A preliminary finite-element analysis of a shallow landslide in the Alki area of Seattle, Washington.

By S. Debray and W.Z. Savage Open-File Report 01-0357 2001

This report is preliminary and has not been reviewed for conformity with U.S.Geological
Survey editorial standards nor with the North American Stratigraphic Code.Any use of
trade names in this publication is for descriptive purposes only and does not imply
endorsement by the U.S.Government.

U.S.Department of the Interior
U.S.Geological Survey

Introduction

The Seattle area has a long history of landslide problems (Tubbs, 1974, Thorsen, 1989, Galster and Laprade, 1991, Baum, and others, 1998). Shallow landslides often initiate in colluvium derived from glacial deposits, are frequently triggered by winter rain storms (Tubbs, 1974), and may mobilize into debris flows that can cause considerable damage (Baum and others, 1998).

In this report we present a preliminary finite-element based stability analyses of a shallow landslide that occurred during the period from December 1996 to early January 1997 near Alki Beach and Duwamish Head at the north end of West Seattle (Figure 1). During this period a series of snowstorms, freezing rain and warm rain produced many debris flows and landslides in the Seattle area (Baum and others, 1998). The shallow landslide that we are analyzing was 18 m high and 75 m long. It mobilized into a debris flow that traveled down a 35-meter-high embankment below the slide damaging the bottom floors of two apartment buildings at the foot of the embankment (Figure 2). In what follows, we briefly outline the geology and hydrology of the Alki landslide site, give a short description of the computational algorithms used in the finite element program, and present the results of the finite element model of the landslide.

Figure 1. Alki landslide location.

Figure 2. View of the Alki landslide area. Photograph taken August 2001 by S. Debray.

Geology and hydrology of the Alki landslide site

Galster and Laprade (1991) identify the following sequence of glacially derived surficial geologic formations in the Seattle area. They are, from top to bottom, Recessional Outwash, Vashon Till, Advance Outwash, Lawton Clay, and the Pre-Vashon. Deposits in this sequence are often overconsolidated, have a wide range of hydraulic conductivities, are laterally heterogeneous, and form steep, landslide-prone, coastal bluffs.

According to Waldron and others (1962) only the Esperance Sand and the Lawton Clay are present at the Alki landslide site. However, Shannon and Wilson (2000) identify, from borehole logging, dense Pre-Vashon sands, silts, and clays below the Lawton Clay at the Alki site. The Esperance Sand is a unit in the Advance Outwash that has been overridden by glacial ice. Generally these outwash deposits are dense, brown and gray, and permeable with fine to coarse sand and silt. Lawton Clay is a glaciolacustrine deposit that consists of very stiff to hard and relatively impermeable clays and silts. Where pervious sand overlies the clay, this clay acts as an aquiclude and ground water is perched in the sand. The Pre-Vashon sediments are interglacial fluvial and lake deposits.

The Alki landslide occurs in an 8- to12-m thick layer of colluvium, a very loose to medium density soil that commonly covers upper, flatter slopes at the Alki site (Shannon and Wilson, 2000). Here the colluvium overlies Lawton clay and is laterally continous with the Esperance Sand. Its looseness results in a higher permeability than that of the underlying Lawton Clay, so that ground water is perched at the contact or in the lower part of the colluvial mantle (Shannon and Wilson, 2000).

Resistant and relatively impervious Vashon Till commonly caps Seattle-area hilltops (Tubbs, 1974, Galster and Laprade, 1991). This layer impedes water infiltration. However, at the Alki slide, till coverage is absent and, thus, surface water can percolate into the underlying Esperance Sand continuing downward until it reaches the relatively impervious Lawton Clay. Groundwater then moves laterally in the Esperance Sand reaching the colluvium and emerging as springs on the hillside. If the rate of infiltration exceeds the capacity of the hydraulic gradient to transmit groundwater to hillside seeps, pore pressures rise and slope failure ensues.

Geotechnical properties of Alki slide materials

A detailed geotechnical investigation of the Alki glacial deposits is beyond the scope of this work. Therefore Alki-site property values are taken from a previously published summary (Savage and others, 2000b) and from data reported by Shannon and Wilson (2000). Peak cohesion (C_p) for the Alki colluvium is taken by Shannon and Wilson (2000) to be zero. We estimate it to be to be 5 KPa (see below). The peak friction angle (Ф_p) for colluvium is 23^o (Shannon and Wilson, 2000). Strength values for the Lawton Clay were those used by Savage and others (2000a) in a finite-element limiting-equilibrium analysis of stability of the Woodway landslide. The estimated geotechnical properties for the units at the Alki site that are used in the finite-element modeling are given in Table 1.

Table 1. Estimated material properties used in finite-element modeling of the Alki landslide. In this table, dry and wet unit weights are denoted by _{dry ,} and _wet, σ is Poisson’s ratio, E is Young’s Modulus, C_p is peak cohesion, and Ф_p is the peak angle of internal friction.

Finite-element modeling of the Alki landslide

Stability of the Alki Landslide is modeled by using Version 7 of the PLAXIS^© finite-element program. This program, designed for geotechnical analysis, features automatic mesh generation, pore pressure generation, a non-linear elastic-plastic Mohr-Coulomb iterative-solution algorithm, and a phi-c-reduction procedure for calculation of safety factors.

The factor of safety, FS, in PLAXIS^© is defined by,

.[D]

Where σ_n΄ is effective normal stress acting on a plane, C and Ф are the input cohesion and angle of internal friction, and C_R and Ф_R are a reduced cohesion and reduced angle of internal friction calculated in the program as products of the input values and a multiplier. The parameters C_R and Ф_R are then iteratively changed until they are just large enough to maintain equilibrium and then used in the above equation to give the factor of safety on an element-by-element basis. When the factor of safety approaches 1, failure is imminent in critically stressed elements. The factor of safety for a slope is the mean of the factors of safety for all elements approaching failure in the finite-element model. The safety factor procedure in PLAXIS^© gives results similar to conventional slip-circle analyses (Savage and others, 2000a) where the safety factor is the ratio of the true strength to the minimum strength required for equilibrium of a postulated slip surface. The geometry of the site as used in the calculation is shown in Figure 3.

[D]

Figure 3. Model of the geometry and geologic layers of the Alki site. Double crosses indicate the model boundaries. Scale 1:3000.

Since the Alki landslide failed after heavy precipitation in the area it is assumed that rising groundwater levels were responsible for slide initiation. To simulate the effect of rising groundwater on the initiation of the Alki landslide a perched water table near the top of the relatively impervious Lawton Clay is raised in the finite-element model from 0-4 meters head to give a factor of safety of 1.07; a value close to the failure value of 1.

[D]

Figure 4. Finite-element mesh used to model the Alki landslide. Scale 1:3000.

            Precise values for the cohesion of the colluvium are not available. Sensitivity results for a range of cohesion between 5KPa and 17 KPa for a perched water table of 4.0 m yields a best model fit for a cohesion of 15.1 KPa (the factor of safety for this value is 1.07).

Table 2. Sensitivity of the factor of safety to cohesion (C) over the range 5-17 KPa.

Predicted displacement magnitudes, [u_x²  + u_y²]^1/2, (u_x and u_y are, respectively, horizontal and vertical displacements) when FS = 1.07 are shown in Figure 5. Displacements in this case are calculated using the elastic-Coulomb plastic algorithm in PLAXIS^©.

[D]

Figure 5. Predicted displacement magnitudes in millimeters. Only the area of interest outlined in Figure 4 is shown. Displacements elsewhere are negligible.

Figures 6a and 6b. Deformation of the mesh is shown in Figure 6a and displacement concentrations in regions at incipient failure are shown in Figure 6b.

Figures 6a and 6b show deformation of the mesh and concentration of displacements calculated by the PLAXIS© phi-c reduction procedure when FS = 1.07. No magnitudes are given for the displacements in Figures 6a and 6b as the phi-c reduction procedure in PLAXIS© generates additional, large, non-physical displacements. However, the shape of the deformed mesh and the pattern of the displacements give an indication of the shape of the failure surface. The predicted failure-surface shape is in reasonable agreement with that produced during the winter of 1996-1997 (Shannon and Wilson, Inc., 2000).

Concluding discussion

The finite element modeling results give a general idea of the mechanism of landsliding at the Alki site in response to a rising perched groundwater table. The position and shape of the failure surface are simple; failure occurred on a surface at the contact between the colluvium and the clay and sand layers triggering a general movement of the colluvium which then mobilized into destructive debris flows.

In conclusion, we suggest that the slide occurred because of high pore pressures in the colluvium resulting from the juxtaposition of the weak colluvium on the transition zone between impervious Lawton clay and overlying Esperance Sand. Finally, although averaged and estimated geotechnical properties gave reasonable results for the Alki slide, a more complete sensitivity analysis for evaluating the effect of geotechnical property variation should be performed.

References

Baum, R.L., Chleborad, A.F., and Schuster, R.L., 1998, Landslides triggered by the winter 1996-97 storms in the Puget Lowland, Washington: USGS Open-File Report 98-239, 16 p.

Galster, R.W., and Laprade,W.T., 1991, Geology of Seattle, Washington, United States of America: Bull. of the Association of Engineering Geologists, v. 28, no. 3, p. 235-302.

Savage, W.Z., Baum, R.L.,Morrissey, M.M., and Arndt B.P., 2000a, Finite element analysis of the Woodway Landslide: Washington, U.S. Geological Survey Bulletin 2180. 9p.

Savage, W.Z., Morrissey, M.M., and Baum, R.L., 2000b, Geotechnical properties for landslide-prone Seattle-area glacial deposits: USGS Open-File Report 00-228, 5 p.

Shannon & Wilson, Inc., 2000, Geotechnical Report, Alki Avenue/Duwamish Head, stabilization project, Seattle, Washington, February 2000, 9 p.

Thorsen, G.W., 1989, Landslide provinces in Washington: in Richard W. Galster, ed., Engineering Geology in Washington: Washington Division of Geology and Earth Resources Bulletin 78, v. I, p. 71-89.

Tubbs, D.W., 1974, Landslides in Seattle: Washington Division of Mines and Geology Information Circular 52, 15 p., scale 1:31680.

Waldron, H.W., Liesch, B.A., Mullineaux, D.R., and Crandell, D.R., 1962, Preliminary geologic map of Seattle and vicinity, Washington: U.S. Geologic Survey Miscellaneous Geologic Investigations Map I-354, scale 1:31680.

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