Multiphysics hillslope processes triggering landslides
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- Borja, R.I., Liu, X. & White, J.A. Acta Geotech. (2012) 7: 261. doi:10.1007/s11440-012-0175-6
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In 1996, a portion of a highly instrumented experimental catchment in the Oregon coast range failed as a large debris flow from heavy rain. For the first time, we quantify the 3-D multiphysical aspects that triggered this event, including the coupled sediment deformation-fluid flow processes responsible for mobilizing the slope failure. Our analysis is based on a hydromechanical continuum model that accounts for the loss of sediment strength due to increased saturation as well as the frictional drag exerted by the moving fluid. Our studies highlight the dominant role that bedrock topography and rainfall history played in defining the failure mechanism, as indicated by the location of the scarp zone that was accurately predicted by our 3-D continuum model.
KeywordsHillslopesLandslidesMultiphysicsSlope stabilityUnsaturated soil
Rainfall-induced landslides and/or debris flows threaten lives and property worldwide. Like earthquakes, they occur with little or no warning, and even with a warning it often applies to very large areas. Examples of high-profile slope failures include the 0.22 m storm of January 4, 1982 that combined with approximately 0.6 m of pre-storm seasonal rainfall, triggering thousands of landslides in the central coast ranges of California. In the San Francisco Bay Area alone, this storm resulted in 24 fatalities and millions of dollars in property damage [9, 31]. In 1985, a 0.56 m rainfall within a 24-h period triggered debris flows in Mameyes, Puerto Rico, resulting in 129 deaths . In 1987, a 0.18 m rainfall in <5 h triggered numerous shallow landslides and debris flows in Rio Limón, Venezuela, resulting in 210 deaths . In 1999, heavy rainfall exceeding 0.9 m over a 3-day period, with daily values >the 1,000-year return period in Vargas, Venezuela , killed 10s of 1,000s due to numerous landslides and severe flooding . And in 2006, heavy rainfall triggered massive landslides in Guinsaugon, Philippines, burying an elementary school along with approximately 246 students and seven teachers .
Despite decades of extensive slope stability model development, the fundamental controls defining the triggering mechanisms of slope failure driven by rainfall are still not well quantified. It is generally known that increased saturation weakens a slope by reducing the capillary pressure holding the sediment particles together. It is also well-known that fluid flow enhances downhill slope movement by exerting frictional drag on the sediment. However, these are qualitative descriptions that do not help much in determining when a given slope will fail under what intensity of rainfall, and at what location will failure initiate if the slope indeed does fail. It is evident that the relevant processes are multiphysical in nature, involving both mechanical and hydrological processes. It is also evident that slope failure is influenced by the slope and bedrock topography, rainfall history, initial and boundary conditions, and the hydromechanical properties of the sediment. Assuming all of these parameters can be constrained, a question arises as to whether there exists a model or a simulation tool that is accurate enough to make scientific predictions of the timing and location of slope failure. Demonstrating the accuracy of a model requires that it be validated against full-scale slopes that are known to have failed from a given rainfall.
In this paper, we show that it is possible to accurately identify hotspots for slope failure initiation using hydromechanical continuum modeling with CB1 as a case study. The slope model satisfies the relevant conservation laws, including the balance of momentum and balance of mass, as well as the governing constitutive laws for sediment deformation and fluid flow. The parameters of the model have been constrained from measurements conducted at the CB1 site as well as from tests of soil samples conducted in the laboratory. New to this paper is a full 3-D treatment of the slope, allowing us to assess the accuracy and limitations of the simplified 2-D representation of the problem [6, 8]. Results of this study have significant implications for an accurate prediction of the location of shallow landslides triggered by rainfall. As an aside, we remark that shallow landslides typically occur when a high-permeability soil is supported underneath by a low-permeability material (such as a bedrock), which traps the groundwater in the overlying soil and causes it to fail. Rainfall-triggered shallow landslides are a frequent occurrence on many hillslopes in Washington and Oregon [3, 11, 15, 20, 24], making this study extremely useful for understanding hillslope processes in those and similar regions. We do, however, limit the scope of this paper to the triggering of the slope failure only. Simulations of the mobilization and eventual deposition of the failed sediment [21, 32] are not included in this work.
2 The CB1 experimental catchment
The CB1 experimental catchment, clear-cut in 1987, is located along Mettman Ridge approximately 15 km north of Coos Bay in the Oregon Coast Range [12, 13]. CB1 is a 51-m-long (860 m2) unchanneled valley with a north-facing aspect and an average slope of 43° (see Figure 1). Three sprinkling experiments were conducted at CB1: experiment #1 conducted in May 1990 at 1.5 mm/h for 6 days, experiment #2 conducted in May 1990 at 3.0 mm/h for 4 days, and experiment #3 conducted in May 1992 at 1.7 mm/h for 7 days. The instrumentation at CB1 characterized the spatial and temporal variability in near-surface hydrologic response for the three experiments and included an exhaustive grid of rain gauges, piezometers, tensiometers, TDR waveguide pairs (for estimating soil-water content), lysimeters, meteorological sensors (on a tower), atmometers, and weirs. Continuous measurements from rainfall, discharge, and total head (from selected piezometers) are available from 1990 through 1996. In November 1996 the CB1 slope failed as a large debris flow, leaving behind one of the most comprehensive hydrological response data sets in existence for a steep, deforested catchment that has experienced slope failure. Figure 1 shows the extent of the debris flow zone resulting from the 1996 event.
The sediment at CB1 is colluvium, a surficial sediment derived from weathered or fresh bedrock, and the soil has no input from eolian transport. The parent rock for the colluvium is an Eocene turbidite sandstone from the Tyee and Flournoy formations. The soils are well mixed, nonplastic (plasticity index of zero), gravelly sands. The geometry and thickness of the colluvium are well defined from soil borings, which were used to generate the slope shown in Fig. 1 (the variation of colluvium thickness is not shown in this figure). Saturated hydraulic conductivity was determined from slug tests, soil-water content, and porosity from TDR measurements, and hysteretic capillary pressure relationships were also established. Studies from the discharge chemistry data indicate that runoff generation occurs primarily from water stored in small, unconnected pores and fractures in the bedrock and saprolite connecting with larger macropores during storms. The tracer data (bromide and isotopically-tagged water) suggest that the two most important flow paths at CB1 are rapid saturated flow through the shallow, fractured bedrock and vertical percolation in the vadose zone [1, 2]. The soil in the catchment is so conductive (saturated hydraulic conductivity Ksat≈ 0.1 cm/s) that neither is Horton overland flow produced nor does the phreatic surface typically reach the slope face during rain storms . The tensiometer data indicate that the flux of water through the unsaturated zone provides a significant control on pore pressure development. Low confining stress triaxial shear tests demonstrate that the colluvium at CB1 is cohesionless (consisting of a sandy matrix); however, lateral root cohesion in clear-cut forests in the Oregon Coast Range is a source of apparent soil cohesion.
3 Mechanistic underpinnings
The colluvium at CB1 is a sandy matrix with a friction angle ranging from 35 to 44° [10, 25–28, 37, 38]. Lateral root cohesion in clear-cut forests in the Oregon Coast Range was estimated to be uniformly <10 kPa  and may have explained how such a steep slope at CB1 had been sustained by the sediment for such a long time. For purposes of analysis, baseline values of 40° for the friction angle, 4 kPa for cohesion, and 25° for dilatancy angle have been used in the simulations. Sensitivity studies to perturbations in these material parameters have been presented in Ref.  to better understand how the results would be influenced by their values. The saturated density of the soil is about 1,600 kg/cu m , and the bulk density at soil water contents of 20–30 % is around 1,200 kg/cu m .
4 Simulations and results
At the beginning of the simulation assuming an impermeable bedrock, which we denote as Case A, a uniform initial pressure of −1.5 kPa was prescribed in the soil representing an approximate initial saturation condition in the colluvium. This is a relatively low suction stress  reflecting the effects of on-and-off precipitation for several days prior to the peak rain. While this may be considered a gross simplification, previous studies [6, 8] suggest that the colluvium would have to be fully saturated for the slope to fail. To model the rainfall event, a time-dependent fluid flux q on the ground surface was applied continually until a seepage face condition was detected, at which point, the boundary condition was switched to a fixed pressure p = 0. In this sequence, a prescribed flux is a natural boundary condition, whereas a prescribed pressure is an essential boundary condition. Formation of a seepage face thus entails switching the boundary condition type on the slope face from natural to essential.
Quantifying the fluid input from the bedrock fractures in CB1 requires a deep understanding of the subsurface flow paths in this steep unchanneled catchment. As noted earlier, tracer studies  revealed two important flow paths through the catchment: vertical percolation in the vadose zone and rapid saturated flow in the colluvium. Flow paths meet in a small area of the colluvium near the upper weir B shown in Fig. 1. Tracer data also revealed that it is in the latter zone where predominantly fresh rain water from the colluvium mixes with high-velocity but long residence time water emerging from the bedrock. The dynamics of this zone dictate the resulting runoff chemistry in general, and the proportions of old and new water in runoff in particular .
It is not possible to distinguish between release of old stored water and flow of new water as sources of runoff during actual winter storms. Fortunately, the hydromechanical model used in this study does not distinguish between the two sources of runoff. In calculating slope deformations, what matters is the current fluid gradient resulting from the imposed fluid fluxes on the colluvium boundary, and not the material origin of the runoff. Thus, we simultaneously prescribed natural rainfall on the slope face and fluid input from the bedrock, the latter resembling a “reverse rain,” to assess the effect of bedrock fracture flows on slope deformation. For Case B, a reverse rain equal to 10 % of the slope rain was prescribed over the entire colluvium–bedrock interface, mimicking a bedrock of uniform fracture density. For Case C, a reverse rain having the same intensity as the slope rain but with a time lag of 10 min was prescribed over a 6-m area on the uphill side of the top weir, mimicking the results of the tracer studies. The intent of these additional simulations was not to capture the actual fluid input from the bedrock, which is unknown, but rather, to simply get a feel for how these additional boundary conditions would impact the mechanism of slope deformation.
5 Mesh sensitivity, rainfall history, and 3-D effects
In a recent article , the authors used a plane strain representation of the CB1 problem to infer the factor of safety for this slope from hydromechanical continuum modeling. The results of their studies highlighted the important role that the pore pressure played in triggering slope failure, as well as demonstrated a remarkable agreement between the continuum hydromechanical and limit equilibrium solutions in predicting the relevant failure mechanisms. Unfortunately, the following results also reveal the inherent deficiencies of a 2-D representation of what is truly a 3-D problem.
We consider a short-duration rainfall of 50 mm/h for 2.5 h applied on the slope face, beginning with the same initial pore pressure of −1.5 kPa in the colluvium and assuming the bedrock to be impermeable. Figure 8 shows the plastic strain contours on the colluvium–bedrock interface generated by this rainfall using the coarser and finer meshes shown in Fig. 2. We see that the finer mesh produced a slightly softer deformation response and resolved the details of deformation more accurately, which is to be expected. However, the coarser mesh captured the essential mechanism of deformation nearly as accurately. In particular, both meshes identified the same hotspots for deformation with the most intense plastic strain as being the zone located approximately 15 m below the actual scarp zone, suggesting a different dominant failure mechanism than the one predicted in the previous section with a different rainfall history. This suggests that rainfall history does have a significant impact on the resulting deformation and failure mechanisms for this slope.
In summary, the results of Fig. 8 suggest the following: (a) the coarser mesh is sufficient for identifying the primary pattern of deformation and mechanism of slope failure; (b) rainfall history has an important effect on the mechanism of deformation and slope failure; and (c) a 2-D representation may not be sufficient to fully characterize the pattern of deformation and failure on a slope that has strong 3-D features.
A 3-D hydromechanical model was developed to investigate a rainfall-induced slope failure at a highly instrumented experimental catchment near the Oregon Coast Range. The model accounts for the loss of sediment shear strength due to increased saturation and the coupled solid deformation-fluid flow processes expected in a slope subjected to intense rainfall infiltration. The model accurately predicted the mechanism of slope failure in the catchment, specifically, the location of the scarp zone, suggesting the potential of 3-D hydromechanical modeling for investigating more general hillslope scenarios. As for the specific catchment investigated in this paper, numerical simulations suggest that the slope failure was triggered by the local topography and rainfall history at the site, while fluid flow through the fractures of the bedrock did not appear to be dominant enough to alter the mechanism of slope failure. However, since failure is an instability problem that is sensitive to small variations of the load, fluid flow through the bedrock fractures could have enhanced the deformation as manifested by the enlarged zone of plastic strain.
The authors are grateful to Drs. Keith Loague and Brian Ebel for numerous discussions pertaining to the CB1 catchment, and to the three anonymous reviewers for their constructive reviews. This work was supported by the US National Science Foundation (NSF) under Contract Numbers CMMI-0824440 and CMMI-0936421 to Stanford University.