# Accession Number:

## AD0260329

# Title:

## NUMERICAL SOLUTIONS OF THE UNDERGROUND SUBSIDENCE PROBLEM

# Descriptive Note:

# Corporate Author:

## BALLISTIC RESEARCH LABS ABERDEEN PROVING GROUND MD

# Personal Author(s):

# Report Date:

## 1961-04-01

# Pagination or Media Count:

## 30.0

# Abstract:

The subsidence problem can be formulated as follows suppose there is an underground cavity of height episilon at some depth below the surface. At the time t 0 the soil begins to subside filling out the cavity and the subsidence continues to move vertically up toward the surface of the earth. It is also assumed that the subsidence occurs along a vertical shaft of a unit cross-section making it a one-dimensional phenomenon. We assume further that the crumbled earth is a continuum whose motion can be simulated by that of a compressible fluid and that the subsidence occurs continuously. The boundary value problem controlling the above described model consists of the partial differential equation of continuity conservation of mass, of the equation of conservation of momentum, and of the conditions on the fixed boundary when t 0 and on the boundary moving with the wave front. Here the equation of the conservation of momentum has been replaced by an assumed relation, based on experience, which takes care of the elasto-plastic properties of the soil. The solution gives the displacement of the wave front as a function of the time, showing that in most cases the subsidence reaches only a certain height and then it stops. Author