Showing papers by "Philippe Davy published in 2000"

Scaling of fracture connectivity in geological formations

Abstract: A new method to quantify fracture network connectivity is developed and applied to analyze two classical examples of fault and joint networks in natural geological formations. The connectivity measure accounts for the scaling properties of fracture networks, which are controlled by the power law length distribution exponent a, the fractal dimension D and the fracture density. The connectivity behavior of fracture patterns depends on the scale of measurement, for a D + 1. Analysis of the San Andreas fault system shows that a < D+1 and that the connectivity threshold is reached only at a critical length scale. In contrast, for a typical sandstone joint pattern, a ≈ D + 1, which is on the cusp where the connectivity threshold is highly sensitive to the minimum fracture length in the system.

Percolation parameter and percolation-threshold estimates for three-dimensional random ellipses with widely scattered distributions of eccentricity and size

Abstract: In fractured materials of very low matrix permeability, fracture connectivity is the first-order determinant of the occurrence of flow. For systems having a narrow distribution of object sizes (short-range percolation), a first-order percolation criterion is given by the total excluded volume which is almost constant at threshold. In the case of fractured media, recent observations have demonstrated that the fracture-length distribution is extremely large. Because of this widely scattered fracture-length distribution, the classical expression of the total excluded volume is no longer scale invariant at the percolation threshold and has no finite limit for infinitely large systems. Thus, the classical estimation method of the percolation threshold established in short-range percolation becomes useless for the connectivity determination of fractured media. In this study, we derive an expression for the total excluded volume that remains scale invariant at the percolation threshold and that can thus be used as the proper control parameter, called the parameter of percolation in percolation theory. We show that the scale-invariant expression of the total excluded volume is the geometrical union normalized by the system volume rather than the summation of the mutual excluded volumes normalized by the system volume. The summation of the mutual excluded volume (classical expression) remains linked to the number of intersections between fractures, whereas the normalized geometrical union of the mutual excluded volume (our expression) can be essentially identified with the percolation parameter. Moreover, fluctuations of this percolation parameter at threshold with length and eccentricity distributions remain limited within a range of less than one order of magnitude, giving in turn a rough percolation criterion. We finally show that the scale dependence of the percolation parameter causes the connectivity of fractured media to increase with scale, meaning especially that the hydraulic properties of fractured media can dramatically change with scale.

Upscaling local-scale transport processes in large-scale relief dynamics

Abstract: The objective of this paper is to discuss the form and parameters of the macroscopic continent-scale erosion law. The law comes from a spatial integration of local transport processes on the resulting topography. It thus depends on the relief/drainage organization that results from the development of geomorphic instabilities such as differential incisions. Assuming local transport processes to depend on local slope and water discharge, we have calculated topographic evolution to derive the characteristic time scales of erosion dynamics. We especially focused on the case of a declining plateau which presents two main phases: a first phase when the drainage pattern establishes, and a declining phase when topography decreases almost exponentially in the absence of tectonic input. The latter phase is characterized by a time scale which depends on the system size, on the organization of the drainage network, and on the parameters of the transport process. We show that the macroscopic erosion law has the characteristics of an abnormal diffusion whose basic time-length exponent a is determined by the parameters of the fluvial process. This result sheds new light on the observed negative correlation between current denudation rates and drainage areas in world-wide fluvial watersheds.

Estimating uplift rate and erodibility from the area-slope relationship: Examples from Brittany (France) and numerical modelling

Abstract: We used the local slope/drainage area relationship to derive the basic erosion and tectonic parameters from a topography. Assuming a dynamic equilibrium between uplift and erosion, this relationship is expected to depend quite simply on the rock erodibility, and on the tectonic uplift. This relationship may then be used to quantify independently the effect of lithological variation on the erodibility, and the uplift rate. We tested the method on a computer simulated topography and showed that the uplift information can be precisely calculated from the topographic analysis alone. We then analysed the topography of Brittany (France), and obtained a good agreement with uplift data from comparative levelling studies and river incision analysis.

Continental collision, gravity spreading, and kinematics of Aegea and Anatolia

Abstract: We have carried out experiments using a layered medium of sand and silicone to investigate the lateral extrusion of a material which spreads over its own weight while being compressed by the advance of a rigid indenter. Boundary conditions in the box mimic those prevailing in the Anatolian-Aegean system. Both shortening in front of the rigid piston, which models the northward motion of Arabia, and extension resulting from the gravity spreading of the sand-silicone layer are necessary to initiate the lateral extrusion. Strike-slip faults accommodate the lateral escape and link the normal faults accompanying gravity spreading with the thrust faults in front of the rigid indenter. Strike-slip faults begin to accommodate extrusion at a late stage in the experiments after the normal and thrust faults have developed. Experiments also show that the initial geometry of the boundary of the spreading layer may result in the formation of two arcs behind which material extends, in a manner analogous to the Hellenic and Cypriot arcs, without invoking a rheological change at the junction of the two arcs. The experiments also suggest that southward motion of the eastern, part of the spreading region is compensated by the northward advance of the piston, which is a possible explanation for the slower movement of the Cypriot arc compared to the Aegean arc.

Analogue modelling of relief dynamics

Abstract: Natural landscape analysis and numerical modelling point to a lack of physical data on relief dynamics. Experimental modelling is therefore an interesting approach for obtaining physical information on eroded systems with runoff transportation and topographic incision. The main technical challenge, in reproducing regional topography at the laboratory scale, is to obtain mm-scale incisions and a limitation of the smoothing action of diffusive transport processes. An experimental design using newly developed rain making apparatus and silica as a model material, satisfies the required conditions, and allows simulation of geomorphic instabilities. An example of “plateau instability” modelling is presented to illustrate the suitability of this experimental procedure.

Spectral and cross-spectral analysis of three hydrological systems

Abstract: The mean hydrological and hydrochemical behaviour is analysed from observed time series on three agricultural catchments, located in different regions of France, named respectively Kervidy, Melarchez and Mercube. The time series are considered as input data or output data. The input data for hydrology and chemistry are respectively rainfall and nitrate leaching, and the output data are represented by stream discharge and nitrate concentration in the stream. The method is based on the spectral analysis of the data. First the spectral density function of each time series is calculated. It appears that nitrate concentrations measured at the outlet of the three catchments exhibit a strong and unique one year periodicity. This periodicity is due to the hydrological regime and the time distribution of the nitrate availability in the soil. Second, we performed a cross-spectral analysis between the input and output data. The catchment is then viewed as a linear and stationary system that converts an input to an output through a transfer function. The transfer function characterizes the behaviour of the catchment and is related to the real physical and chemical processes. For each catchment, the observed transfer functions for water and nitrate are determined in the spectral domain from the data. By comparing the observed frequency transfer function with the spectral signature of the- oretical model, we identify for each catchment: ( i ) the major processes that govern water and nitrate transfer and ( ii ) the characteristic time scale of these processes. The spectral and cross-spectral method appear to be valuable in identifying the main transfer processes operating in the different catchments.