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Stability analysis of Hub dam under rapid drawdown

  • Mohammed Mohsin Salman EMAIL logo , Ahmed Kamil Abraheim and Ali Mohammed Ali Naji Al-Attabi
Published/Copyright: February 7, 2024
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Open Engineering
From the journal Open Engineering Volume 14 Issue 1

Abstract

The purpose of this study was to calculate the Hub dam’s slope stability analysis in a rapid drawdown scenario. Using the slide software, we compared four distinct analytic techniques – the Bishop, Janbu, ordinary way of slicing, and Morgenstern-Price approach – to determine whether or not a given slope would remain stable at the highest possible water level. According to the simulation outcomes, the portion of the dam upstream directly impacts the safety factor. The upstream safety factors, calculated using the Bishop approach, are 2.122 for steady-state seepage and 2.023 for the fast drawdown scenario. This ensures the Hub dam’s stability even under rapid drawdown conditions.

Keywords: slope stability; Hub dam; earth dam; finite element method; factor of safety; rapid drawdown; Bishop method

1 Introduction

Embankment dams require careful design that considers stability analysis during fast drawdown. Rapid drawdown removes the water’s stabilizing influence on the upstream face, but the embankment’s pore-water pressures may still be considerable. This allows for a significant weakening of the dam’s upstream face. The permeability and storage features of the embankment materials dramatically affect the dissipation of pore-water pressure. High-permeability materials drain quickly during the fast drawdown, whereas low-permeability materials require a long time to drain [1].

Installing drains at the foot of the upstream slope and the intermediate level can relieve hydrodynamic pressure in the upstream shell and reduce the stress of the phreatic line and pore water. These upstream drains can drain the upstream slope to achieve a more horizontal orientation of the equipotential lines. They significantly impact upstream slope stability during drawdown [2].

Upstream slopes are particularly vulnerable during drawdowns. There is a threat to the upstream slope when the opposing upstream water pressure no longer exists. Hydrodynamic pressure from fast decline causes the upstream shell to collapse. Seepage begins from the soil inside the dam body and moves up the upstream slope. Forces exerted downhill on the upstream slope by seepage and hydrodynamic pressures. Conditions where the water level next to the slope is rapidly dropped are the most common for sudden drawdown stability calculations. The phrase “Sudden” drawdown refers to the analytical assumption that drawdown is very rapid and that drainage does not occur in low-permeability materials. We utilize drained strengths for materials with permeabilities larger than 104 cm s2 during drawdown [3].

Here, we utilize SLIDE to calculate the safety factor with finite elements in a steady-state seepage and rapid drawdown scenario from elevation (EL) 346 m to EL 250 m. Excess pore pressure occurs when pounding water in upstream side circumstances (undrained loading) rapidly draws down the soil’s pore pressure over a short period. Low-permeability materials, such as clays, may have this behavior. The so-called “B-bar” approach takes the relationship between pore pressure and vertical tension as its starting point. For the sake of argument, let us say that:

(1) ∆ u = B ̅ ∆ σ V ,

where ∆u is the excess pore water pressure caused by drawdown condition, B ̅ (B-bar) is the overall pore pressure coefficient for earth fill material, and ∆ σ V is the change in effective vertical stress.

It is clear from equation (1) that the excess pore pressure value depends on the (B-bar) coefficient. The soil’s composition and characteristics determine the (B-bar) coefficient’s value. If the (B-bar) coefficient is zero or very close to zero, the ground may drain freely, and there will be no pore water pressure buildup on the upstream side. There is an upstream surplus pore pressure if the (B-bar) coefficient is close to 1. Select low-permeability soils if the (B-bar) coefficient is close to 1, which indicates a crucial situation of fast depletion on the upstream side [4].

There are many techniques for determining a soil slope’s stability. The slopes’ “stability is assessed by determining the factor of safety (FOS) dependent on the soil’s properties, representing the failure strength. Cohesion (C) and internal friction angle (ø) influence failure resistance. The resistance to failure depends on cohesion (C) and the angle of internal friction (φ). When the ground surface slows, forces are generated – the important forces induced in the slopes” [5]. Comprehensive knowledge of the material characteristics, the issue geometry, the analytical method, and the failure consequences informs the selection of the safety factor [6].

2 Bishop’s simplified method

The simplified Bishop approach disregards the inter-slice shear forces, so the normal or horizontal force is assumed to better describe the inter-slice troops [7]. The usual force on the base of each slice is obtained by applying pressure in the vertical direction (Bishop, 1954).

Whitman and Bailey [8] pointed out that the error of the safety factor value obtained by this analysis method is usually less than 5%. You can use the simplified FOS method to calculate the value of the safety factor [8]:

(2) M i ( θ ) = cos θ i 1 + tan θ i tan ∅ ̅ FOS ,

(3) FOS = ∑ i = 1 i = n [ c ̅ ∆ X i + ( W i − U i ∆ X i ) tan ∅ ̅ ] [ 1 / M i ( θ ) ] ∑ i = 1 i = n W i sin θ i ,

where c and ϕ are effective shear strength parameters for the soil at the base of the slice, n is the number of slices, W i is the weight of the slice, θ i is the slope of the slice, U i is the average pore water pressure at the bottom of the slice and is equal to u i = h i × γ w, and h i is the height of the water in the piezometer placed at the bottom of the slice. Since FOS is a factor on both sides of equation (2), the only way to find a solution is through trial and error. However, there is a rapid convergence of practices. The figure also expresses M i (θ) (equation (1); Figure 1).

Figure 1 Values of (θ) M i [9].
Figure 1

Values of (θ) M i [9].

The aforementioned two methods (the ordinary method and the simplified Bishop method) are presented in Figure 2, which shows the differences between the two methods.

Figure 2 General slip surface and the force acting on a typical slice according to [10]. (a) Ordinary method. (b) Bishop method.
Figure 2

General slip surface and the force acting on a typical slice according to [10]. (a) Ordinary method. (b) Bishop method.

3 Case study

The Hub dam is located in Hub, Pakistan, a neighboring neighborhood of Karachi, at 67 ° .5′ East and 25 ° .15′ North, over the Hub River, as shown in Figure 3. Before flowing into the Arabian Sea, the Hub River travels 220 miles across tertiary rock terrain, starting at around 6,000 ft in the Kirthar Range. The catchment area of the Hub River, which extends for about 3,410 square miles up to the dam site, determines how much water flows into the reservoir. A combined homogenous earth dam is a Hub dam. The three components of the dam are the foundation, shell, and filter blanket. Tables 1 and 2 describe the material characteristics and geological parameters of the Hub dam [11].

Figure 3 Hub dam location.
Figure 3

Hub dam location.

Table 1

Material properties of Hub dam

No. Material type Hydraulic conductivity (ft/s)
1 Foundation 3.225 × 10−6
2 U/S shell 2.000 × 10−5
3 D/S shell 2.000 × 10−5
4 Filter blanket 3.280 × 10−2
Table 2

Geological parameters of Hub dam

Material C ( KN / m 2 ) θ ( ° ) γ ( KN / m 3 ) K (m/d)
Foundation 275 45 20 3.225 × 10−6
Shell 0 35 19 2 × 10−5
Blanket 0 30 18.5 3.28 × 10−2

The domains are described using a finite element mesh with three-node triangular elements, as shown in Figure 4. The total number of nodes and elements in the mesh is 12,495; our analysis begins with a choice of element numbers, chosen when those numbers no longer affect the values of the solutions at hand. In this case, the chosen element numbers result from mesh generation in response to a modification to the photic surface.

Figure 4 Hub dam (a) typical cross-section of Hub dam. (b) Finite element mesh for the Hub dam.
Figure 4

Hub dam (a) typical cross-section of Hub dam. (b) Finite element mesh for the Hub dam.

4 Analysis and discussion

4.1 Seepage by using Slide software

Figures 5 and 6 show that researchers used the Slide program to create a 2D Hub dam. The steady-state study assumed that the water volume would remain constant throughout time. The steady-state equation is time-independent and does not consider the volumetric water content function. The saturated coefficient of permeability is the single input parameter. Under the given boundary conditions, the solution output will reveal the shift in the pore water pressure, conductivity, etc.

Figure 5 The pore pressure head and discharge volume of Hub dam.
Figure 5

The pore pressure head and discharge volume of Hub dam.

Figure 6 The most critical slip surface. (a) For steady-state condition before rapid drawdown, FOS = 2.122. (b) For the rapid drawdown condition from EL. 346 m to EL. 250 m, FOS = 2.023.
Figure 6

The most critical slip surface. (a) For steady-state condition before rapid drawdown, FOS = 2.122. (b) For the rapid drawdown condition from EL. 346 m to EL. 250 m, FOS = 2.023.

4.2 Stability analysis of slope

This part relates to the results obtained from this study, including seepage and stability analysis through earth dams, emphasizing the performance of materials available for earth dams. The study was conducted by analyzing Hub Dam using the Slide program.

The slip surface types used in the present analysis are circular slip surfaces, which is the most commonly used method. According to this method, the analysis method used is the equilibrium method (LEM). The strength model used in this analysis is Mohr–Coulomb. The limit equilibrium method according to Bishop and Morgenstern-Price presented by computer program is applied to define the potential slip surface and to calculate the factor of safety of the dam slopes.

Before the rapid drawdown scenario, the FOS, which measures the stability of a slope relative to landslide danger, was a safety factor at 2.112.

When the reservoir is at its maximum conservation level, or EL 346 m, over an extended period, a constant seepage situation develops in the dam embankment, and the reservoir empties quickly. Rapid declination means stability on just the upstream slope.

Table 3 shows the overarching findings of the Hub dam’s slope stability investigation.

Table 3

Value of FS for many methods

No. Analysis method FS for steady-state seepage FS for rapid drawdown condition
1 Bishop 2.122 2.023
2 Morgenstern–Price 2.122 2.023
3 Ordinary slice 2.109 2.018
4 Janbu 2.144 2.018

The slope stability against landslide risk is represented by safety factor (FOS), which is determined using the Bishop method. The slope stability in the rapid drawdown was examined. In a rapid drawdown of water level, deformation and crack occurred in the dam model at the upstream slope.

5 Conclusion

Here, SLIDE V.6.0 utilized finite elements to calculate the safety factor for steady-state seepage and fast drawdown conditions between ELs 346 and 250 m. In this study, boundary conditions were no-flow on both sides to explain the results. According to the simulation outcomes, the dam upstream portion directly impacts the safety factor. Using the Bishop technique, the upstream safety factors are 2.122 under a steady-state seepage situation and 2.023 in a fast drawdown scenario. This ensures the Hub dam’s stability even under rapid drawdown conditions.

  1. Conflict of interest: The authors state that there is no conflict of interest.

  2. Funding information: We declare that the manuscript was done depending on the personal effort of the author, and there is no funding effort from any side or organization.

  3. Data availability statement: Most datasets generated and analyzed in this study are in this submitted manuscript. The other datasets are available on reasonable request from the corresponding author with the attached information.

References

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Received: 2023-05-30
Revised: 2023-06-29
Accepted: 2023-07-20
Published Online: 2024-02-07

© 2024 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/eng-2022-0497
Keywords for this article
slope stability; Hub dam; earth dam; finite element method; factor of safety; rapid drawdown; Bishop method
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