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| Titel |
A generalized Nadai failure criterion for both crystalline and clastic rocks based on true triaxial tests |
| VerfasserIn |
Bezalel Haimson, Chandong Chang, Xiaodong Ma |
| Konferenz |
EGU General Assembly 2016
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| Medientyp |
Artikel
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| Sprache |
en
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 18 (2016) |
| Datensatznummer |
250129071
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| Publikation (Nr.) |
 EGU/EGU2016-9135.pdf |
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| Zusammenfassung |
| The UW true triaxial testing system enables the application of independent compressive loads
to cuboidal specimens (19×19×38 mm) along three principal directions. We used the
apparatus to conduct extensive series of experiments in three crystalline rocks (Westerly
granite, KTB amphibolite, and SAFOD granodiorite) and three clastic rocks of different
porosities [TCDP siltstone (7%), Coconino sandstone (17%), and Bentheim sandstone
(24%)]. For each rock, several magnitudes of σ3 were employed, between 0 MPa and
100-160 MPa, and for every σ3, σ2 was varied from test to test between σ2 = σ3 and σ2=(0.4
to 1.0) σ1.Testing consisted of keeping σ2and σ3constant, and raising σ1to failure
(σ1,peak).
The results, plotted as σ1,peakvs. σ2for each σ3 used, highlight the undeniable effect of
σ2on the compressive failure of rocks. For each level of σ3, the lowest σ2 tested (σ2 = σ3)
yielded the data point used for conventional-triaxial failure criterion. However, for
the same σ3 and depending on σ2 magnitude, the maximum stress bringing about
failure (σ1,peak) may be considerably higher, by as much as 50% in crystalline
rocks, or 15% in clastic rocks, over that in a conventional triaxial test. An important
consequence is that use of a Mohr-type criterion leads to overly conservative predictions of
failure.
The true triaxial test results demonstrate that a criterion in terms of all (three principal
stresses is necessary to characterize failure. Thus, we propose a ‘Generalized Nadai Criterion’
(GNC) based on Nadai (1950), i.e. expressed in terms of the two stress invariants at failure
(f), τoct,f = βσoct,f, where τoct,f = 1/3[(σ1,peak −σ2)2+(σ2 −σ3)2+(σ3 −σ1,peak)2]0.5 and
σoct,f = (σ1,peak + σ2 + σ3)/3, and β is a function that varies from rock to rock. Moreover,
the criterion depends also on the relative magnitude of σ2, represented by a parameter b [=
(σ2 – σ3)/(σ1,peak – σ3)]. For each octahedral shear stress at failure (τoct,f), the lowest mean
stress (σoct,f) causing failure is when b = 0 (or when σ2 = σ3), and the magnitude of σoct,f
increases with the b value, reaching the highest mean stress at failure when b = 1
(or when σ2 = σ1,peak). Since the number of bparameters tested for each τoct,f
magnitude is finite, interpolation between adjacent tested b values should yield fairly
accurate failure criteria even in cases where the respective b value has not been
tested.
In the crystalline rocks the criterion τoct,f = β (σoct,f) is represented by a power-law
function. So for example, in Westerly granite, the GNC for the two extreme b values tested
are:
τoct,f = 2.71(σoct,f)0.85(for b=0) and τoct,f = 1.57(σoct,f)0.89(for b=0.4)
In the clastic rocks τoct,f = β (σoct,f) is best fitted by a second-order polynomial
equation. So for example, in Bentheim sandstone, the GNC for b= 0 and b= 1, respectively,
are:
τoct,f = 2.98 + 1.139σoct,f – 0.0036σoct,f2 and τoct,f = -5.82 + 0.836σoct,f –
0.0017σoct,f2 |
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