13 Elastic Wave Propagation Modeling During Exploratory Drilling …
177
13.3.4 The Destruction Criterion
The chapter considers potential destruction at all points of the integration domain.
Within the framework of the linear elastic medium model, it is possible to determine
the possibility of fracture at a specific point. The destruction process itself is not
considered. To determine the points of destruction, the Mises criterion is used [15]:
T mises =
1
√
2
(T xx − p)
2
+
T yy − p
2 + (T zz − p)
2
+ 2T 2
xy + 2T 2
xz + 2T 2
yz > y s ,
where p =
T xx + T yy + T zz
/3 is the average stress, and y s is the shear stress limit,
which value for ice is equal to 1 MPa.
13.3.5 The Drill Model
Modern drills have a rather complex device, often combining percussion and rotational mechanisms. In this chapter, we are primarily interested in the wave pattern
that occurs when drilling in a specific geological model. Therefore, for simplicity,
we represent the impact of the drill as a point source with a Ricker pulse of 30 Hz
and an amplitude coefficient 10
12 . It can be written with formula:
R(t) = A
1 − 2π
2 f
2 t
2
ex p
−π
2 f
2 t
2
,
where A is the coefficient of compression, and f is the frequency.
Ricker pulse is represented in Fig. 13.3 for the case of frequency 0.4 Hz and
amplitude coefficient 1.
Fig. 13.3 Ricker pulse
177
13.3.4 The Destruction Criterion
The chapter considers potential destruction at all points of the integration domain.
Within the framework of the linear elastic medium model, it is possible to determine
the possibility of fracture at a specific point. The destruction process itself is not
considered. To determine the points of destruction, the Mises criterion is used [15]:
T mises =
1
√
2
(T xx − p)
2
+
T yy − p
2 + (T zz − p)
2
+ 2T 2
xy + 2T 2
xz + 2T 2
yz > y s ,
where p =
T xx + T yy + T zz
/3 is the average stress, and y s is the shear stress limit,
which value for ice is equal to 1 MPa.
13.3.5 The Drill Model
Modern drills have a rather complex device, often combining percussion and rotational mechanisms. In this chapter, we are primarily interested in the wave pattern
that occurs when drilling in a specific geological model. Therefore, for simplicity,
we represent the impact of the drill as a point source with a Ricker pulse of 30 Hz
and an amplitude coefficient 10
12 . It can be written with formula:
R(t) = A
1 − 2π
2 f
2 t
2
ex p
−π
2 f
2 t
2
,
where A is the coefficient of compression, and f is the frequency.
Ricker pulse is represented in Fig. 13.3 for the case of frequency 0.4 Hz and
amplitude coefficient 1.
Fig. 13.3 Ricker pulse