Page 7 - 05 albarello
P. 7
Finite element modelling of the recent-present deformation pattern in the Calabrian are and surrounding regions
by isotropic elastic shells, convergent and di- 3. Numerical procedure and model
vergent boundaries by isotropic elastic ele- parametrization
ments characterized by values of elastic param-
eters much lower (severa! orders of magnitude) Numerica! modelling has been carried out
than those of the surrounding «stable» areas. by a finite element procedure in a piane stress
Transform faults are simulated by orthotropic approximation (Calladine, 1983). The numeri-
elastic elements (Love, 1944; Lekhniskii, ca! algorithm employs six-node isoparametric
1981) characterized by values of elastic param- triangu1ar shell elements with cubie basis func-
eters in the direction of the shear trend several tions. The resulting set of algebric equations
orders of magnitude lower than those in the has been solved by the Newton's method. Fur-
perpendicular direction. To obtain strain values ther details on the numerica! technique are
of the order of magnitude of those actually ob- given by Sewell (1986).
served in active faults (Sibson and Ramsay,
1982; Sibson, 1984; Smith and Bruhn, 1984; Figure 4 shows the model finally adopted. The
Williams and Richardson, 1991), the ratio be- grid is constituted by 231 triangular piane shell
tween the values of the Young modulus parai- elements whose sides connect 123 nodes. Given
lei and perpendicular to the shear zone (Ex and the relatively small dimension of the elements,
Ey resrectively) bave to be of the order of earth curvature has been considered negligible.
103-lO . To avoid this high ratio producing un-
realistic high strains in the direction of the The elastic behaviour of the shell elements
fault, the Poisson coefficient in direction of the in «stable» blocks is controlled by the isotropic
shear zones has to be very low. Poisson coefficient and by the «conventional
elastic modulus» given by the product between
To better understand this point, let us con- the Young modulus E and the elastic thickness
sider, for example, the simple case of a planar h, which is representative of the mechanical
section of an orthotropic body characterized by lithospheric layer (Calladine, 1983). In the
modelling bere considered, we choose to as-
Ex » Ey and by Poisson coefficients Vx and Vy- sume for ali stable blocks a unique value of the
conventional elastic modulus (2 · 1015 Pa m)
This condition is supposed to simulate the be- which corresponds to values of Young modulus
haviour of a transcurrent discontinuity with a
shear oriented along the y axis. If this shear is and elastic thickness respectively equal to ro11
loaded by a uniaxial compression along the x
Pa and 20 km) and of Poisson modulus (0.25).
axis (rrxx t= rryy = 0), linear elasticity implies In fact, since lateral variations of mechanical
lithospheric thickness in the study area never
that: · exceed one order of magnitude (Viti et al.,
1997), one may reasonably expect that also the
If Vy is significantly different from zero, the corresponding variations of short-term strain
strain induced in the y direction (parallel to the accumulation rates do not exceed one order of
shear) would become unrealistically high due magnitude. Instead, strain accumulation rates
to the large E)Ey ratio. In order to overcome in deformation belts are generally at least two
this problem, a null value of Vy has been as- orders of magnitude greater than those in the
sumed in the modelling of shear zones. Despite surrounding stable areas (Pfiffner and Ramsay,
the fact that this choice is meaningless from 1982; Lachenbruch and Sass, 1992; Bodri and
the mechanical point of view and produces Iizuka, 1993). Thus, it seems reasonable to as-
unrealistic stress/strain relations within shear sume that the effect of large tectonic disconti-
zones, realistic strain and displacement fields nuities on the strain and displacements fields is
can be obtained in this way. Due to these prob- much greater than the one induced by lateral
lems, the results of modelling will be consid- variations in lithospheric thickness and thus
ered significant only from the kinematic point that the last ones could be neglected in the nu-
of view. merica! analysis. This conclusion is also sup-
ported by the results of some preliminary nu-
merica! computations.
839
