== 0. Replication of Gaume & Puzrin (2021) 'The Dyatlov case' == L0=7.236 m lambda0=52.36 r1=7.753 phi_min=18.11 deg phi_max(lambda0)=22.91 deg hw0_min=0.236 m (paper 0.24) hw0_max=0.444 m (paper 0.44) dt_min=7.21 h (paper 7.2) dt_max=13.55 h (paper 13.5) tension crack at lcw=4.95 m (paper 4.95); width B=8.81 m (paper 8.8); line mass=815 kg/m; slab mass=7.2 t; volume=20.6 m^3 c= 300 Pa: hw0_min=0.000 hw0_max=0.000 -> immediate failure at cut c= 400 Pa: hw0_min=0.040 hw0_max=0.042 -> delayed release c= 440 Pa: hw0_min=0.236 hw0_max=0.444 -> delayed release c= 450 Pa: hw0_min=0.285 hw0_max=inf -> delayed release only if wind snow does not sinter c= 500 Pa: hw0_min=0.531 hw0_max=inf -> delayed release only if wind snow does not sinter c= 600 Pa: hw0_min=1.023 hw0_max=inf -> delayed release only if wind snow does not sinter == 1. Delay vs weak-layer slope angle (all other parameters as in the paper) == alpha=22 deg: phi_min=12.16 phi_max(l0)=17.81 hw0=[inf,inf] m dt=[inf,inf] h -> no release (wind load never reaches peak strength) alpha=23 deg: phi_min=13.15 phi_max(l0)=18.65 hw0=[inf,inf] m dt=[inf,inf] h -> no release (wind load never reaches peak strength) alpha=25 deg: phi_min=15.13 phi_max(l0)=20.34 hw0=[5.228,inf] m dt=[159.49,inf] h -> delayed release only if wind snow does not sinter alpha=28 deg: phi_min=18.11 phi_max(l0)=22.91 hw0=[0.236,0.444] m dt=[7.21,13.55] h -> delayed release alpha=30 deg: phi_min=20.10 phi_max(l0)=24.65 hw0=[0.000,0.000] m dt=[0.00,0.00] h -> immediate failure at cut == 2. Regime map == == 3. Delay vs deposition flux Q == alpha=23: no delayed release with paper parameters (no release (wind load never reaches peak strength)) alpha=30: no delayed release with paper parameters (immediate failure at cut) Sturm&Stuefer envelope at w=5 m/s: Q_lower=1.15e-04, Q_upper=7.27e-02 kg/m/s Sturm&Stuefer envelope at w=8 m/s: Q_lower=2.45e-03, Q_upper=2.35e-01 kg/m/s Sturm&Stuefer envelope at w=10 m/s: Q_lower=1.04e-02, Q_upper=4.11e-01 kg/m/s Sturm&Stuefer envelope at w=12 m/s: Q_lower=3.41e-02, Q_upper=6.48e-01 kg/m/s w= 5 m/s: dt_max = 1.49 h (upper-bound flux) ... 940.35 h (lower-bound flux) w= 8 m/s: dt_max = 0.46 h (upper-bound flux) ... 44.31 h (lower-bound flux) w= 9 m/s: dt_max = 0.34 h (upper-bound flux) ... 20.61 h (lower-bound flux) w=10 m/s: dt_max = 0.26 h (upper-bound flux) ... 10.39 h (lower-bound flux) w=12 m/s: dt_max = 0.17 h (upper-bound flux) ... 3.18 h (lower-bound flux) w=15 m/s: dt_max = 0.10 h (upper-bound flux) ... 0.74 h (lower-bound flux) == 4. Sensitivity (one-at-a-time, +/-10 % or +/-1 deg) around the paper's point == alpha_deg 28.000 -1: dt=[ 15.62, inf] (delayed release only if wind snow does not sinter); +1: dt=[ 2.63, 2.91] (delayed release) phi_deg 20.000 -1: dt=[ 2.53, 2.77] (delayed release); +1: dt=[ 16.76, inf] (delayed release only if wind snow does not sinter) c 440.000 -44: dt=[ 0.61, 0.62] (delayed release); +44: dt=[ 13.80, inf] (delayed release only if wind snow does not sinter) h0 0.500 -0.05: dt=[ 15.02, inf] (delayed release only if wind snow does not sinter); +0.05: dt=[ 0.00, 0.00] (immediate failure at cut) hc 0.100 -0.01: dt=[ 7.36, inf] (delayed release only if wind snow does not sinter); +0.01: dt=[ 7.07, 11.16] (delayed release) lc 4.000 -0.4: dt=[ 7.40, inf] (delayed release only if wind snow does not sinter); +0.4: dt=[ 7.19, 10.13] (delayed release) le0 1.000 -0.1: dt=[ 3.95, 4.69] (delayed release); +0.1: dt=[ 10.87, inf] (delayed release only if wind snow does not sinter) rho 300.000 -30: dt=[ 13.08, inf] (delayed release only if wind snow does not sinter); +30: dt=[ 1.33, 1.41] (delayed release) rho_w 400.000 -40: dt=[ 7.21, inf] (delayed release only if wind snow does not sinter); +40: dt=[ 7.21, 11.76] (delayed release) K0 0.500 -0.05: dt=[ 9.82, inf] (delayed release only if wind snow does not sinter); +0.05: dt=[ 4.60, 6.03] (delayed release) Q 0.008 -0.0008: dt=[ 8.01, 15.06] (delayed release); +0.0008: dt=[ 6.55, 12.32] (delayed release) == 5. Low-slope window: (phi, c) combinations giving a 9.5-13.5 h release (Q = 0.008) == alpha=22: delayed-release cells=2226, cells overlapping 9.5-13.5 h=281; phi range with any delayed release: 5.0-16.8 deg window: phi 5.0-15.2 deg, c 400-988 Pa alpha=23: delayed-release cells=2406, cells overlapping 9.5-13.5 h=315; phi range with any delayed release: 5.0-17.8 deg window: phi 5.0-16.2 deg, c 400-1025 Pa alpha=25: delayed-release cells=2748, cells overlapping 9.5-13.5 h=403; phi range with any delayed release: 5.0-19.2 deg window: phi 5.0-18.0 deg, c 400-1125 Pa alpha=28: delayed-release cells=3229, cells overlapping 9.5-13.5 h=543; phi range with any delayed release: 5.0-21.8 deg window: phi 5.0-20.2 deg, c 425-1262 Pa alpha=30: delayed-release cells=3533, cells overlapping 9.5-13.5 h=646; phi range with any delayed release: 5.0-23.2 deg window: phi 5.0-21.5 deg, c 450-1350 Pa == 6. Critical crack length (Gaume et al. 2017 form) for comparison == alpha=21 D=0.5 m: tau_p=940 Pa, a_c=0.45 m alpha=21 D=1.0 m: tau_p=1440 Pa, a_c=0.36 m alpha=23 D=0.5 m: tau_p=933 Pa, a_c=0.39 m alpha=23 D=1.0 m: tau_p=1426 Pa, a_c=0.26 m alpha=25 D=0.5 m: tau_p=925 Pa, a_c=0.33 m alpha=25 D=1.0 m: tau_p=1411 Pa, a_c=0.16 m alpha=28 D=0.5 m: tau_p=913 Pa, a_c=0.24 m alpha=28 D=1.0 m: tau_p=1386 Pa, a_c=0.00 m alpha=30 D=0.5 m: tau_p=904 Pa, a_c=0.18 m alpha=30 D=1.0 m: tau_p=1368 Pa, a_c=0.00 m (a_c of order 0.2-0.45 m -- far shorter than the ~6.5 m cut and the ~5 m wind-loaded zone -- means that once the weak layer yields over the cut, self-sustained propagation is plausible; a_c = 0 marks cases where the slab is already at failure; this is a scale check with the anticrack formula, not a replication of the paper.)