Landslide triggering by rain infiltration

<jats:p>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 <jats:italic>A</jats:italic>/<jats:italic>D</jats:italic><jats:sub>0</jats:sub>, where <jats:italic>D</jats:italic><jats:sub>0</jats:sub> is the maximum hydraulic diffusivity of the soil and <jats:italic>A</jats:italic> is the catchment area that potentially affects groundwater pressures at a prospective landslide slip surface location with areal coordinates <jats:italic>x</jats:italic>, <jats:italic>y</jats:italic> and depth <jats:italic>H</jats:italic>. Times greater than <jats:italic>A</jats:italic>/<jats:italic>D</jats:italic><jats:sub>0</jats:sub> are necessary for establishment of steady background water pressures that develop at (<jats:italic>x</jats:italic>, <jats:italic>y</jats:italic>, <jats:italic>H</jats:italic>) 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 (<jats:italic>x</jats:italic>, <jats:italic>y</jats:italic>, <jats:italic>H</jats:italic>), but they do not trigger slope failure. Failure results from rainfall over a typically shorter timescale <jats:italic>H</jats:italic><jats:sup>2</jats:sup>/<jats:italic>D</jats:italic><jats:sub>0</jats:sub> 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 <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/wrcr8630-math-0001.gif" xlink:title="urn:x-wiley:00431397:media:wrcr8630:wrcr8630-math-0001" />, where <jats:italic>g</jats:italic> 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, <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/wrcr8630-math-0002.gif" xlink:title="urn:x-wiley:00431397:media:wrcr8630:wrcr8630-math-0002" />, which depends only on normalized time, <jats:italic>t</jats:italic>*. Use of <jats:italic>R</jats:italic>(<jats:italic>t</jats:italic>*) 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.</jats:p>