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Stochastic Analysis and Applications Volume 37, 2019 - Issue 6
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Articles

An SDE model for deterioration of rock surfaces

E. J. AllenDepartment of Mathematics and Statistics, Texas Tech University, Lubbock, TX, USACorrespondence[email protected]
Pages 1012-1027 | Received 29 May 2019, Accepted 23 Jun 2019, Published online: 03 Jul 2019
 
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Abstract

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.

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