Rocks with elasticity in mantle convection
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Інститут геофізики ім. С.I. Субботіна НАН України
2010
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| Zitieren: | Rocks with elasticity in mantle convection / Yu. Rebetsky // Геофизический журнал. — 2010. — Т. 32, № 4. — С. 138-139. — Бібліогр.: 7 назв. — англ. |
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irk-123456789-1030942016-06-14T03:04:11Z Rocks with elasticity in mantle convection Rebetsky, Yu. 2010 Article Rocks with elasticity in mantle convection / Yu. Rebetsky // Геофизический журнал. — 2010. — Т. 32, № 4. — С. 138-139. — Бібліогр.: 7 назв. — англ. 0203-3100 http://dspace.nbuv.gov.ua/handle/123456789/103094 en Геофизический журнал Інститут геофізики ім. С.I. Субботіна НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
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Article |
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Rebetsky, Yu. |
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Rebetsky, Yu. Rocks with elasticity in mantle convection Геофизический журнал |
| author_facet |
Rebetsky, Yu. |
| author_sort |
Rebetsky, Yu. |
| title |
Rocks with elasticity in mantle convection |
| title_short |
Rocks with elasticity in mantle convection |
| title_full |
Rocks with elasticity in mantle convection |
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Rocks with elasticity in mantle convection |
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Rocks with elasticity in mantle convection |
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rocks with elasticity in mantle convection |
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Інститут геофізики ім. С.I. Субботіна НАН України |
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2010 |
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Rocks with elasticity in mantle convection / Yu. Rebetsky // Геофизический журнал. — 2010. — Т. 32, № 4. — С. 138-139. — Бібліогр.: 7 назв. — англ. |
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Геофизический журнал |
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AT rebetskyyu rockswithelasticityinmantleconvection |
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2025-07-07T13:16:57Z |
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2025-07-07T13:16:57Z |
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1836994231275618304 |
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Rocks with elasticity in mantle convection
Yu. Rebetsky, 2010
Institute of Physics of the Earth, RAS, Moscow, Russia
reb@ifz.ru
All modern mantle convection equations are
based on pure viscous media model, which has com-
pressibility only in frames of thermoelastic problem
solution (impact of temperature on volume change
and absence of such impact from pressure — pos-
itive and negative elastic dilatation and from devia-
tor stresses — inelastic dilatation) [Trubitsyn, 2008].
Analyzing the results obtained in these studies one
may ask: how much we can trust these results?
This question follows from our knowledge that man-
tle is a rigid crystalline rock and not a fluid; and
also from understanding the difference in mecha-
nisms of viscous fluid flow and ductile behavior of
solid body.
It is well-known that Poisson coefficient of crys-
talline rocks varies in wide range from 0.15 to 0.40,
most often observed values are 0.25, which essen-
tially differs from values for fluids — 0.5. Seismic
data in the crust and mantle are compatible with
coefficient close to 0.25, except some local ano-
malous areas, which are mostly concentrated in the
crust. This let us assume that mantle rocks have
elastic properties and their ability to flow is condi-
tioned by rather low yield strength magnitude; (elas-
ticity) in the lithosphere and high rates of diffusion
and re-crystallization processes in the low mantle.
Taking into account the knowledge of real rock state
it is interesting to understand what we are missing,
when in mantle convection problem we replace duc-
tile flow of solid rocks having elasticity by viscous
fluid flow without elasticity.
In the recent publications [Rebetsky, 2008] it has
been shown that in the problem of gravitational for-
ces acting on rock massive, triaxial pressure with
depth goes closer to lithostatic (weight of the rock
column) due to inelastic deformation taking place
in confined conditions (neighbor rocks, which are in
the same conditions, limits horizontal spreading.
Such deformation under gravitational forces leads
to the increment of confining stresses in horizontal
direction and to the vertical compaction in the same
time [Jager, 1962]. This mechanism could be called
as gravitational elasto-plastic compaction. If the
rocks react on gravitational loading only in elastic
manner, then for Poisson coefficient 0.25 horizontal
pressure would be only 1/3 of vertical one [Dinnik,
1926]. Inelastic strains developing under lateral con-
fining stresses brings additional horizontal confin-
ing stresses and elastic compaction of rocks [Re-
betsky, 2008]. If the rocks as fluids would have Pois-
son coefficient 0.5 (ideal rubber) then gravitational
stresses will not cause deviatory stresses and nor-
mal stresses in any direction will be equal to rock
column weight.
Inelastic deformation at different tectonoshpere
levels is conditioned by different mechanisms: in
the crust — due to fracture flow (upper and middle
crust) or quasi plastic midgrain flow (lower crust)
when Coulomb stresses reach threshold value; in
under crust lithosphere — due to the ductility flow
[Nikolaevsky, 1996] when deviatory stresses reach
yield strength; in lower mantle — due to the diffu-
sion and re-crystallization mechanisms of viscous
flow. If the rock specimen which underwent such
elasto-plastic compaction under gravitational forces
will be drilled out from rock massive (maintaining
horizontal confining condition) then only additional
horizontal confining stresses occurred at gravitatio-
nal compaction stage will be left. In the rock speci-
men not healed at post-deformation stage by later
mineralization these stresses will disappear practi-
cally immediately after canceling lateral confine-
ment. For the rock specimen having such new for-
mation, sudden destruction may occur after ex-
tracting the specimen from drilling holder. In this
case, above mentioned additional confining pres-
sure should be treated as residual stress forming
in the specimen specific type of mutually com-
pensating stress state.
What happened when we drill out the rock speci-
men from certain depth? In such case, first of all the
weight of upper layers are canceled, relaxation oc-
curs, but stress relaxation is not complete. In such
relaxation conditions, when lateral confinement still
acts, vertical stresses completely dropped; and hori-
zontal ones — according to Poisson coefficient —
elastic relaxation law. For rocks having =0.25 only 1/
3 of overlaying column weight (lithostatic pressure) is
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relaxed. Elastic relaxation law together with lateral
confinement and erosion processes at surface condi-
tions occurrence in rocks residual stresses when ver-
tical uplift, what was marked at first time in [Good-
man, 1989]. It has to be noted, if rocks would have
Poisson elastic coefficient 0.5 (rubber), then elastic
relaxation of gravitational stress state leads to equal
decrement of both vertical and horizontal stresses,
what actually happened in all modern computation of
mantle convection.
Evaluations of the gravitational stress state energy
are known 2.5 1032 J. It is by three orders larger than
kinetic energy of the planet and by four orders larg-
er than energy of thermal convection. Our evalua-
tions show that residual horizontal stresses of grav-
itational stress state (2/3 of lithostatic pressure and
=0.25) compose circa half of total energy of elas-
tic strains. This energy will relax through vertical
convection movements causing additional (relative
to ideal viscous fluid) plastic deformations, which
finally will be transitioned into heating. Comparing
the residual stress energy of unit volume released
when uplifting from the core up to upper mantle
boundary with the work spent on vertical transfer-
ring of this volume in thermal convection we will get
8 109 J O 3 109 J respectively. Thus, energy confined
in residual stress state is more than the energy
spent on vertical uplift of unit volume.
Therefore, our analysis has demonstrated that in
all modern computations of thermal convection in the
mantle in solutions is missing one of the most impor-
tant components in energy balance — residual stress
state conditioned by gravitational elastic-plastic com-
paction. In the presentation in the frames of traditional
viscous model the problem will be posed and the sol-
ving equations followed from it, which take into ac-
count existence of the residual stresses in mantle and
its impact on mantle convection will be given.
The research is supported by RFBR grant 09—
05—012130.
Dinnik A. N. About rock pressure and calculation co-
lumn of circle mine // Ingeniring worker. — 1926. —
� ���— P� �—�� (in Russian).
Goodman R. E. Introduction to rock mechanics. (2nd
Edition). — New York: John Wileyand Sons, 1989.
— 583 p.
Jager J. C. Elasticity Fracture and Flow. — London:
Methuen and Co. LTD, 1962. — 208 p.
Nikolaevsky V. N. Geomechanics and fluid dynamics.
— Moscow: Nedra, 1996. — 446 p. (in Russian).
References
Rebetsky Yu. L. Mechanism of tectonic stress gener-
ation in the zones of high vertical movements // Fiz.
Mezomekh. — 2008. — 11, ��1. — P. 66.
Rebetskii Yu. L. Possible mechanism of horizontal
compression stress generation in the Earth’s crust
// Doklady Earth Sciences. — 2008. — 423A, ��9.
— P. 1448—1451.
Trubitsyn V. P. Equations of termal convection for un-
compressibility viscous mantle with phase transi-
tion // Phys. Earth. — ������— � ����— P� ��— �
(in Russian).
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