Gravity-driven instabilities: Interplay between state-and velocity-dependent frictional sliding and stresscorrosion damage cracking

摘要

We model the progressive maturation of a heterogeneous mass toward a gravity-driven instability, characterized by the competition between frictional sliding and tensioncracking, using an array of slider blocks on an inclined basal surface, which interact viaelastic-brittle springs. A realistic state- and rate-dependent friction law describes theblock-surface interaction. The inner material damage occurs via stress corrosion. Threeregimes, controlling the mass instability and its precursory behavior, are classified as afunction of the ratio T_c/T_fof two characteristic timescales associated with internal damage/creep and with frictional sliding. For T_c/Y_f 1, the whole mass undergoes a series ofinternal stick and slip events, associated with an initial slow average downward motion ofthe whole mass, and progressively accelerates until a global coherent runaway is observed.For T_c/Tf 1, creep/damage occurs sufficiently fast compared with nucleation of sliding,causing bonds to break, and the bottom part of the mass undergoes a fragmentationprocess with the creation of a heterogeneous population of sliding blocks. For theintermediate regime T_c/T_f~1, a macroscopic crack nucleates and propagates along thelocation of the largest curvature associated with the change of slope from the stablefrictional state in the upper part to the unstable frictional sliding state in the lower part. Theother important parameter is the Young modulus Y which controls the correlation length ofdisplacements in the system.