PISM, A Parallel Ice Sheet Model  stable v2.1.1 committed by Constantine Khrulev on 2024-12-04 13:36:58 -0900

◆ update_impl()

void pism::OptTillphiYieldStress::update_impl ( const YieldStressInputs inputs,
double  t,
double  dt 
)
privatevirtual

Update the till yield stress for use in the pseudo-plastic till basal stress model. See also IceBasalResistancePlasticLaw.

Updates yield stress \( \tau_c \) based on modeled till water layer thickness from a Hydrology object. We implement the Mohr-Coulomb criterion allowing a (typically small) till cohesion \( c_0 \) and by expressing the coefficient as the tangent of a till friction angle \( \varphi \) :

\[ \tau_c = c_0 + (\tan \varphi) N_{till}. \]

See [Paterson] table 8.1 regarding values.

The effective pressure on the till is empirically-related to the amount of water in the till. We use this formula derived from [Tulaczyketal2000] and documented in [BuelervanPeltDRAFT]:

\[ N_{till} = \min\left\{P_o, N_0 \left(\frac{\delta P_o}{N_0}\right)^s 10^{(e_0/C_c) (1 - s)}\right\} \]

where \( s = W_{till} / W_{till}^{max} \), \( W_{till}^{max} \) =hydrology_tillwat_max, \( \delta \) =basal_yield_stress.mohr_coulomb.till_effective_fraction_overburden, \( P_o \) is the overburden pressure, \( N_0 \) =basal_yield_stress.mohr_coulomb.till_reference_effective_pressure is a reference effective pressure, \( e_0 \) =basal_yield_stress.mohr_coulomb.till_reference_void_ratio is the void ratio at the reference effective pressure, and \( C_c \) =basal_yield_stress.mohr_coulomb.till_compressibility_coefficient is the coefficient of compressibility of the till. Constants \( N_0, e_0, C_c \) are found by [Tulaczyketal2000] from laboratory experiments on samples of till.

If basal_yield_stress.add_transportable_water is yes then \( s \) in the above formula becomes \( s = (W + W_{till}) / W_{till}^{max} \), that is, the water amount is the sum \( W+W_{till} \).

Reimplemented from pism::MohrCoulombYieldStress.

Definition at line 198 of file OptTillphiYieldStress.cc.

References pism::Geometry::bed_elevation, pism::Geometry::cell_type, pism::YieldStressInputs::geometry, pism::Geometry::ice_surface_elevation, m_t_eps, m_t_last, m_update_interval, PISM_ERROR_LOCATION, pism::MohrCoulombYieldStress::update_impl(), and update_tillphi().