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Critical loading of pillar arrays having previously eliminated elements

Derda Tomasz

Journal of Applied Mathematics and Computational Mechanics

2023

Vol. 22, nr 4

18--29

The paper analyzes critical loads of pillar arrays with fraction of elements removed prior to actual critical loading. Two different methods of elimination are considered. In the first case, a fraction p of weakest pillars is physically removed from the array. The second method relies on conducting a subcritical preloading. When the sudden loading is applied to the system, the destruction follows in a cascade-like manner. Subsequent cascades take place due to the redistribution of load. We explore different types of load redistribution. It turns out that the type of load transfer as well as the distribution of pillar-strength-thresholds are of crucial importance regarding the strength enhancement of critically loaded pillar arrays.

A statistical damage model with implications for precursory seismicity

Lee Y.-T., Turcotte D., Rundle J., Chen C.-C.

Acta Geophysica

2012

Vol. 60, no. 3

638-663

Acoustic emissions prior to rupture indicate precursory damage. Laboratory studies of frictional sliding on model faults feature accelerating rates of acoustic emissions prior to rupture. Precursory seismic emissions are not generally observed prior to earthquakes. To address the problem of precursory damage, we consider failure in a fiber-bundle model. We observe a clearly defined nucleation phase followed by a catastrophic rupture. The fibers are hypothesized to represent asperities on a fault. Two limiting behaviors are the equal load sharing p = 0 (stress from a failed fiber is transferred equally to all surviving fibers) and the local load sharing p = 1 (stress from a failed fiber is transferred to adjacent fibers). We show that precursory damage in the nucleation phase is greatly reduced in the local-load sharing limit. The local transfer of stress from an asperity concentrates nucleation, restricting precursory acoustic emissions (seismic activity).