Showing papers by "Philippe Davy published in 2003"

Laboratory experiments simulating the geomorphic response to tectonic uplift

Abstract: [1] We present the results of an experimental study of topography dynamics under conditions of constant precipitation and uplift rate. The experiment is designed to develop a complete drainage network by the growth and propagation of erosion instabilities in response to tectonic perturbations. The quantitative analysis of topographic evolution is made possible by using telemetric lasers that perform elevation measurements at an excellent level of precision. We focus our study on the effect of initial surface organization and of uplift rate on both the transient dynamics and the steady state forms of topography. We show that the transient phase is strongly dependent on the initial internally drained area, which is found to decrease exponentially with time. The topography always reaches a steady state whose mean elevation depends linearly on uplift rate with a strictly positive value when uplift is zero. Steady state surfaces are characterized by a well-defined slope–area power law with a constant exponent of −0.12 and an amplitude that depends linearly on uplift rate with a strictly positive value when uplift is zero. These results are consistent with a stream power law erosion model that includes a nonnegligible threshold for particle detachment. Uncertainty regarding the sediment transport length is resolved by calibrating the transient dynamics with a surface process model. Reappraising published results on the linear dependency between mean elevation, or relief, and denudation rate, we suggest that an erosion threshold is worth considering for large-scale systems.

Connectivity properties of two‐dimensional fracture networks with stochastic fractal correlation

Abstract: [1] We present a theoretical and numerical study of the connectivity of fracture networks with fractal correlations. In addition to length distribution, this spatial property observed on most fracture networks conveys long-range correlation that may be crucial on network connectivity. We especially focus on the model that comes out relevant to natural fracture network: a fractal density distribution for the fracture centers (dimension D) and a power law distribution for the fracture lengths (exponent a, n(l) ∼ l−a). Three different regimes of connectivity are identified depending on D and on a. For a D + 1 the connectivity is ruled by fractures much smaller than the system size with a strong control of spatial correlation; the connectivity now decreases with system scale. Finally, for the self-similar case (a = D + 1), which corresponds to the transition between the two previous regimes, connectivity properties are scale invariant: percolation threshold corresponds to a critical fractal density and the average number of intersections per fracture at threshold is a scale invariant as well.

Constraints on the long-term colluvial erosion law by analyzing slope-area relationships at various tectonic uplift rates in the Siwaliks Hills (Nepal)

Abstract: [1] The large database of topographic form and uplift rates that exists for the Siwaliks Hills (central Nepal) makes possible a thorough analysis of the long-term erosion model. The study especially focuses on drainage areas larger than 5.10−3 km2, fixed by the database resolution, and smaller than 1 km2 above which a fluvial signature is recorded. This area range corresponds to colluvial valleys in which the dominant erosion process is likely debris flow. We evaluate a phenomenological model wherein erosion is considered to depend on drainage area and slope. We test this model by assuming that the uplift rate is in approximate equilibrium with erosion. The stream power law model, formulated by analogy to river incision and transport problems, is found to be consistent with data since an inverse power law relationship between slope and drainage area is systematically observed between 7.10−3 and ∼1 km2, with little variability on the exponent ∼−0.24. Thanks to the range of uplift rates, we obtain constraints on the slope dependency of erosion law, which appears linear and which predicts a significant erosion threshold. The linear dependence on slope in the debris-flow zone is consistent with findings by Kirby and Whipple [2001] in the fluvial downstream zone and with the linear relationship between local relief and uplift rate documented by Hurtrez et al. [1999]. The transition between this colluvial-channel regime and the fluvial regime appears quite sharp in contrast with recent studies, but the latter regime is not sufficiently documented to derive definite conclusions.

Stereological analysis of fractal fracture networks

Abstract: [1] We assess the stereological rules for fractal fracture networks, that is, networks whose fracture-to-fracture correlation is scale-dependent with a noninteger fractal dimension D. We first develop the general expression of the probability of intersection p(l, l′) between two populations of fractures of length l and l′. We then derive the stereological function that gives the fracture distribution seen in 2-D outcrops or 1-D scan lines for an original three-dimensional (3-D) distribution. The case of a fractal fracture network with a power law length distribution, whose exponent a is independent of D, is particularly developed, but the results can, however, be extended to any other length distributions. The analytical results were tested using a numerical model that generates 3-D discrete fractal fracture networks. The corresponding 1-D and 2-D length distributions are still described by a power law with exponents a1-D and a2-D that are related to the original 3-D exponent by a3-D = a1-D + 2 and a3-D = a2-D + 1, respectively, regardless of the fractal dimension. The density distributions of fractures in two or one dimensions remain fractal but with a dimension that depends on both the original 3-D distribution and the power law length exponent a. The fractal dimension of 2-D or 3-D fracture networks cannot be directly inferred from one-dimensional scan-line data sets unless a is known. We found a good adequacy between our predictions and measurements made on a few natural data sets. We propose also an original method for measuring the fractal dimension from the variations of the average number of fracture intersections per fracture.

Cross‐correlation between length and position in real fracture networks

Abstract: [1] By analyzing local geometrical properties of a dense multiscale fracture pattern, we characterized statistically the correlations between length and position of a fracture. Apart from some resolution effects, we show that the mean distance between a fracture center and its nearest neighbor is correlated to its length l such as d ∼ l0.3. Likewise, the average area around each fracture center within which no other fracture portion is lying has an ellipsoidal shape whose factor of anisotropy is correlated to l. The long axis, along fracture strike, is correlated to l such as d ∼ l0. 25–0.3. The short axis remains invariant, about equal to the equivalent distance in a random fractal. At small scale (i.e., less than 1 m which is bed thickness) the shield area is isotropic. In addition to refining of geometrical model of fracture networks, such observations place some constraints on the stress interactions that prevail during fracture growth.