Slider-Block Friction Model for Landslides: Application to Vaiont and La Clapiere Landslides

Accelerating displacements preceding some catastrophic landslides have been found empirically to follow a time-to-failure power law, corresponding to a finite-time singularity of the velocity $v \sim 1/(t_c-t)$ [{\it Voight}, 1988]. Here, we provide a physical basis for this phenomenological law based on a slider-block model using a state and velocity dependent friction law established in the laboratory and used to model earthquake friction. This physical model accounts for and generalizes Voight's observation: depending on the ratio $B/A$ of two parameters of the rate and state friction law and on the initial frictional state of the sliding surfaces characterized by a reduced parameter $x_i$, four possible regimes are found. Two regimes can account for an acceleration of the displacement. We use the slider-block friction model to analyze quantitatively the displacement and velocity data preceding two landslides, Vaiont and La Clapi\`ere. The Vaiont landslide was the catastrophic culmination of an accelerated slope velocity. La Clapi\`ere landslide was characterized by a peak of slope acceleration that followed decades of ongoing accelerating displacements, succeeded by a restabilizing phase. Our inversion of the slider-block model on these data sets shows good fits and suggest to classify the Vaiont (respectively La Clapi\`ere) landslide as belonging to the velocity weakening unstable (respectively strengthening stable) sliding regime.Comment: shortened by focusing of the frictional model, Latex document with AGU style file of 14 pages + 11 figures (1 jpeg photo of figure 6 given separately) + 1 tabl

Gravity-driven instabilities: interplay between state-and-velocity dependent frictional sliding and stress corrosion damage cracking

We model the progressive maturation of a heterogeneous mass towards a gravity-driven instability, characterized by the competition between frictional sliding and tension cracking, using array of slider blocks on an inclined basal surface, which interact via elastic-brittle springs. A realistic state- and rate-dependent friction law describes the block-surface interaction. The inner material damage occurs via stress corrosion. Three regimes, controlling the mass instability and its precursory behavior, are classified as a function of the ratio $T_c/T_f$ of two characteristic time scales associated with internal damage/creep and with frictional sliding. For $T_c/T_f \gg 1$, the whole mass undergoes a series of internal stick and slip events, associated with an initial slow average downward motion of the whole mass, and progressively accelerates until a global coherent runaway is observed. For $T_c/T_f \ll 1$, creep/damage occurs sufficiently fast compared with nucleation of sliding, causing bonds to break, and the bottom part of the mass undergoes a fragmentation process with the creation of a heterogeneous population of sliding blocks. For the intermediate regime $T_c/T_f \sim 1$, a macroscopic crack nucleates and propagates along the location of the largest curvature associated with the change of slope from the stable frictional state in the upper part to the unstable frictional sliding state in the lower part. The other important parameter is the Young modulus $Y$ which controls the correlation length of displacements in the system.Comment: 40 pages, 13 figure

A mechanistic ecohydrological model to investigate complex interactions in cold and warm water‐controlled environments: 1. Theoretical framework and plot‐scale analysis

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95321/1/jame60.pd

Two-phase flow infiltration equations accounting for air entrapment effects

Water infiltration into the unsaturated zone is potentially affected by air compression ahead of the wetting front. Analytical infiltration equations accounting for air compression, air counterflow, and flow hysteresis in a porous medium were derived on the basis of the Green and Ampt [1911] assumptions. Air compression ahead of the wetting front was predicted using the perfect gas law. The capillary pressure at the wetting front was found to vary between the dynamic water-bubbling value and the dynamic air-bubbling value of the material. These equations, accounting also for the effects of macropores near the soil surface, turned out to be simpler than the traditional Kostiakov [1932] and the Philip [1957a, b, c, d] equations. The equation parameters are physically meaningful and can be readily obtained from field measurements of the natural saturated hydraulic conductivity and soil water retention or pressure infiltrometer data. Experimental testing showed that the equations are reasonably accurate

Comparison of three hydraulic property measurement methods

Hydraulic functions of soils may differ depending on the different measuring methods used. The performance of three different methods for measuring soil-hydraulic properties of a heterogeneous field were evaluated. The experiments were conducted using three different sizes of undisturbed soil cores collected systematically along a 31 m long transect of a well drained sandy loam soil having three soil horizons (Ap, 0-0.25 m; C1, 0.25-0.55 m; C2, 0.55-1.00 m). The laboratory studies involved: (1) detailed unsteady drainage-flux experiments performed on fifteen columns of 1 m length and 0.3 m diameter; (2) combined crust test and hot air methods applied to thirty columns of 0.2 m length and 0.2 m diameter and to a subset of sixty cylinders of 0.1 m length and 0.045 m diameter, respectively, taken from the Ap horizon; and (3) desorption experiments carried out on a total of one hundred eighty cores of 0.051 m length and 0.05 m diameter collected evenly from the three horizons, Mean soil hydraulic properties were inferred from experimental data characterizing either selected depths or the soil profile as a whole. The results revealed considerable differences among estimated mean soil properties as obtained with different measuring techniques. Although the application of scaling theory substantially reduced variation in the measured pressure heads (h) and conductivities (K), the results revealed that scaling parameters determined from soil pressure head were not identical to scaling factors determined from hydraulic conductivity. The results also show that K scaling factors in general were much more variable than h scaling factors, and that the observed variability in scaling factors also depend upon the measurement technique used. (C) 1997 Elsevier Science B.V

Modeling of Two Different Water Uptake Approaches for Mono- and Mixed-Species Forest Stands

To assess how the effects of drought could be better captured in process-based models, this study simulated and contrasted two water uptake approaches in Scots pine and Scots pine-Sessile oak stands. The first approach consisted of an empirical function for root water uptake (WU1). The second approach was based on differences of soil water potential along a soil-plant-atmosphere continuum (WU2) with total root resistance varying at low, medium and high total root resistance levels. Three data sets on different time scales relevant for tree growth were used for model evaluation: Two short-term datasets on daily transpiration and soil water content as well as a long-term dataset on annual tree ring increments. Except WU2 with high total root resistance, all transpiration outputs exceeded observed values. The strongest correlation between simulated and observed annual tree ring width occurred with WU2 and high total root resistance. The findings highlighted the importance of severe drought as a main reason for small diameter increment. However, if all three data sets were taken into account, no approach was superior to the other. We conclude that accurate projections of future forest productivity depend largely on the realistic representation of root water uptake in forest model simulations