Approach to Developing Design Guidelines for Horizontal Drain Placement to Improve Slope Stability

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1 Approach to Developing Design Guidelines for Horizontal Drain Placement to Improve Slope Stability Rosemary W.H. Carroll 1, Greg Pohll 1, Donald M. Reeves 1 and Tom Badger 2 1 Desert Research Institute, Nevada System of Higher Education,Rosemary.Carroll@dri.edu, Greg.Pohll@dri.edu, Matt.Reeves@dri.edu, Reno, NV USA 2 Washington State Department of Transportation, BadgerT@wsdot.wa.gov ABSTRACT The presence of groundwater is one of the most critical factors contributing to the instability of hillslopes. A common solution to stabilize hillslopes is the installation of horizontal drains to lower the water table surface within the potentially unstable mass. Drainage effectively reduces pore pressure, resulting in increased shear strength within the failure zone, and thereby improving the resistance to slope instability. Due to the complex geometry of slopes, heterogeneity and anisotropic nature of hydraulic conductivity, and the transient nature of groundwater, the designing of such drains can be a difficult task. Design practice of horizontal drains for slope stabilization has mostly relied on empiricism and judgment, resulting in varied success. Evaluation of two separate sites in Washington (US 101 MP69.8 and US 101 MP 321) will illustrate how to characterize the hydrogeology, approximate recharge, parameterize MODFLOW to estimate water levels under pre-drained and drained conditions, and provide a clear methodology for drainage design to meet design storm criteria. INTRODUCTION There have only been limited studies which have described and quantified the many parameters controlling horizontal drainage design and/or evaluated the feasibility of using a system of horizontal drains to lower groundwater levels in hillsides (e.g. Lau and Kenney, 1984; Pathmanathan, 2009). Existing drainage design guidelines exist primarily in the agricultural literature with the US Department of Interior (1978) consolidating early research for irrigated lands. In general, work falls into two distinct categories: steady-state, and transient-based methods. Since slope stability problems are likely to occur under intense and/or prolonged precipitation events over relatively short periods, the steady-state design equations are not appropriate for drainage design if slope stability is the primary objective. Transient design equations rely on analytic solutions to the groundwater flow equation and require a number of simplifying assumptions such as parallel and regular spacing of subsurface drains, and homogeneous hydraulic conductivity (e.g. Schmid and Luthin 1964; Wooding and Chapman, 1966; Fipps and Skaggs 1989). Although these conditions may not be met in real field situations, the analytic design equations may prove useful for preliminary design by providing first-cut approximations. In many situations the complexity of the field site requires the use of a numerical model to develop accurate estimates of water table position under drainage conditions. Highly heterogeneous hydraulic conductivity fields and/or complex drainage geometries are examples of conditions that require a more a more robust modeling approach compared to analytic equations. Cai et al. (1998) simulated the effect of horizontal drains on water table position using a three-dimensional finite element model. They extended the modeling effort by integrating a three-dimensional elasto-plastic shear strength finite element model to calculate a global safety factor. The models were used to investigate the influence of drain spacing, orientation, and length, rainfall intensity, and hydraulic conductivity on the increase in the safety factor. Likewise, Rahardjo et al. (2003) performed a rigorous measurement campaign combined with numerical modeling to determine the effectiveness of horizontal drains for slope stability. One of the key findings is that shallow drains are ineffective in improving the stability of a slope and drains are most effective when placed at the lowest elevation possible. The basic tenet is to lower the main water table, with less emphasis placed on direct capture of infiltration. If installed a significant distance into the hillslope at the lowest possible elevation, drains will effectively capture the majority of groundwater and have the largest effect on lowering the water table. These results are also consistent with the research findings of Lau and Kenney (1984), and Martin et al. (1994). Parametric studies have also shown that drains located in the

2 upper region of a slope are of no real significance if additional deeper drains are in the lower part of a slope. The water table will eventually be reduced to the lowest drain level and any drains above the bottom drain will no longer be effective. The only exception to this rule might be for site conditions that have the ability to setup significant perched water table conditions. If a low permeability layer exists at depth, precipitation events may induce a perched water table, which may cause the slope to fail. The findings of Rahardjo, et al. (2003) are important when considering which type of model is best for drainage design. If water table position is the most important aspect of slope stability and the physical processes and matric pressures within the vadose become less significant, then one can rely on saturated models, such as MODFLOW (Harbaugh, et al., 2000) for use in drainage design. This significantly reduces the complexity of the analysis and may allow for the use of analytic solutions for many field conditions. One still has to determine the net infiltration that contributes to groundwater recharge following a precipitation event, but this analysis can most likely be de-coupled from the groundwater analysis. SITE DESCTIPTION Two landslides along highway US 101 in Western Washington were selected (MP69.8 and US 101 MP 321) to illustrate how to characterize hydrogeology, approximate recharge, parameterize MODFLOW and estimate water levels under pre-drained and drained conditions. Site MP69.8 was chosen to reflect a relatively simple system containing mostly clayey residual soils and disturbed claystone of the Lincoln Creek Formation, while site MP321 reflects a more complex three-layered system of glacial outwash and tills. In both cases, higher than average winter rains caused large slope movements and drains were installed to lower water levels and improve slope stability. MODELING APPROACH The choice of MODFLOW is based on its availability and modular structure incorporating several packages believed important to characterizing water table elevations in slopes susceptible to failure. Important packages include those defining Physical & Hydrogeological Characterization of Site MODFLOW Development & Calibration Pre-Drain/Drain general head boundaries, specified heads, drains, recharge and the GMG solver. The approach to developing drain placement design guidelines is iterative (Fig. 1) and includes a comparison to analytic/graphical methods. Analytic/Graphic al Methods Compare Approaches Establish Guidelines Design Storm Generation (recharge) MODFLOW Yes Compute Factor of Safety F s > 1 New Drain Configuration Figure 1. Iterative approach to designing guidelines for horizontal drain placement No Basic Model Structure MODFLOW development and calibration strategies are similar between sites, with basic approach displayed in Fig. 2. Current model status and challenges include: Development of a one-layer steady state model for MP69.8 in which average water levels prior to any drain installment were calibrated by adjusting hydraulic conductivity in the landslide mass and general head boundary (GHB) conductance. Average recharge estimated at approximately 25% annual precipitation (or ft/day = 15.6 inch/year). Root mean squared error

3 (rmse) of the calibrated water levels is equal to 0.96 ft, or 1%. Transient models for MP69.8 were developed for the following scenarios: pre-drain winter water levels (calibrated to H1A-05 December 2005). rmse = 1.2 ft (1% error); pre-drain summer water levels (calibrated to H1A-05 6/8/2005 to 9/29/2005). rmse = (3% error). A single calibration of both winter and summer events is proving difficult. Work is ongoing to develop a solution. A steady state model for MP321 was developed using three layers to reflect site geology. Zonation and pilot point approaches to hydraulic conductivity fields were tested. Later, the three-layer model was converted into a one layer model to improve model stability given numeric instability occurs in steep, thin, perched systems. rmse = 6.3 (4.9% error). A transient model of MP321 was developed in three layers, then one layer, spanning 5/6/2009 to 5/10/2010 with drains modeled. Observed data matched includes H-3A-95 and H-1A-95. rmse = 3.9 ft. general head (a) nrow = 195 ncol = 125 cell dimension = 5 ft by 5 ft drain configuration specified head (Hood Canal) H-1A-95 water table land surface (b) no flow basalt H-1A-95 Water Level (ft) (c) Observed Predicted with MODFLOW days in simulation Figure 2: MODFLOW approach to MP321. (a) Areal view showing land surface contours at 20 ft, boundary conditions and drain configuration. (b) Cross section of water table surface in relation to land surface. (c) Observed and predicted water levels at site H-1A-95.

4 Recharge and Design Storms Recharge is found to be the single most sensitive parameter in early numeric model development. Recharge is estimated using the SCS curve number (CN) approach (SCS, 1972) based on its simplicity, acceptance, and extensive use in a variety of hydrologic, erosion and water quality models (e.g. CREANS, EPIC, SWRRB, AGNPS). The primary assumption in this approach is that after initial infiltration the amount of runoff will depend on land surface cover, land use, soil type and antecedent moisture conditions. The SCS approach assumes that the ratio of actual to maximum potential infiltration is equal to the ratio of actual to maximum potential for runoff. The resulting equation is, Fa S e =. (1) P P I a where I a is the initial abstraction (infiltration) that occurs at the beginning of a storm (no ponding). P e is the actual depth of excess precipitation or direct runoff. This is always less than or equal to the cumulative precipitation depth (P). F a is the additional depth of water retained in the watershed after runoff has begun. Empirically I a = 0.2S where S is the maximum potential retention of water and is a function of CN where S equates to (1000/CN) 10. Recharge is computed as precipitation minus runoff (P P e ). A CN is assigned according to soil type as catalogued in western Washington (WSDE WQP, 2005) and vegetation type and status. Modifications to the CN based on antecedent conditions and steep slopes (Huang et al., 2006) are done to test sensitivity of recharge to range of applicable CN. Two hour precipitation data collected on site are used to calculate recharge assuming storms are separated by 24 hours of no precipitation. Model calibration uses actual precipitation records, but worst case storms will test drain configurations in successfully reducing pore pressures in the subsurface. Design storms will use SCE 24-hr storms based on dimensionless rainfall distributions from the National Weather Service records. These design storms distribute the volume of rainfall based on a chosen return periods (e.g. 6 months to 100 year storms). Factor of Safety The ability of hillslopes to resist downward movement is determined by the material s shear strength (S s ). Shear strength is a function of the slopes normal component to gravity (i.e. normal stress, σ), pore water pressure (p) within the material and mechanical properties of the material including cohesion (C) and its internal friction (φ), and is expressed as (Freeze and Cherry, 1979), = C + ( σ p) tanφ. (2) S s Water in the soil material plays the duel role of increasing the weight of the soil mass thereby increasing the driving forces of sliding (shear stress,τ) while simultaneously reducing the resisting force through reduced shear strength (p is subtracted from σ in eq. 2). Slope stability is often evaluated in terms of the factor of safety (F s ), which is the ratio of the resisting and driving forces on the soil mass (S s /τ). If F s is less than one, failure is imminent, while a value between 1.25 and 1.4 is considered satisfactory for road cuts. For the simplified condition of translational sliding along a relatively planar surface and a water table coincident with slope, F s can be calculated as (Ritter, 2004), F s C + ( γ mγ w) z cos γz sin β cos β 2 β tanφ =. (3) Where γ and γ w are the unit weight of the slope material and water, respectfully, z is the thickness of the slope material above the slide plane, m is the vertical height of the water above the slide plane expressed as a fraction of the total thickness and β is the slope of the ground surface. Under more complex conditions (e.g. slip systems of irregular geometry, C and φ vary along the slip surface) then a more sophisticated method of analysis such as the conventional method of slices (i.e. Bishop, 1955) is required. In addition, water-table response to precipitation events is seldom simple. Slope stability is highly influenced by porewater pressures, which are greatly dependent on the hillslope configuration,

5 intensity and duration of rainfall/snowmelt, groundwater flow regime, and the saturated hydraulic properties of the hillslope material. SUMMARY The iterative approach between MODFLOW, used to establish pore pressures along a relatively steep profile based on complex geometries, hydraulic heterogeneity and variable recharge, along with geotechnical calculations of the factor of safety, is a novel means to develop guidelines for alternative drain arrays. Complexity of sites varies and where appropriate analytical solutions can be used. However, for many sites a practical knowledge of groundwater influences on slope stability via numeric models will aid in more properly estimating appropriate drain placement. ACKNOWLEDGMENTS Thank you to the Washington State Department of Transportation and the other sponsoring State Departments of Transportation for funding of this project under DRI contract REFERENCES Bishop, A.W., The use of the slip circle in the stability analysis of slopes. Geotechnique. 5. pp Cai, F., K. Ugai, A Wakai, and Q. Li, Effects of horizontal drains on slope stability by threedimensional finite element analysis, Computers and Geotechnics, 23(4), Fipps, G., and W. Skaggs, Influence of slope on subsurface drainage of hillsides, Water Resources Research, 25(7), Freeze, R. A., and J. A. Cherry, Groundwater, Prentice-Hall, Inc., New Jersey, 604p Harbaugh, A. W., E.R. Banta, M.C. Hill, and M.G. McDonald, MODFLOW-2000, The U.S. Geological Survey Modular Ground-Water Model User Guide to Modularization Concepts and the Ground-Water Flow Process, U.S. Geological Survey Open File Report 00-92, Reston, Virginia. Huang, M., Gallichand, J., Wang, Z. and M. Goulet, A modification to the Soil Conservation Service curve number method for steep slopes in the Loess Plateau of China. Hydrological Processes. 20, Lau, K.C., and T.C. Kenney, Horizontal drains to stabilize clay slopes. Canadian Geotechnical Journal 21 (2), Pathmanathan, M. L., Numerical Simulation of the Performance of Horizontal Drains for Subsurface Slope Stabilization, M.S. Thesis, Washington State University, 95p. Rahardjo, H., K. J. Hritzuk, E. C. Leong, and R. B. Rezaur, Effectiveness of horizontal drains for slope stability, Engineering Geology, 69, Ritter, J.B., Landslides and Slope Stability Analysis : using an infinite slope model to delineate areas susceptible to translational sliding in the Cincinnati OH area. Department of Geology, Wittenberg University. Schmid, P., and J. Luthin, The drainage of sloping lands, Journal of Geophysical Research, 69(8), Soil Conservation Service (SCS), National Engineering Handbook, section 4. Hydrolgy. U.S. Department of Agriculture. Washington, DC. U.S. Department of the Interior, Drainage Manual, Water Resources Technical Publication, Washington, D.C., 286p. Western State Department of Ecology Water Quality Program, Stormwater management in Western Washington. Vol III: Hydrologic Analysis and Flow Control Design/BMPs. Publication No Wooding, R. A., and T. J. Chapman, Groundwater flow over a sloping impermeable layer. 1: Application of the Dupuit-Forchheimer assumption, Journal of Geophysical Research, 71(12),