Riad Hassani

An integrated mechanical model of the San Andreas Fault in central and northern California

Several lines of evidence support the general view of the San Andreas fault system (SAFS) as a major lithospheric weakness in a generally transpressive plate margin setting. However, the influence of the weakness of the SAFS on the observed stress and deformation fields is not straightforward because factors such as interactions between the brittle upper crust and ductile lower crust, lateral fault strength variation, and the amount of convergence may all be important. The goal of this study is to model steady state deformation, relative fault-parallel velocity, and crustal stress orientations in central and northern California using realistic rheologies and boundary conditions. Using a simplified three-dimensional (3-D) finite element analysis in large strain, we model the SAFS in 2-D cross sections with no stress or strain variations along strike. We investigate the influence of different parameters such as the frictional properties of the fault zone and the adjacent crust, the viscous properties of the lower crust as determined by its thermal structure, and the thermal structure of the lithosphere. Our model appears to provide a good conceptual framework for some first-order aspects of actively deforming plate margins such as the SAFS. The following findings emerge from a variety of numerical experiments: (1) The difference in the manner of transpressive strain partitioning in central and northern California can be explained by different fault strengths and the manner in which heat flow varies with distance from the fault. (2) Only the combination of a weak fault (with an effective friction coefficient of ≈0.1) and a strong lateral heat flow variation predicts approximately correct stress directions in the crust adjacent to the SAFS.

3D mechanical modeling of the GPS velocity field along the North Anatolian fault

The North Anatolian fault (NAF) extends over 1500 km in a complex tectonic setting. In this region of the eastern Mediterranean, collision of the Arabian, African and Eurasian plates resulted in creation of mountain ranges (i.e. Zagros, Caucasus) and the westward extrusion of the Anatolian block. In this study we investigate the effects of crustal rheology on the long-term displacement rate along the NAF. Heat flow and geodetic data are used to constrain our mechanical model, built with the three-dimensional finite element code ADELI. The fault motion occurs on a material discontinuity of the model which is controlled by a Coulomb-type friction. The rheology of the lithosphere is composed of a frictional upper crust and a viscoelastic lower crust. The lithosphere is supported by a hydrostatic pressure at its base (representing the asthenospheric mantle). We model the long-term deformation of the surroundings of the NAF by adjusting the effective fault friction and also the geometry of the surface fault trace. To do so, we used a frictional range of 0.0^0.2 for the fault, and a viscosity varying between 10 19 and 10 21 Pa s. One of the most striking results of our rheological tests is that the upper part of the fault is locked if the friction exceeds 0.2. By comparing our results with geodetic measurements [McClusky et al., J. Geophys. Res. B 105 (2000) 5695^5719] and tectonic observations, we have defined a realistic model in which the displacement rate on the NAF reaches V17 mm/yr for a viscosity of 10 19 Pa s and a fault friction of 0.05. This strongly suggests that the NAF is a weak fault like the San Andreas fault in California. Adding topography with its corresponding crustal root does not induce gravity flow of Anatolia. Rather, it has the counter-intuitive effect of decreasing the westward Anatolian escape. We find a poor agreement between our calculated velocity field and what is observed with GPS in the Marmara and the Aegean regions. We suspect that the simple lithosphere model is responsible for this discrepancy. Taking into account the weaknesses of these deforming regions should allow us to build a more realistic model that would match ground observations more appropriately. On the other hand, our results fit well GPS measurements in central Anatolia, setting the basis of modeling crustal strain in Turkey. B 2003 Elsevier Science B.V. All rights reserved.

A mixed finite element method and solution multiplicity for Coulomb frictional contact

Abstract This paper is concerned with the discrete contact problem governed by Coulomb’s friction law. We propose and study a new technique using mixed finite elements with two multipliers in order to determine numerically critical friction coefficients for which multiple solutions to the friction problem exist. The framework is based on eigenvalue problems and it allows to exhibit non-uniqueness cases involving an infinity of solutions located on a continuous branch. The theory is illustrated with several computations which clearly show the accuracy of the proposed method.

Mechanical analysis of a natural example of onland gravity gliding: The role of river incision and deposition

Gravity gliding implies rigid translation of a body down a slope where displacements are parallel to a tilted detachment plane. Although large-scale gravity gliding is commonly observed offshore, under conditions of high fluid overpressure and abundant upslope sedimentary supply, its occurrence on land is debated. We investigate the mechanical feasibility of such a process as well as the role of fluvial incision and sedimentation down the slope in the initiation of the gliding. We use a two-dimensional (2-D) finite element model combined with a 2-D failure analysis approach. The numerical models simulate the deformation and provide quantitative estimates of the failure criteria at the head and toe of the overburden. Analytical solutions approximate the numerical results by taking into account the fluvial incision and sedimentation, the internal friction angle, and the thickness and length of the overburden. Our models are based on a field example in the Andean foothills of Argentina, where gravity gliding of a 1000 m thick section is suspected above a crustal-scale anticline. The incision and sedimentation reduce and strengthen, respectively, the downslope resistance to contractional failure. The critical slope at which the gliding is initiated is reduced by fluvial incision and increased by sedimentation. We show that tectonic uplift may lead to large-scale gravity gliding on land where the overburden thickness is less than 2000 m. Incision facilitates and localizes the frontal shortening. Incision greater than 1000 m may trigger gliding for overburden up to 4000 m thick, while sedimentation thicker than 1000 m inhibits gliding. These results show that thin-skinned onland gravity gliding could be common in tectonically active regions where incision is important.

Analysis of Eigenvalue Problems Modelling Friction: Sufficient Conditions of Non-Uniqueness for the Elastic Equilibrium

This study is concerned with the Coulomb frictional contact problem in elastostatics. Introducing a convenient eigenvalue problem, it becomes possible to establish sufficient conditions of non-uniqueness for the continuous model. It can be also proven that these sufficient conditions are fulfilled under appropriate hypotheses.

Calcul de l'evolution de la permeabilite des reservoirs sedimentaries contenant des argiles; application a la zone de la faille de Bray (bassin de Paris)

We propose a model for simulating the changes in porosity and permeability caused by hydrothermal diagenesis in sedimentary aquifer where salinity, temperature and fluid flow vary in space and time. Such modifications of the hydrodynamic properties of the medium are bounded to geochemical reactions and groundwater flow. Fluid velocity is particularly low in deep reservoirs (typically less than 1 m/year). Then, the local equilibrium simplification, which is justified by a set of world-wide data of the chemical composition of groundwater, can be implemented toward straightforward transient calculations. In the model presented here, the coupled processes of fluid flow, temperature and chemical species transport are solved using well established methods. The originality of the model is the development carried on to predict the permeability evolution controlled by the mineral dissolution and precipitation. Usually to simulate permeability changes modelers use the classical porosity-permeability model based on statistical analyses of in situ or laboratory measurements. However, hydraulic conductivity changes are not controlled solely by porosity changes, but also depend on pore-scale structure transformations. Depending on the mineral type, the precipitation or dissolution of the same quantity of volumetric quantity will induce very different changes in the hydraulic conductivity. Principally clay minerals depict a wide range of atypical organisations of different microstructural characteristics of the porous media. The spatial distribution of these characteristics cannot be modelled at basin scale. Away from both too complicated and too unrealistically simplified approach, the model presented here is based on the calculation of the permeability evolution from the change in the mineral fraction due to mineral precipitation and dissolution. To simplify, the minerals are divided into two groups: clay minerals and non-clay minerals. The specific contribution of clay minerals is controlled by a single weighting coefficient. This coefficient is associated to the proportion of poorly connected porosity that characterize clay structure, albeit it is presently impossible to propose any quantitative relationship between the value of this parameter and the microstructural characteristics of the diagenetic clays. The model is tested here to simulate the evolution of the porosity and the permeability in a peculiar zone of the Paris Basin. The study area of several hundred meters large is inside the Dogger aquifer, close to the Bray fault zone where invasion of saline water from Triassic formation takes place. This zone is characterised by high thermal and salinity gradient as well as by the superposition of sub-horizontal regional flow and ascendant fault-controlled flow: it is an ideal case study for examining the importance of taking into account the specific contribution by clay minerals when computing permeability evolution. This study is proposed as a parameter sensibility analysis: - to compare the relative influence of the clay weighting coefficient, the temperature, the salinity, and the cementation exponent on the computed evolution of the permeability, - to discuss the consequences of the introduction of the clay weighting coefficient in comparison to the classical porosity - permeability evolution model, - to simulate various evolution scenarios of past and future thermal and geochemical constraints and their consequences on the evolution of the permeability changes in the Bray fault zone taking into account uncertainties on the value of the clay weighting coefficient and on the cementation exponent. Forty-one simulations of one million years were necessary to cover a large spectrum of the expected variations of each parameter. The results show that: - the local variation of the permeability depends on the time evolution of temperature and of salinity, and on the values of the cementation exponent of the porosity-permeability law and of the clay weighting coefficient. Within reasonable ranges of these four parameters, their influence on the permeability changes is of the same order of magnitude, - the influence of the clay weighting coefficient on the porosity evolution is negligible. Feedback effects of permeability evolution on the porosity evolution, through the change in the flow regime, is minor, - by the use of a classical model without a clay weighting coefficient, permeability and porosity present the same pattern of evolution: they both increase or decrease. By the use of the clay weighting coefficient, in some places the permeability and porosity can show opposite evolution. One increases when the other decreases even for low values of the coefficient, - in the vicinity of the fault, the model predict an increase of permeability independently of potential temperature and salinity modifications and whatever the clay mineral weighting coefficient is: Bray fault sealing is unlikely as long as head gradient is maintained in the fracture zone.