] == 'all':
ods['TAU'] = o3.recorder.ElementsToArrayCache(
osi, eles=eles, arg_vals=['stress'], dt=rec_dt)
else:
for i in range(len(outs['TAU'])):
ind = np.argmin(abs(ele_depths - outs['TAU'][i]))
ods['TAU'].append(
o3.recorder.ElementToArrayCache(osi,
ele=eles[ind],
arg_vals=['stress'],
dt=rec_dt))
if otype == 'STRS':
ods['STRS'] = []
if isinstance(outs['STRS'], str) and outs['STRS'] == 'all':
ods['STRS'] = o3.recorder.ElementsToArrayCache(
osi, eles=eles, arg_vals=['strain'], dt=rec_dt)
else:
for i in range(len(outs['STRS'])):
ind = np.argmin(abs(ele_depths - outs['STRS'][i]))
ods['STRS'].append(
o3.recorder.ElementToArrayCache(osi,
ele=eles[ind],
arg_vals=['strain'],
dt=rec_dt))
ods['time'] = o3.recorder.TimeToArrayCache(osi, dt=rec_dt)
# Run the dynamic analysis
o3.algorithm.Newton(osi)
o3.system.SparseGeneral(osi)
o3.numberer.RCM(osi)
o3.constraints.Transformation(osi)
o3.integrator.Newmark(osi, newmark_gamma, newmark_beta)
o3.rayleigh.Rayleigh(osi, a0, a1, 0, 0)
o3.analysis.Transient(osi)
o3.test_check.EnergyIncr(osi, tol=1.0e-7, max_iter=10)
# Define the dynamic analysis
ts_obj = o3.time_series.Path(osi,
dt=asig.dt,
values=asig.velocity * 1,
factor=c_base)
o3.pattern.Plain(osi, ts_obj)
o3.Load(osi, sn[-1][0], [1., 0.])
o3.analyze(osi, int(analysis_time / analysis_dt), analysis_dt)
o3.wipe(osi)
out_dict = {}
for otype in ods:
if isinstance(ods[otype], list):
out_dict[otype] = []
for i in range(len(ods[otype])):
out_dict[otype].append(ods[otype][i].collect())
out_dict[otype] = np.array(out_dict[otype])
else:
out_dict[otype] = ods[otype].collect().T
return out_dict
def gen_response(period, xi, asig, etype, fos_for_dt=None):
# Define inelastic SDOF
mass = 1.0
f_yield = 1.5 # Reduce this to make it nonlinear
r_post = 0.0
# Initialise OpenSees instance
osi = o3.OpenSeesInstance(ndm=2, state=0)
# Establish nodes
bot_node = o3.node.Node(osi, 0, 0)
top_node = o3.node.Node(osi, 0, 0)
# Fix bottom node
o3.Fix3DOF(osi, top_node, o3.cc.FREE, o3.cc.FIXED, o3.cc.FIXED)
o3.Fix3DOF(osi, bot_node, o3.cc.FIXED, o3.cc.FIXED, o3.cc.FIXED)
# Set out-of-plane DOFs to be slaved
o3.EqualDOF(osi, top_node, bot_node, [o3.cc.Y, o3.cc.ROTZ])
# nodal mass (weight / g):
o3.Mass(osi, top_node, mass, 0., 0.)
# Define material
k_spring = 4 * np.pi**2 * mass / period**2
# bilinear_mat = o3.uniaxial_material.Steel01(osi, fy=f_yield, e0=k_spring, b=r_post)
mat = o3.uniaxial_material.Elastic(osi, e_mod=k_spring)
# Assign zero length element, # Note: pass actual node and material objects into element
o3.element.ZeroLength(osi, [bot_node, top_node],
mats=[mat],
dirs=[o3.cc.DOF2D_X],
r_flag=1)
# Define the dynamic analysis
# Define the dynamic analysis
acc_series = o3.time_series.Path(osi, dt=asig.dt, values=-1 *
asig.values) # should be negative
o3.pattern.UniformExcitation(osi, dir=o3.cc.X, accel_series=acc_series)
# set damping based on first eigen mode
angular_freq = o3.get_eigen(osi, solver='fullGenLapack', n=1)[0]**0.5
period = 2 * np.pi / angular_freq
beta_k = 2 * xi / angular_freq
o3.rayleigh.Rayleigh(osi,
alpha_m=0.0,
beta_k=beta_k,
beta_k_init=0.0,
beta_k_comm=0.0)
o3.set_time(osi, 0.0)
# Run the dynamic analysis
o3.wipe_analysis(osi)
# Run the dynamic analysis
o3.numberer.RCM(osi)
o3.system.FullGeneral(osi)
if etype == 'central_difference':
o3.algorithm.Linear(osi, factor_once=True)
o3.integrator.CentralDifference(osi)
explicit_dt = 2 / angular_freq / fos_for_dt
analysis_dt = explicit_dt
elif etype == 'implicit':
o3.algorithm.Newton(osi)
o3.integrator.Newmark(osi, gamma=0.5, beta=0.25)
analysis_dt = 0.001
else:
raise ValueError()
o3.constraints.Transformation(osi)
o3.analysis.Transient(osi)
o3.test_check.EnergyIncr(osi, tol=1.0e-10, max_iter=10)
analysis_time = asig.time[-1]
outputs = {
"time": [],
"rel_disp": [],
"rel_accel": [],
"rel_vel": [],
"force": []
}
rec_dt = 0.002
n_incs = int(analysis_dt / rec_dt)
n_incs = 1
while o3.get_time(osi) < analysis_time:
o3.analyze(osi, n_incs, analysis_dt)
curr_time = o3.get_time(osi)
outputs["time"].append(curr_time)
outputs["rel_disp"].append(o3.get_node_disp(osi, top_node, o3.cc.X))
outputs["rel_vel"].append(o3.get_node_vel(osi, top_node, o3.cc.X))
outputs["rel_accel"].append(o3.get_node_accel(osi, top_node, o3.cc.X))
o3.gen_reactions(osi)
outputs["force"].append(-o3.get_node_reaction(
osi, bot_node, o3.cc.X)) # Negative since diff node
o3.wipe(osi)
for item in outputs:
outputs[item] = np.array(outputs[item])
return outputs
def site_response(sp,
asig,
freqs=(0.5, 10),
xi=0.03,
dy=0.5,
analysis_time=None,
outs=None,
rec_dt=None,
etype='variable',
forder=1.0):
"""
Run seismic analysis of a soil profile
Parameters
----------
sp: sfsimodels.SoilProfile object
A soil profile
asig: eqsig.AccSignal object
An acceleration signal
Returns
-------
"""
if analysis_time is None:
analysis_time = asig.time[-1]
if outs is None:
outs = {
'ACCX': [0]
} # Export the horizontal acceleration at the surface
osi = o3.OpenSeesInstance(ndm=2, ndf=2, state=3)
assert isinstance(sp, sm.SoilProfile)
sp.gen_split(props=['shear_vel', 'unit_mass'], target=dy)
req_dt = min(sp.split["thickness"] / sp.split['shear_vel']) / 8
thicknesses = sp.split["thickness"]
n_node_rows = len(thicknesses) + 1
node_depths = np.cumsum(sp.split["thickness"])
node_depths = np.insert(node_depths, 0, 0)
ele_depths = (node_depths[1:] + node_depths[:-1]) / 2
unit_masses = sp.split["unit_mass"] / forder
grav = 9.81
ele_width = min(thicknesses)
total_soil_nodes = len(thicknesses) * 2 + 2
# Define nodes and set boundary conditions for simple shear deformation
# Start at top and build down?
sn = [[o3.node.Node(osi, 0, 0), o3.node.Node(osi, ele_width, 0)]]
for i in range(1, n_node_rows):
# Establish left and right nodes
sn.append([
o3.node.Node(osi, 0, -node_depths[i]),
o3.node.Node(osi, ele_width, -node_depths[i])
])
# set x and y dofs equal for left and right nodes
o3.EqualDOF(osi, sn[i][0], sn[i][1], [o3.cc.X, o3.cc.Y])
# Fix base nodes
o3.Fix2DOF(osi, sn[-1][0], o3.cc.FIXED, o3.cc.FIXED)
o3.Fix2DOF(osi, sn[-1][1], o3.cc.FIXED, o3.cc.FIXED)
# define materials
ele_thick = 1.0 # m
soil_mats = []
eles = []
prev_id = -1
for i in range(len(thicknesses)):
y_depth = ele_depths[i]
sl_id = sp.get_layer_index_by_depth(y_depth)
sl = sp.layer(sl_id)
mat = sl.o3_mat
if sl_id != prev_id:
mat.build(osi)
soil_mats.append(mat)
prev_id = sl_id
# def element
nodes = [sn[i + 1][0], sn[i + 1][1], sn[i][1],
sn[i][0]] # anti-clockwise
eles.append(
o3.element.SSPquad(osi, nodes, mat, o3.cc.PLANE_STRAIN, ele_thick,
0.0, -grav))
for i, soil_mat in enumerate(soil_mats):
if hasattr(soil_mat, 'update_to_linear'):
print('Update model to linear')
soil_mat.update_to_linear()
# Gravity analysis
o3.constraints.Transformation(osi)
o3.test_check.NormDispIncr(osi, tol=1.0e-5, max_iter=30, p_flag=0)
o3.algorithm.Newton(osi)
o3.numberer.RCM(osi)
o3.system.ProfileSPD(osi)
o3.integrator.Newmark(osi, 5. / 6, 4. / 9) # include numerical damping
if etype == 'variable':
o3.analysis.VariableTransient(osi)
g_args = [0.5, 0.1, 2, 5]
else:
o3.analysis.Transient(osi)
g_args = [0.5]
fail = o3.analyze(osi, 40, *g_args)
if fail:
return
for i, soil_mat in enumerate(soil_mats):
if hasattr(soil_mat, 'update_to_nonlinear'):
print('Update model to nonlinear')
soil_mat.update_to_nonlinear()
if o3.analyze(osi, 50, *g_args):
print('Model failed')
return
print('finished nonlinear gravity analysis')
# reset time and analysis
o3.set_time(osi, 0.0)
o3.wipe_analysis(osi)
n = 10
# omegas = np.array(o3.get_eigen(osi, solver='fullGenLapack', n=n)) ** 0.5 # DO NOT USE fullGenLapack
omegas = np.array(o3.get_eigen(osi, n=n))**0.5
periods = 2 * np.pi / omegas
print('response_periods: ', periods)
o3.constraints.Transformation(osi)
o3.test_check.NormDispIncr(osi, tol=1.0e-8, max_iter=6, p_flag=0)
o3.numberer.RCM(osi)
o3.system.ProfileSPD(osi)
# o3.algorithm.NewtonLineSearch(osi, 0.75)
# o3.integrator.Newmark(osi, 0.5, 0.25)
if etype == 'variable':
# o3.analysis.VariableTransient(osi)
o3.opy.analysis('VariableTransient')
dyn_args = [20, 0.01, 0.0005, 0.01, 3]
else:
o3.analysis.Transient(osi)
dyn_args = [20, 0.01]
omega_1 = 2 * np.pi * freqs[0]
omega_2 = 2 * np.pi * freqs[1]
a0 = 2 * xi * omega_1 * omega_2 / (omega_1 + omega_2)
a1 = 2 * xi / (omega_1 + omega_2)
o3.rayleigh.Rayleigh(osi, a0, 0, a1, 0)
o3.extensions.to_py_file(osi, f'opy_var_integration_{etype}.py')
# o3.test_check.NormDispIncr(osi, tol=1.0e-7, max_iter=10)
rec_dt = 0.001
ods = {}
for otype in outs:
if otype == 'ACCX':
ods['ACCX'] = []
if isinstance(outs['ACCX'], str) and outs['ACCX'] == 'all':
ods['ACCX'] = o3.recorder.NodesToArrayCache(osi,
nodes=sn[:][0],
dofs=[o3.cc.X],
res_type='accel',
dt=rec_dt)
else:
for i in range(len(outs['ACCX'])):
ind = np.argmin(abs(node_depths - outs['ACCX'][i]))
ods['ACCX'].append(
o3.recorder.NodeToArrayCache(osi,
node=sn[ind][0],
dofs=[o3.cc.X],
res_type='accel',
dt=rec_dt))
if otype == 'TAU':
ods['TAU'] = []
if isinstance(outs['TAU'], str) and outs['TAU'] == 'all':
ods['TAU'] = o3.recorder.ElementsToArrayCache(
osi, eles=eles, arg_vals=['stress'], dt=rec_dt)
else:
for i in range(len(outs['TAU'])):
ind = np.argmin(abs(ele_depths - outs['TAU'][i]))
ods['TAU'].append(
o3.recorder.ElementToArrayCache(osi,
ele=eles[ind],
arg_vals=['stress'],
dt=rec_dt))
if otype == 'STRS':
ods['STRS'] = []
if isinstance(outs['STRS'], str) and outs['STRS'] == 'all':
ods['STRS'] = o3.recorder.ElementsToArrayCache(
osi, eles=eles, arg_vals=['strain'], dt=rec_dt)
else:
for i in range(len(outs['STRS'])):
ind = np.argmin(abs(ele_depths - outs['STRS'][i]))
ods['STRS'].append(
o3.recorder.ElementToArrayCache(osi,
ele=eles[ind],
arg_vals=['strain'],
dt=rec_dt))
ods['time'] = o3.recorder.TimeToArrayCache(osi, dt=rec_dt)
acc_series = o3.time_series.Path(osi, dt=asig.dt, values=asig.values)
o3.pattern.UniformExcitation(osi, dir=o3.cc.X, accel_series=acc_series)
# Run the dynamic analysis
inc = 1
o3.record(osi)
while o3.get_time(osi) < analysis_time:
print(o3.get_time(osi))
if o3.analyze(osi, *dyn_args):
print('failed')
break
o3.wipe(osi)
out_dict = {}
for otype in ods:
if isinstance(ods[otype], list):
out_dict[otype] = []
for i in range(len(ods[otype])):
out_dict[otype].append(ods[otype][i].collect())
out_dict[otype] = np.array(out_dict[otype])
else:
out_dict[otype] = ods[otype].collect().T
return out_dict