Limit analysis is used in civil engineering to predict the maximum strength that a structure can sustain before the rupture. My thesis aimed to develop this theory for geological structures (as accretionary wedges or fold-and-thrust belts) in order to predict fault positions and their evolution. The method has been first validated by proving that the critical taper, for a simple triangular wedge, is properly captured.
This study reveals that weakening of the ramp, accounted for by a decrease of the friction angle, is necessary to have a finite life span. A thrusting sequence can thus be predicted until the apparition of an out-of-sequence :
Force evolution (normalized) versus shortening (normalized), each rupture indicates a new thrust. In black : active fault, in red : previous faults
This new method demonstrates how each rheological or geometrical parameter can influence the number, the spacing or the lifetime of thrusts. For example : a decrease of the basal friction leads to an increase of the number of thrusts, an increase of the weakening results in an increase of the life span of a thrust.
For more details :
N. Cubas, Y.M. Leroy, B. Maillot (2008), Prediction of thrusting sequences in accretionary wedges, Journal of Geophysical Research, B12412, doi : 10.1029/2008JB005717
An inverse study, comparing sandbox experimental results with mechanical predictions, has been carried out to validate the theory. As the theory predicts positions, dips and lifetime of thrusts from the rheological parameters, inversion will consist in retrieving the sand rheology from the final geometry of experiments.
3 steps were necessary :
1st step : We have developped an experimental set-up optimizing the reproducibility of the experiences and minimizing the side walls effects. (The experiments were realised in the analogue experiment laboratory of the university of Cergy-Pontoise.)
The experiment consists in sliding by a fixed amount a stable sand wedge prolonged by a flat sand layer.
To accomodate the shortening, two thrusts appear.
2nd step : The quantitative comparison requires to estimate the intrinsic variability of the experimental results. Therefore, only one experiment repeated 10 times has been studied. And a statistical analysis has been conducted to construct the statistical model of each observable :
a mean (or median) and its standard deviation (or mean deviation) are determined.
3rd step : Probabilities distributions for the rheological parameters of the experiment are provided by the inverse problem :
Internal friction, basal friction (sand on glass), friction after weakening and slip amount necessary for that weakening are thus determined.
Coming soon :
N. Cubas, B. Maillot, C. Barnes, Statistics of the experimental growth of a sand wedge (submitted).
N. Cubas, B. Maillot, C. Barnes, Inversion of sandbox experiments (in prep.)
Three different applications, approaches, were possible :
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➡ This new method can be used to predict the evolution of a wedge, knowing its rheology,
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➡ Or, the rheological parameters of a structure can be deduced from its geometry. For the Nankaï wedge (profil NT62-8, from Morgan et Karig, 1995)
we find 27° for the internal friction and 9° for the basal friction (Cubas et al., 2008).
Red : active and incipient thrusts, yellow : optimized thrust with the limit analysis.
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➡ The theory can also be applied to compare various kinematical models by calculating the forces required. The method has been applied to the Tromen and Pampa Tril folds of the Agrio fold-and-thrust belt, in Agentina. Two kinematical models are proposed for this two folds, one in favor of a thick-skinned origin, and another in favor of a shallower décollement. The objective was to provide mechanical arguments to the discussion.
thick-skinned model thin-skinned model
It is shown that the thick-skinned model is favored in the case of a fault reactivation. If magmatic material can intrude along faults, the second hypothesis is then prefered.
