Borehole stability in brittle rock - A tool for evaluation of borehole breakouts and in-situ stress
Typ
Examensarbete för masterexamen
Program
Infrastructure and environmental engineering (MPIEE), MSc
Publicerad
2019
Författare
Felldin, Nils-Erik
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
This thesis deals with the simulation of progressive failures in boreholes, a phenomenon known as
borehole breakouts. Borehole breakouts or spalling are common in holes and tunnels subject to large
differential in-situ stresses. The aim was to produce a simulation tool in MATLAB using a conformal
mapping method based on the work of Gerolymatou (2019).
An interactive graphical tool was coded to design a geometry and to evaluate its conformal mapping
from a unit circle. A script was coded for determining stress distributions and checking for rock failure
with the Mohr-Couloumb and Hoek-Brown failure criterion. Using this script it was also possible to
iterate failure and generate new boundaries for simulating borehole breakouts.
By using the designed tool example mappings of several geometries are shown in an attempt to
quantify the performance of the mapping method. The secondary stress state of a circular hole was
compared to the Kirsch (1898) solution and the stresses around a tunnel geometry was compared to a
MATLAB Finite Element Model (FEM). Finally, results of a few borehole breakout simulations are
presented.
The mapping was shown to perform best for geometries defined by smooth continuous curves. The
method of determining secondary stresses around symmetric regions is functional, however the FEM
comparison of an asymmetric tunnel geometry demonstrated that the code needs further adaptation to
correctly evaluate stresses around arbitrary geometries. Simulations of progressive borehole breakouts
are possible if dealing with boundary oscillations stemming from the mapping. Oscillations are handled
by using filters smoothing the boundary and optionally by also smoothing secondary stresses. A few
ideas are presented on how the smoothing implementation can be improved to increase performance of
breakout simulation.
As an example of how breakout simulation can be used to find in-situ stresses from measured real
world breakouts, breakout depth and width from simulations are shown as functions of the in-situ stress.
Such functions could potentially be used to match measured real world breakouts to the maximum in-situ
stress, if the minor in-situ stress is determined by a method such as hydraulic fracturing and if the rock
can be accurately modelled by a failure criterion.
Beskrivning
Ämne/nyckelord
Borehole breakouts , Conformal mapping