The soil moisture characteristic may be modeled as a power curve combined with a short parabolic section near saturation to represent gradual air entry. This two-part function—together with a power function relating soil moisture and hydraulic conductivity—is used to derive a formula for the wetting front suction required by the Green-Ampt equation. Representative parameters for the moisture characteristic, the wetting front suction, and the sorptivity, a parameter in the infiltration equation derived by Philip (1957), are computed by using the desorption data of Holtan et al. (1968). Average values of the parameters, and associated standard deviations, are calculated for 11 soil textural classes. The results of this study indicate that the exponent of the moisture characteristic power curve can be predicted reasonably well from soil texture and that gradual air entry may have a considerable effect on a soil's wetting front suction.

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Empirical equations for some soil hydraulic properties

Landsliding in response to rainfall involves physical processes that operate on disparate timescales. Relationships between these timescales guide development of a mathematical model that uses reduced forms of Richards equation to evaluate effects of rainfall infiltration on landslide occurrence, timing, depth, and acceleration in diverse situations. The longest pertinent timescale is A/D0, where D0 is the maximum hydraulic diffusivity of the soil and A is the catchment area that potentially affects groundwater pressures at a prospective landslide slip surface location with areal coordinates x, y and depth H. Times greater than A/D0 are necessary for establishment of steady background water pressures that develop at (x, y, H) in response to rainfall averaged over periods that commonly range from days to many decades. These steady groundwater pressures influence the propensity for landsliding at (x, y, H), but they do not trigger slope failure. Failure results from rainfall over a typically shorter timescale H2/D0 associated with transient pore pressure transmission during and following storms. Commonly, this timescale ranges from minutes to months. The shortest timescale affecting landslide responses to rainfall is H/g, where g is the magnitude of gravitational acceleration. Postfailure landslide motion occurs on this timescale, which indicates that the thinnest landslides accelerate most quickly if all other factors are constant. Effects of hydrologic processes on landslide processes across these diverse timescales are encapsulated by a response function, R(t*) = t*/π exp (−1/t*) − erfc (1/t*), which depends only on normalized time, t*. Use of R(t*) in conjunction with topographic data, rainfall intensity and duration information, an infinite-slope failure criterion, and Newton's second law predicts the timing, depth, and acceleration of rainfall-triggered landslides. Data from contrasting landslides that exhibit rapid, shallow motion and slow, deep-seated motion corroborate these predictions.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2000WR900090

Landslide triggering by rain infiltration

A framework is provided for scaling and scale issues in hydrology. The first section gives some basic definitions. This is important as researchers do not seem to have agreed on the meaning of concepts such as scale or upscaling. ‘Process scale’, ‘observation scale’ and ‘modelling (working) scale’ require different definitions. The second section discusses heterogeneity and variability in catchments and touches on the implications of randomness and organization for scaling. The third section addresses the linkages across scales from a modelling point of view. It is argued that upscaling typically consists of two steps: distributing and aggregating. Conversely, downscaling involves disaggregation and singling out. Different approaches are discussed for linking state variables, parameters, inputs and conceptualizations across scales. This section also deals with distributed parameter models, which are one way of linking conceptualizations across scales. The fourth section addresses the linkages across scales from a more holistic perspective dealing with dimensional analysis and similarity concepts. The main difference to the modelling point of view is that dimensional analysis and similarity concepts deal with complex processes in a much simpler fashion. Examples of dimensional analysis, similarity analysis and functional normalization in catchment hydrology are given. This section also briefly discusses fractals, which are a popular tool for quantifying variability across scales. The fifth section focuses on one particular aspect of this holistic view, discussing stream network analysis. The paper concludes with identifying key issues and gives some directions for future research.

/pdf/scale-issues-in-hydrological-modelling-a-review-1x61lpwqjr.pdf

Scale issues in hydrological modelling: A review

Theory of Infiltration

We review rainfall thresholds for the initiation of landslides world wide and propose new empirical rainfall thresholds for the Central European Adriatic Danubian South-Eastern Space (CADSES) area, located in central and southern Europe. One-hundred-twenty-four empirical thresholds linking measurements of the event and the antecedent rainfall conditions to the occurrence of landslides are considered. We then describe a database of 853 rainfall events that resulted or did not result in landslides in the CADSES area. Rainfall and landslide information in the database was obtained from the literature; climate information was obtained from the global climate dataset compiled by the Climate Research Unit of the East Anglia University. We plot the intensity-duration values in logarithmic coordinates, and we establish that with increased rainfall duration the minimum intensity likely to trigger slope failures decreases linearly, in the range of durations from 20 minutes to ∼12 days. Based on this observation, we determine minimum intensity-duration (ID) and normalized-ID thresholds for the initiation of landslides in the CADSES area. Normalization is performed using two climatic indexes, the mean annual precipitation (MAP) and the rainy-day-normal (RDN). Threshold curves are inferred from the available data using a Bayesian statistical technique. Analysing the obtained thresholds we establish that lower average rainfall intensity is required to initiate landslides in an area with a mountain climate, than in an area characterized by a Mediterranean climate. We further suggest that for rainfall periods exceeding ∼12 days landslides are triggered by factors not considered by the ID model. The obtained thresholds can be used in operation landslide warning systems, where more accurate local or regional thresholds are not available.

Rainfall thresholds for the initiation of landslides in central and southern Europe

§ 34. 1. The permeability and capillarity constants of soil have been defined.2. The movements of air and water through three types of soil have been measured and shewn to conform to equations connecting the rate of motion with the above constants.3. It is suggested that the measurement of S, Pα, Pω and K is of more importance than, and should replace, the determination of the sizes of the soil particles as in the usual “mechanical analysis” of soils.In conclusion, we have to acknowledge our indebtedness to Professors T. R. Lyle and R. J. A. Barnard for valuable advice and suggestions and to the Victorian Government for financial assistance towards the expenses of this research.

Studies on Soil Phyics.

The usefulness of soil analyses depends largely on the ease with which they may be compared with one another and, to this end, more or less successful attempts have been made to replace the ordinary columns of figures by a suitable graph, so that “he who runs may read.”

W. Heber Green

Papers

Studies on Soil Phyics.

The Representation of Soil Analyses by the Device of Double Plotting