def test_constant_vs_quadratic_tensile_slip():
""" Compare constant and quadratic slip elements"""
n_elements = 1
mu = np.array([3e10])
nu = np.array([0.25])
elements = []
element = {}
L = 10000
x1, y1, x2, y2 = bem2d.discretized_line(-L, 0, L, 0, n_elements)
for i in range(0, x1.size):
element["x1"] = x1[i]
element["y1"] = y1[i]
element["x2"] = x2[i]
element["y2"] = y2[i]
elements.append(element.copy())
elements = bem2d.standardize_elements(elements)
# Observation coordinates for far-field calculation
n_pts = 100
width = 20000
x = np.linspace(-width, width, n_pts)
y = np.linspace(-width, width, n_pts)
x, y = np.meshgrid(x, y)
x = x.flatten()
y = y.flatten()
# Just a simple forward model for the volume
displacement_constant_slip = np.zeros((2, x.size))
stress_constant_slip = np.zeros((3, x.size))
displacement_quadratic_slip = np.zeros((2, x.size))
stress_quadratic_slip = np.zeros((3, x.size))
for i, element in enumerate(elements):
displacement, stress = bem2d.displacements_stresses_constant_linear(
x,
y,
element["half_length"],
mu,
nu,
"constant",
"slip",
0,
1,
element["x_center"],
element["y_center"],
element["rotation_matrix"],
element["inverse_rotation_matrix"],
)
displacement_constant_slip += displacement
stress_constant_slip += stress
for element in elements:
quadratic_coefficients = np.array(
[1, 1, 1]) # constant slip quadratic element
displacement, stress = bem2d.displacements_stresses_quadratic_farfield_coefficients(
quadratic_coefficients,
x,
y,
element["half_length"],
mu,
nu,
"slip",
0,
1,
element["x_center"],
element["y_center"],
element["rotation_matrix"],
element["inverse_rotation_matrix"],
)
displacement_quadratic_slip += displacement
stress_quadratic_slip += stress
np.testing.assert_almost_equal(displacement_constant_slip,
displacement_quadratic_slip)
np.testing.assert_almost_equal(stress_constant_slip,
stress_quadratic_slip,
decimal=1)
import bem2d
from importlib import reload
import bem2d
import matplotlib.pyplot as plt
bem2d = reload(bem2d)
# List of elements for forward model
n_elements = 2
mu = np.array([3e10])
nu = np.array([0.25])
elements = []
element = {}
L = 10000
# x1, y1, x2, y2 = bem2d.discretized_line(-L, 0, L, 0, n_elements)
x1, y1, x2, y2 = bem2d.discretized_line(-L, -L, L, L, n_elements)
for i in range(0, x1.size):
element["x1"] = x1[i]
element["y1"] = y1[i]
element["x2"] = x2[i]
element["y2"] = y2[i]
elements.append(element.copy())
elements = bem2d.standardize_elements(elements)
# Observation coordinates for far-field calculation
n_pts = 100
width = 20000
x = np.linspace(-width, width, n_pts)
y = np.linspace(-width, width, n_pts)
x, y = np.meshgrid(x, y)
PARAMETERS["density"]) # Shear wave speed (m/s)
PARAMETERS["eta"] = PARAMETERS["mu"] / (
2 * PARAMETERS["cs"]) # Radiation damping coefficient (kg / (m^2 * s))
PARAMETERS["d_c"] = 0.05 # state evolution length scale (m)
PARAMETERS["f_0"] = 0.6 # baseline coefficient of friction
PARAMETERS["block_velocity_x"] = 1e-9
PARAMETERS["block_velocity_y"] = 0
PARAMETERS["v_0"] = 1e-6 # reference velocity
# Create fault elements
N_ELEMENTS = 50
N_NODES = 3 * N_ELEMENTS
ELEMENTS_FAULT = []
ELEMENT = {}
L = 10000
x1, y1, x2, y2 = bem2d.discretized_line(-L, 0, L, 0, N_ELEMENTS)
# Modify y1, and y2 for a sinusoidal fault
amplitude = 0.0
y1 = amplitude * np.sin(2 * np.pi * x1 / L)
y2 = amplitude * np.sin(2 * np.pi * x2 / L)
for i in range(0, x1.size):
ELEMENT["x1"] = x1[i]
ELEMENT["y1"] = y1[i]
ELEMENT["x2"] = x2[i]
ELEMENT["y2"] = y2[i]
ELEMENT["a"] = 0.015 # frictional a parameter ()
ELEMENT["b"] = 0.020 # frictional b parameter ()
ELEMENT["sigma_n"] = 50e6 # normal stress (Pa)
ELEMENTS_FAULT.append(ELEMENT.copy())
bem2d = reload(bem2d)
plt.close("all")
PLOT_ELEMENTS = False
# Material properties
mu = 30e9
nu = 0.25
# Define elements
elements_surface = []
elements_fault = []
element = {}
# Create topographic free surface elements
x1, y1, x2, y2 = bem2d.discretized_line(-10e3, 0, 10e3, 0, 60)
y1 = -1e3 * np.arctan(x1 / 1e3)
y2 = -1e3 * np.arctan(x2 / 1e3)
for i in range(0, x1.size):
element["x1"] = x1[i]
element["y1"] = y1[i]
element["x2"] = x2[i]
element["y2"] = y2[i]
element["name"] = "surface"
elements_surface.append(element.copy())
elements_surface = bem2d.standardize_elements(elements_surface)
# Create constant slip curved fault
x1, y1, x2, y2 = bem2d.discretized_line(-7e3, 0e3, 0, 0, 30)
y1 = 3e3 * np.arctan(x1 / 1e3)
y2 = 3e3 * np.arctan(x2 / 1e3)
import bem2d.newton_rate_state
bem2d = reload(bem2d)
plt.close("all")
""" Taken from Ben's 1d example:
http://tbenthompson.com/post/block_slider/ """
# TODO: Save information from rupture problem as .pkl/.npz
# TODO: Try rupture problem with variations in a-b. Do I have to pass elements_* dict to do this?
elements_fault = []
element = {}
L = 10000
mu = 3e10
nu = 0.25
x1, y1, x2, y2 = bem2d.discretized_line(-L, 0, L, 0, 50)
for i in range(0, x1.size):
element["x1"] = x1[i]
element["y1"] = y1[i]
element["x2"] = x2[i]
element["y2"] = y2[i]
elements_fault.append(element.copy())
elements_fault = bem2d.standardize_elements(elements_fault)
n_elements = len(elements_fault)
# Constant slip partial derivatives
slip_to_displacement, slip_to_traction = bem2d.constant_linear_partials(
elements_fault, elements_fault, "slip", mu, nu)
# Quadratic slip partial derivative
nu = 0.25
n_pts = 102
width = 5
x = np.linspace(-width, width, n_pts)
y = np.linspace(-width, width, n_pts)
x, y = np.meshgrid(x, y)
x = x.flatten()
y = y.flatten()
# Define elements
elements_surface = []
elements_fault = []
element = {}
# Traction free surface
x1, y1, x2, y2 = bem2d.discretized_line(-5, 0, 5, 0, 20)
for i in range(0, x1.size):
element["x1"] = x1[i]
element["y1"] = y1[i]
element["x2"] = x2[i]
element["y2"] = y2[i]
element["name"] = "surface"
elements_surface.append(element.copy())
elements_surface = bem2d.standardize_elements(elements_surface)
# Constant slip fault
x1, y1, x2, y2 = bem2d.discretized_line(-1, -1, 0, 0, 1)
for i in range(0, x1.size):
element["x1"] = x1[i]
element["y1"] = y1[i]
element["x2"] = x2[i]
import bem2d
import matplotlib.pyplot as plt
bem2d = reload(bem2d)
# Material and geometric constants
plt.close("all")
SLIP_TYPE = "tensile_slip"
print(SLIP_TYPE)
mu = 3e10
nu = 0.25
n_elements = 10
elements = []
element = {}
L = 10000
x1, y1, x2, y2 = bem2d.discretized_line(-L, 0, L, 0, n_elements)
for i in range(0, x1.size):
element["x1"] = x1[i]
element["y1"] = y1[i]
element["x2"] = x2[i]
element["y2"] = y2[i]
elements.append(element.copy())
elements = bem2d.standardize_elements(elements)
# Convert to dictionary of lists
elements_DL = pd.DataFrame(elements).to_dict("list")
# Convert back to list of dictionaries
elements_LD = pd.DataFrame(elements_DL).to_dict("records")
print(elements == elements_LD)