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# https://pyrocko.org - GPLv3 # # The Pyrocko Developers, 21st Century # ---|P------/S----------~Lg----------
''' Analytical Griffith crack model '''
help='Width equals to 2*a', default=1.)
help='Poisson ratio', default=.25)
help='Shear modulus [Pa]', default=1.e9)
help='Stress drop array:' '[sigi3_r - sigi3_c, sigi2_r - sigi2_c, sigi1_r - sigi1_c]' '[dstress_Strike, dstress_Dip, dstress_Tensile]', default=num.array([0., 0., 0.]))
def a(self): ''' Half width of the crack '''
def youngsmod(self): ''' Shear (Youngs) modulus '''
return 2. * self.shearmod * (1. + self.poisson)
''' Calculation of dislocation at crack surface along x2 axis
Follows equations by Pollard and Segall (1987) to calculate dislocations for an infinite 2D crack extended in x3 direction, opening in x1 direction and the crack extending in x2 direction.
:param x_obs: Observation point coordinates along x2-axis. If :math:`x_{obs} < -a` or :math:`x_{obs} > a`, output dislocations are zero :type x_obs: :py:class:`numpy.ndarray`, ``(N,)``
:return: dislocations at each observation point in strike, dip and tensile direction. :rtype: :py:class:`numpy.ndarray`, ``(N, 3)`` '''
x_obs = num.array(x_obs)
factor, num.tile( 2. * (1. - self.poisson) / self.shearmod, (1, 2)))
self.stressdrop * num.sqrt( self.a**2 - num.tile(x_obs[crack_el, num.newaxis], (1, 3))**2) * \ factor
''' Calculation of dislocation at crack surface along x2 axis
Follows equations by Pollard and Segall (1987) to calculate displacements for a circulat crack extended in x2 and x3 direction and opening in x1 direction.
:param x_obs: Observation point coordinates along axis through crack centre. If :math:`x_{obs} < -a` or :math:`x_{obs} > a`, output dislocations are zero :type x_obs: :py:class:`numpy.ndarray`, ``(N,)``
:return: dislocations at each observation point in strike, dip and tensile direction. :rtype: :py:class:`numpy.ndarray`, ``(N, 3)`` '''
x_obs = num.array(x_obs)
factor, num.tile( 4. * (1. - self.poisson) / (self.shearmod * num.pi), (1, 2)))
self.stressdrop * num.sqrt( self.a**2 - num.tile(x_obs[crack_el, num.newaxis], (1, 3))**2) * \ factor
''' Calculation of displacement at crack surface along x1-axis
Follows equations by Pollard and Segall (1987) to calculate displacements for an infinite 2D crack extended in x3 direction, opening in x1 direction and the crack tip in x2 direction.
:param x1_obs: Observation point coordinates along x1-axis. :type x1_obs: :py:class:`numpy.ndarray`, ``(N,)``
:return: displacements at each observation point in strike, dip and tensile direction. :rtype: :py:class:`numpy.ndarray`, ``(M, 3)`` ''' displ = num.zeros((x1_obs.shape[0], 3))
if self.stressdrop[0] != 0.: sign = num.sign(x1_obs) x1_ratio = x1_obs / self.a
displ[:, 0] = ( num.sqrt((x1_ratio)**2 + 1.) - num.abs( x1_ratio) ) * self.stressdrop[0] * self.a / self.shearmod * sign
return displ
''' Calculation of displacement at crack surface along x2-axis
Follows equations by Pollard and Segall (1987) to calculate displacements for an infinite 2D crack extended in x3 direction, opening in x1 direction and the crack tip in x2 direction.
:param x2_obs: Observation point coordinates along x2-axis. :type x2_obs: :py:class:`numpy.ndarray`, ``(N,)``
:return: displacements at each observation point in strike, dip and tensile direction. :rtype: :py:class:`numpy.ndarray`, ``(N, 3)`` '''
crack_el = (x2_obs >= -self.a) & (x2_obs <= self.a)
displ = num.zeros((x2_obs.shape[0], 3))
if self.stressdrop[1] != 0.: factor = (1. - 2. * self.poisson) / (2. * self.shearmod)
displ[crack_el, 2] = \ self.stressdrop[1] * factor * x2_obs[crack_el]
sign = num.sign(x2_obs)
displ[~crack_el, 2] = \ self.stressdrop[1] * factor * self.a * sign[~crack_el] * ( num.abs(x2_obs[~crack_el] / self.a) - num.sqrt(x2_obs[~crack_el]**2 / self.a**2 - 1.))
return displ
''' Calculation of displacement at crack surface along different axis
Follows equations by Pollard and Segall (1987) to calculate displacements for an infinite 2D crack extended in x3 direction, opening in x1 direction and the crack tip in x2 direction.
:param x1_obs: Observation point coordinates along x1-axis. If x1_obs = 0., displacment is calculated along x2-axis :type x1_obs: :py:class:`numpy.ndarray`, ``(M,)`` :param x2_obs: Observation point coordinates along x2-axis. If x2_obs = 0., displacment is calculated along x1-axis :type x2_obs: :py:class:`numpy.ndarray`, ``(N,)``
:return: displacements at each observation point in strike, dip and tensile direction. :rtype: :py:class:`numpy.ndarray`, ``(M, 3)`` or ``(N, 3)`` '''
if type(x1_obs) is not num.ndarray: x1_obs = num.array(x1_obs) if type(x2_obs) is not num.ndarray: x2_obs = num.array(x2_obs)
if (x1_obs == 0.).all(): return self._displ_infinite2d_along_x2(x2_obs) elif (x2_obs == 0.).all(): return self._displ_infinite2d_along_x1(x1_obs)
'GriffithCrack'] |