Devils Lake in North Dakota.

Background

The dam investigated in this research is Devils Lake in North Dakota. It had an elevation of 1459.59 feet, but was rebuilt due to a requirement to bring the embankment to an elevation of 1468.60 feet. This was done to meet dam safety standards for its maximum elevation that would allow for natural flow to Sheyenne River at 1458 feet. The increase in precipitation between 1993 and 1999 resulted in a doubled size lake, rising over 26.5 feet. Different federal research was conducted to study the flow mechanism of the dam other than dependence on natural overflow or evaporation (Rosenberg, 2000), but a cheaper solution of raised elevation and method to divert water with lower maximum discharge capability was used, which is insufficient for its capacity.

Figure 1: Historical Elevations of Devils Lake (USGS, 2007)

With these large water fluctuations over long time periods, and lack of natural outlet the dam is prone to fail.The main factors that influence embankment failure mostly depend on its geometry, material composition, insufficient compaction during the construction phase which causes particle migration, and the forces it is subjected to both internally and externally. These failures results to instability of the dam which induces seepage, drawdown, and sliding under different conditions. For this study, seepage and slope stability analysis are conducted for a steady state and drawdown condition to help determine the pore water pressure and factor of safety for stability.

Introduction

Embankments dams are structures built for the main purpose of flood control, hydroelectric power generation, and irrigation purposes. They are constructed on soft materials and are prone to failure from the action of water filling. Embankment dams are grouped into earth-fill dams as embankment dam and rock-fill dams as concrete dams, where the former takes longer to reach equilibrium compared to the later. There are several factors to be considered in selecting an earth dam type such as: topography; foundation conditions; and socio-economic studies. In selecting and building an earth dam, factors such as foundation soils, construction activities, environmental impacts, are considered before using locally available materials for its construction to protect the stability of operation and loading conditions against seepage, drawdown effects and overtopping at the crest (Ismail, and K. Gey, 2012 and Zeidan, 1993).

This study reviews on previous research conducted for the flow mechanism due to the increased elevation and volume of the dam. The different soil configuration and their corresponding permeability coefficients are used in the finite element analyses to determine the phreatic surface, change in water head from upstream to downstream, pore water dissipation for three conditions of seepage, slope stability and rapid drawdown of the embankment with time. These conditions are evaluated at steady state with constant head and transient states with different time steps to determine the embankments resistance to failure and rate of pore water dissipation. Using Finite element simulation of GeoStudio at these conditions, the corresponding factor of safety where the increasing water level will not affect the structural stability of the dam is determined and conclusions made on the hydraulic head variation from the fluctuation events at various time steps.

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The result from seepage analysis is used in limit equilibrium slope stability analyses of both the upstream and downstream slopes of the dam. The analytical method used to assess its slope stability is the Spencer’s Method at transient state, for Mohr Coulomb strength envelope of the material mode. In the limit equilibrium analyses, three cases of operations are analyzed; steady state seepage, rapid fast drawdown (Instantaneous), and rapid slow drawdown of the reservoir. By changing the boundary conditions and the different material composition while studying the individual changes, good conclusions are made for the problem statement and best cost-effective flow mechanism is recommended.

For an existing dam there is a need for continuous reevaluation of its stability. Achieving this, proper consideration and representation is given to the analysis procedure as there is danger in relying too much on slope stability analyses for existing dams (USACE, 2003). To remedy this problem, proper representation of the dam behavior through previously conducted field investigations and research into the historical design, later reconstruction and existing records, as well as the performance of the embankment can help with effective simulation. With these, stability analyses provide a useful tool for assessing the stability of existing dams and evaluating other failure mechanisms that could arise, while providing measures to mitigate the issues of flow.

2.1  GeoStudio Modelling

SEEP/W is a finite element CAD software for analyzing groundwater seepage and excess pore-water pressure dissipation problems within a porous material. One of the applications of SEEP/W is to simulate seepage flow and discharge through the soil, to determine the porewater pressure distribution for SLOPEW analysis and excess pore pressure for volume change and consolidation. It was developed in this study to investigate seepage and slope stability analysis for this case study of an embankment dam. The result of the SEEP/W is used to evaluate the stability of the embankment dam by considering ranges of analyses from simple saturated steady-state condition, to sophisticated saturated/unsaturated time-dependent problems. Depending on the amount of pore water dissipation with time, it can model both saturated and unsaturated flow behavior of the dam: for steady-state saturated flow analysis of constant volume, and analyze seepage as a function of time considering the infiltration process of high precipitation, where the changes in excess pore water pressure cannot be neglected.

It has two main material property requirements function for every region: The volumetric water content function and hydraulic conductivity. For a material in its saturated state only, the volumetric water is not required, so Ksat is used, while the saturated/unsaturated requires volumetric water content function for its conductivity. The volumetric water content function is added as a data point function for each material, this creates a material water content curve based on literature at saturated water content at 0.5 ft3/ft3. A lower conductivity with large variation signifies very high energy required for water flow, at no continuous flow, residual water content is reached.

2.2  Failure mechanism

2.2.1Seepage Analysis:

During flooding events, seepage is one major failure mechanism of an earthen structure. The rate at which seepage develops depend on the permeability of the embankment materials, and for increasing fluctuations in the water level during flooding, more seepage process is induced to cause structural instability. The use of impervious core, riprap blanket, sand drain has been proposed to help reduce the path of flow line in a dam, which represents the seepage phenomenon through the dam has helped prevent loss of embankment material. Estimating the amount of seepage of the dam is very important for design and construction especially in earth dam structures.

Seepage failures account for more than 35% of all earth dam failures and about 25% of structural failures of the dam (Elshemy, 2002). The seepage flow of water through embankment regions depends on some properties like the soil media, type of flow, and the boundary conditions. Different methods have been developed to solve seepage problems, these methods can be classified as analytical, experimental and numerical methods. A measure of the potential energy is the total head, which is the sum of pressure head and elevation head. According to Darcy’s Law, the volume rate of flow per unit area is directly proportional to the rate of change of head. Below is a general governing equation for seepage through earth dams can be considered as (Elshemy, 2002 and Zeidan, 1993).

[ ] + [ ] + [ ] = ……………….. (1)

where, Kx, Ky and Kz are the coefficients of permeability in x, y and z directions, respectively, S is specific yield

= p/Ɣw + z = total fluid head,

P = pressure, Ɣw = unit weight of water and z = elevation head.

Equation (1) is known as Laplace’s equation which is considered as the governing equation for groundwater three-dimensional flow through aquifers.

2.2.2                 Drawdown

 

Drawdown is the lowering of water level in made structures of natural slopes due to water withdrawal. A change in external water level without allowing the time needed for the drainage of the slope soils, a sudden or rapid drawdown. With the occurrence of rapid drawdown, a decrease in the slope stability of the dam may lead to slope failures (Berilgen, 2007). At full capacity of the reservoir, the phreatic surface within the embankment is established for the seepage analysis in the steady state. The phreatic surface line, porewater pressure, and total water head is solved and shown at time 0 – seconds, indicating no loss in water storage capacity. The results of the steady state seepage state are used as input for limit equilibrium analyses in SLOPEW.

When a reservoir level rises or drops faster than the embankment can absorb or drain off, the change is called RAPID. If a rapid drawdown takes place after d embankment is at equilibrium, internal loads develop upstream of the structure, causing slope failure. It also causes stability failure in the natural slopes of the structure leading to spillways. The stability of the embankment dam slopes under this drawdown condition for steady state and transient conditions needs to be evaluated for the safety analysis of the supporting slopes. Both undrained and drained shear strength parameters of the material in the dam are used in the analyses (USACE ,2003)

Figure 2: Phreatic Surface for Rapid Drawdown

In transient condition, the soil at upstream face of the impervious zone comes equilibrium under the submerged unit weight of the filter and slope protection. Deeper down this zone, the soil has overburden pressure and experience effect of seepage forces between it and the extreme face of the impervious zone. The unit weight of the filter is increased, doubling the driving force in the drained condition, causing a critical slide surface below the extreme face of the impervious zone at its lowest confining pressure during high precipitation in the upstream face. If the upstream zone is not drained, driving force increases from submerged weight of d shell due to the saturated weight. If the upstream zone is free draining during drawdown, driving force increases from the submerged weight due to the drained weight of the upstream shell. However, if the drainage of the upstream zone is still taking place due to drawdown, stability of the upstream slope in the drawdown level of the reservoir with water seeping out of the upstream shell downstream should be evaluated for its appropriate factor of safety against failure.

Conditions for Rapid Drawdown

•         A drop-in water level will result to a drop-in stabilizing force as the weight of water is removed. on the upstream face.

•         Low permeability will result to slow dissipation of excess pore pressures which leads to slope failure with time.

2.2.3        Slope Stability Analysis:

The purpose of slope stability analysis is to determine the factor of safety of a failure surface, where the resisting shear strength along the surface needs to be greater than the driving shear stress (Huang, 2014).

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https://www.youtube.com/watch?v=5lYnf1bYDRs 

Huang, Y. H. (2014). Slope Stability Analysis by the Limit Equilibrium Method: Fundamentals and Methods. American Society of Civil Engineers (ASCE).

Berilgen, M. M. (2007). Investigation of stability of slopes under drawdown conditions. Computers and Geotechnics, 34(2), 81-91.

Lowe J, Karafiath L. (1960). Stability of earth dams upon drawdown. Proceedings of the first Panamerican conference on soil mechanics and foundation engineering, Mexico City, Vol. 2.

Duncan JM, Wrigth SG, Wong KS. (1990) Slope stability during rapid drawdown. Proceedings of the H. Bolton seed memorial symposium, Vol. 2

Wright SG, Duncan JM. (1987). An examination of slope stability computation procedures for sudden drawdown, US Army Corps Engineering. Waterway Experiment Station, Vicksburg.