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An SDE model for deterioration of rock surfaces. (English) Zbl 1425.74315

Summary: A stochastic differential equation (SDE) is derived and examined for approximately modeling the breaking down of rock surfaces through random processes. The rock surfaces include, for example, surfaces of historical monuments, gravestones, or natural rock formations. Rock surfaces break down through wear, weathering, and erosion. During weathering, rocks are worn away and fractured into smaller pieces while in erosion, the rock pieces are transported through actions, for example, of air, water, and gravity. In the mathematical model developed in the present investigation, it is assumed that environmental actions cause particles or pieces of a rock to gradually break off with erosion occurring simultaneously, that is, the rock pieces are transported away immediately after separation.

MSC:

74L10 Soil and rock mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
60H30 Applications of stochastic analysis (to PDEs, etc.)
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
37H10 Generation, random and stochastic difference and differential equations
86A60 Geological problems
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
74A45 Theories of fracture and damage
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References:

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