View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Infoscience - École polytechnique fédérale de Lausanne Computers and Geotechnics 49 (2013) 79–89 Contents lists available at SciVerse ScienceDirect Computers and Geotechnics journal homepage: www.elsevier.com/locate/compgeo Early warning thresholds for partially saturated slopes in volcanic ashes ⇑ John Eichenberger, Alessio Ferrari, Lyesse Laloui Ecole Polytechnique Fédérale de Lausanne (EPFL), School of Architecture, Civil and Environmental Engineering (ENAC), Laboratory for Soil Mechanics (LMS), EPFL-ENAC-LMS, Station 18, CH-1015 Lausanne, Switzerland article info abstract Article history: Rainfall-induced landslides in steep soil slopes of volcanic origin are a major threat to human lives and Received 20 March 2012 infrastructure. In the context of constructing early warning systems in regions where extensive data Received in revised form 15 October 2012 on landslide occurrences and associated rainfall are inexistent, physically-based tools offer the possibility Accepted 5 November 2012 to establish thresholds for measurable field quantities. In this paper, a combined finite element infinite slope model is presented to study the transient hydraulic response of volcanic ash slopes to a series of rainfall events and to estimate seasonal safety factors. Furthermore, analytical considerations of partially Keywords: saturated infinite slopes are made to define capillary stress thresholds for a landslide early warning Partially saturated soil system. Volcanic ash Slope stability Ó 2012 Elsevier Ltd. All rights reserved. Early warning threshold Rain infiltration Seepage analysis 1. Introduction vador claimed >500 casualties [5], and in 1998, thousands of land- slides were caused by Hurricane Mitch throughout all of Central Two rainfall-induced landslides in volcanic ashes, which oc- America with >9000 casualties [7]. In particular, due to the loose curred towards the end of the wet season of 2005, caused material structure from the depositional process, narrow grain-size distri- damage and production losses in a quarry situated along the hill- bution, degree of weathering and collapsibility, failed soil masses slopes of Irazu volcano in Costa Rica. As a consequence of these from volcanic deposits are often reported to turn into rapid flow landslide events, the quarry owner decided to install an early slides or debris flows with catastrophic consequences in the runout warning system to reduce the landslide risk for the future. Since zones [8]. At the origin, the involved materials are mostly in a state shallow rainfall-induced landslides are hydraulically-driven first- of partial saturation. time failures, it was decided to include as primary element contin- In this paper, analytical considerations with an infinite slope uous in situ pore water pressure, water content and rainfall mea- model are made to establish preliminary pore water pressure surements in the early warning system and to add alarm thresholds for partially saturated slopes of variable steepness in thresholds for those field variables. Due to the absence of informa- the first step. In the second step, a physically-based model that tion on past landslide events and associated rainfall patterns for consists of two semi-coupled parts is presented. The first part is the establishment of empirical thresholds, an alternative proce- a finite element soil column model for the transient analyses of dure is presented in this paper to establish thresholds in a preli- vertical rain infiltration in partially saturated volcanic ash. Based minary phase and to study the pore water pressure response and on laboratory results, an empirical relationship that links the vol- safety factors of volcanic ash slopes throughout a rainy season. canic ash coefficient of permeability to the degree of saturation Rainfall-induced landslides in steep soil slopes of volcanic ori- and void ratio is proposed. The latter is shown to have a significant gin are common around the world and have caused massive effect on the transient pore water pressure response to rain infil- destruction and the loss of lives (Italy [1,2]; Hong Kong [3]; Central tration. The second part is an infinite slope model for calculating America [4–6]). In particular, in Central America, the populated the safety factors in variably saturated soils. This part is coupled areas surrounded by steep volcano slopes are highly vulnerable to the first part of the model in the sense that the vertical profiles to rainfall- and earthquake-induced landslides that are triggered of the pore water pressure and degree of saturation resulting from in loose volcanic soils. In 2001, the Las Colinas landslide in El Sal- the transient finite element simulations are used as inputs for cal- culating the safety factor profiles at each time step. On one hand, the proposed model enables studying the hydraulic response of ⇑ Corresponding author. Tel.: +41 21 693 23 14; fax: +41 21 693 41 53. E-mail addresses: john.eichenberger@epfl.ch (J. Eichenberger), alessio.ferrar- volcanic ash slopes with different average bulk densities to a series i@epfl.ch (A. Ferrari), lyesse.laloui@epfl.ch (L. Laloui). of rainfall events. On the other hand, the transient slope safety 0266-352X/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compgeo.2012.11.002 80 J. Eichenberger et al. / Computers and Geotechnics 49 (2013) 79–89 factors for the range of considered slope angles provide a quantita- volcanic air-fall ash deposits or colluvia [22]. The volcanic ash tive appreciation of the effect of different rainfall patterns on slope deposits are fairly homogeneous with the presence of very few stability. blocks. Depending on the slope angle, the thickness of the ash cov- er varies between 5 m and 30 m [22]. For the transient calculation of rain infiltration and pore water pressure diffusion in the volcanic 2. Physically-based approach for the preliminary establishment ash deposits, a finite element soil column model is setup as shown of early warning thresholds in Fig. 1. The model is constructed using the finite element code LAGAMINE [23,24]. The model represents a homogeneous, isotro- Physically-based models for slope stability analyses at the pic soil column that is 6 m high, 1 m wide and composed of catchment scale often and primarily consist of a hydraulic model 10 Â 70 quadrilateral Q8P8 finite elements (8 nodes with quadratic for calculating the pore water pressure diffusion in an idealised shape functions for solid displacement and pore water pressure). slice of a slope as a function of stationary or transient rainfall input. Because the soil cover is shallow, a passive pore air pressure (pa) The hydraulic model is coupled to an infinite slope stability model that is equal to the atmospheric pressure (patm) is assumed. for the subsequent calculation of slope safety factors [9–13]. The mass conservation for the pore fluid is given by the follow- Although this type of model is constrained by its simplified ing equation: assumptions regarding the hydraulic and mechanical boundary and initial conditions, as well as a rigid body assumption for the @ðnSrqwÞ s þ r ðq nSrvwÞQ ¼ 0; ð1Þ mechanical description, it presents the following advantages. @t w where n (–) is the soil porosity, Sr (–) represents the degree of sat- 1. The model is a reasonable starting point for cases in which field 3 uration, qw (kg/m ) is the intrinsic water mass density, vw (m/s) measurements are not available or the data is of poor quality. represents the velocity of water and Qs (kg/m3 s) is the specific rate This is not the case for empirical methods that rely on extensive source/sink. Nodal displacements are impeded for a purely hydrau- landslide occurrence and associated rainfall data for establish- lic analysis. Here, nSrvw = qw is the mean velocity of water given by ing rainfall intensity-duration thresholds. Darcy’s law for variably saturated soils, 2. For cases in which planar slope failure surfaces are prevailing, int critical pore water pressure or soil water content levels can be cwK Á kr;w pw qw ¼ Á r þ z ; ð2Þ calculated at different soil depths and for variable slope angles lw cw and soil strength properties. This is of particular interest for the where Kint (m2) is the intrinsic permeability of the medium, k (–) preliminary establishment of pore water pressure thresholds r,w is the water relative permeability, l (kg/ms) is the fluid dynamic for single slope scale landslide early warning systems for which w viscosity and c (N/m3) is the unit weight of water. The governing field measurements are not available. w Eq. (1) is closed by introducing the equation of state for pore water 3. Thresholds that are established with physically-based models and a constitutive law that relates the degree of saturation (S )to are more objective than those established by means of empiri- r the matric suction (s = p À p ). Details regarding the water reten- cal methods. Such thresholds result from general equilibrium atm w tion curve and water relative permeability function are given in the considerations, while empirical methods rely mostly on a sub- next section. The equation of state for pore water is written as jective definition of thresholds, separating rainfall events that lead to landslides from those that do not. @q q @p w ¼ w w ; ð3Þ 4. For cases in which the hydraulic model accurately reproduces @t vw @t the governing time-dependent subsurface flow processes and where 1/v (PaÀ1) is the compressibility of water. Eq. (1) can now planar slope failure surfaces are prevailing, critical rainfall w be rewritten in a pressure form as thresholds and actual slope safety factors can systematically be established as a function of local rainfall history and for var- iable slope angles and soil strength properties. 5. In conjunction with a grid-based Geographic Information Sys- tem (GIS), a relative susceptibility index can be calculated for q [mm/h] each cell unit and assembled in a relative landslide susceptibil- s [kPa] 20 0 ity map [6,8,14–16].