Introduction

Two main zones called an inner zone of soil (core material) and an outer zone of rock fill (shell fill material) described as embankment dams, which also known as zoned embankment dam. Embankment dam is constructed from locally available materials by reducing the transportation cost and processing cost; this dam is widely constructed almost all over the world. In the world, about 14,000 large dams were registered up to the recent day, and from this list, more than 70% of them were earth and rock fill dam (Narita 2000). In the last tenth years, a number of small dams have been constructed in Ethiopia for the purpose of water supply and irrigation to serve the domestic and cattle (Asmelash and Claudia 2015). According to Jalalinejad and Nikbakht (2016), the embankment dam with a clay core has a good ability in terms of seepage caused forces and stress.

Different shape of core geometry specifically inclined and vertical are widely constructed in different country with different side slope of embankment dam (Nayebzadeh and Mohammadi 2011). A thick core is more useful than thin core to overcome a problem of pore water dissipation and sudden draw down; but it should be economized in a safe way (Mohammadi et al. 2013). When weak rocks (especially sedimentary rocks) like shale, clay stone and the like are found in dam foundation the foundation cannot bear the dam structure that lead to shear failure (Gangopadhyay 1993). Thanh et al. (2013) say that in geotechnical engineering, the slope stability is the main aspect; therefore, the dam design should take care for slope stability.

The Gidabo rock fill dam has 2H:1V side slope and 22 m height from bed-level Ethiopian water work design and supervision enterprise (WWDSE 2008a). For this small dam, this slope is little bit gentle which is not recommended as it consumes a slightly huge rock fill material with this height. While dam design the most economical and safe stability should be given a great emphasis, though this dam lacks to compare the different slope and selection of less volume of construction material. According to the Roshani and Farsadizadeh (2012), the best way of dimension selection should be based on economical view and seepage protection through the core of dam. Hence, the weight of dam constructed on this weak foundation should be kept within save limit. Wuletaw (2007) and Vahdati (2014) state that when large volume of rock fill filled on weak foundation, there is a probability of settlement. Therefore, this study is intended to fill this gap by identifying best side slope, which makes much volume of shell material safe without affecting the dam stability.

Bedrocks near dam axis and reservoir area consist a sequence of inter-bedded pyroclastic fall deposits and rare tertiary basic lava and the right abutment is characterized by thick soil, weathered rock, and weak ignimbritic rock. The central parts of the left abutment consist slightly weathered ignimbrite, ignimbritic tuff, and have moderate quality (WWDSE 2009). This indicates that there is weak foundation under the dam; therefore, deformation character of the dam was checked.

The primary objective of this study is to show the effect of side slope and clay core shape on the stability of embankment dam and bring alternative dam design that saves the construction material for Gidabo rock fill dam.

Materials and methods

Location

Gidabo dam irrigation project is located in Ethiopia, within the boundary of Oromia Regional state and South nation nationality and peoples regional state (SNNPR state). Specifically, Abaya district of West Guji zone in Oromia region and Dale district of Sidama zone in SNNPR state near Dilla town to east of Lake Abaya, which is 375 km from Addis Ababa the capital city of Ethiopia (Fig. 1). The geographical location of the area is between 6°20′ and 6°25′N Latitude and 38°05′ and 38°10′E Longitude, at an average elevation of 1190 m a.s.l (WWDSE 2009).

Fig. 1
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Location map of the Gidabo dam site

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Seismicity of the area

The Ethiopian seismicity is generally confined within the Afar and main Ethiopian rift valley (MER); the MER pass from northeast to south west of the country. Hence, the Gidabo irrigation project is located in southern part of the country in the MER, which is seismically active area. As seismic zone of Ethiopia, the study area (Gidabo irrigation project) falls in active region. The Gidabo dam site is located between 0.15 and 0.2 of horizontal seismic coefficient (WWDSE 2008a). The frequent dam failures happen due to soil liquefaction (Lopez-Quero and Moreta 2008); so the seismicity increases this problem and should be evaluated well.

Parameters determined

  • Permeability coefficient and shear strength parameter of the shell, core and foundation materials has been adopted from final design report of Gidabo dam as shown in Table 1 (WWDSE 2009).

    Table 1 Material parameters for different zones of dam (WWDSE 2008b)
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Method used for analysis

For this study, the Geo-Studio Software is used to analyze the dam under different loading conditions. Currently, stability and seepage can be analyzed using geotechnical software called Geo-studio. Geo-Studio is one of the numerical modeling software developed by Geo-Studio international based on limit equilibrium and finite element principles, developed especially for the analysis of seepage, stability, deformation of geotechnical structures etc. Its package includes tools like SEEP/W (for seepage modeling), SLOPE/W (for stability modeling), SIGMA/W (for stress and deformation modeling), QUAKE/W (for dynamic modeling), TEMP/W (for thermal modeling), CTRAN/W (for contaminate modeling) and VEDOSE/W (for vadose zone modeling) (Geo-Slope International Ltd. 2012). In this tool, the calculation of stability for equation of factor of safety is determined with ratio of shear strength to equilibrium shear stress (Duncan and Wright 2005).

Results and discussion

Dam zoning and geometry

It has been discussed earlier in this document that Gidabo rock fill dam originally being designed with 2H:1V upstream and 2H:1V to 1.75H:1V downstream side slope that consume large fill material with exaggerated factor of safety (WWDSE 2008a). To solve this problem, a steeper side slope that reduces the shell material consumption is used as an alternative design and all required analysis has been done for the new dam alternative. This topic is supported with the investigation of Wuletaw (2007) and Vahdati (2014), with the verification that when large volume of rock fills filled on weak foundation there is a probability of settlement.

The alternative design of the outer shell slopes with 1.8H:1V for upstream and 1.5H:1V for downstream is selected based on stability analysis made (Table 3). Revision of the dam cross section has been in line with the guideline by Khanna et al. (2014, 2015, 2017) and USSD (2011). Hence, the newly introduced dam has 1.8H:1V upstream and 1.5H:1V downstream side slope, 0.5H:1V of core side slope, and the same berm length, position of berm, dam crest, and top core thickness of original size was adopted as shown in Fig. 2.

Fig. 2
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The newly introduced Gidabo dam clay core shape and side slope

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Fig. 3
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Upstream factor of safety when base width of core is 23.2 m

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Effect of side slopes on stability

For side slope selection, the static slope stability under different loading conditions is conducted and compared based on their safety factor values. The respective values for different loading conditions are presented in Table 2. In earth and rock fill dams (zoned embankment), inclination of upstream slope is usually in the range of 2.50H:1V–1.70H:1V. Nevertheless, in some cases, the upstream slope is as flat as 3.00H:1V–1.40H:1V. The inclination of downstream slope is usually in the range of 2.25H:1V–1.50H:1V. Nevertheless, in some cases, the downstream slope is as flat as 2.50H:1V–1.25H:1V (Khanna et al. 2014). According to Khanna et al. (2014, 2017), for the earth dam, gentler side slope is preferable and for rock fill dam, the steeper side slope is adopted. So by considering these ranges, for upstream from 3H:1V to 1.5H:1V and for downstream side 2.5H:1V–1.3H:1V range is taken for comparison.

Table 2 The comparisons of side slopes depend on different loading conditions
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From Table 2, it was shown that the flatter side slope has the highest factor of safety and as the side slope becomes steeper, the factor of safety of the dam decreases. To select the side slope, one should take care that whether the slope is stable to fulfill the design requirements and reduce the construction material.

From listed upstream side slopes in Table 2, the 3H:1V, 2.5H:1V and 1.8H:1V fulfill the design criteria, from those the 1.8H:1V upstream and 1.5H:1V downstream side slope is selected by considering the reduction of shell fill material, while fulfilling the safety requirement according to USACE (2003). Hence, the alternative side slope for Gidabo embankment dam that will be used under economical construction criteria of minimum quantity of earthwork is 1.8H:1V for upstream to 1.5H:1V for downstream.

This result is in line with the Khanna et al. (2015) that state a designer has to arrive at a dam section that has steep side slopes so that quantity of earthwork should be minimum without violating the minimum design requirements.

Effect of clay core shape

Effect of clay core by changing the size of base width

The Gidabo dam has 22 m height from bed level and the thickness of the core that are the most stable should be between 11 and 31 m. Having 1.8H:1V and 1.5H:1V upstream and downstream side slopes, respectively, with clay core top width 3 m, different clay core base width was taken (Table 3) based on the selection criterion by Khanna et al. (2017). This journal states that the base widths of clay core depend on the dam height, and the most stable width should be within the range of 50–150% of the dam height.

Table 3 Effects of clay core shapes by reducing upstream core base thickness
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The main advantage of core wall is to protect the excessive seepage of the dam. This part of dam is highly influenced by the dam slope, but the effect of core wall structure is not well defined/unclear up to today (Li and Chen 2015).

When the base width of clay core increases, the factor of safety slightly decreases and when the width of core decreases, the factor of safety slightly increases. This is due to that the clay core material has lower shear strength parameters than the shell material, and there is high pore water pressure in the core than the shell, this pore water pressure destabilizes the dam safety, as it is disturbing force type; this measurement is the same with Khanna et al. (2017) and Nayebzadeh and Mohammadi (2011). The clear trend of factor of safety at normal pool level (NPL) is shown in a graph form as shown in Fig. 4.

Fig. 4
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Factor of safety at NPL by changing upstream base width

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When the width of clay core reduces the seepage amount slightly increase and vice versa, because the primary purpose of clay core is to reduce the seepage. Therefore, when the thickness of clay core reduces or increases, both the stability and seepage quantity should be kept to optimum size.

When the thickness of downstream core increases as a result of upstream core decrease, there is high decrement of factor of safety (Table 4), which shows that the increment of clay core thickness to downstream side reduces the stability of dam; therefore, the clay core thickness increment to the downstream side is not recommended. This is due that the increment of clay core to downstream easily susceptible to destabilizing effect of horizontal destabilizing force, especially it affects the factor of safety of downstream side. When core made an inclination to downstream, the core is pushed upward by horizontal water pressure and upward vertical pressure by pore water pressure that easily stored under a core.

Table 4 Effects of clay core by reducing U/S core base with increasing the D/S base
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As the downstream base width of the core decreases while upstream base width remains the same, there is no much change in the stability of the dam and the dam stays stable. As the upstream core width increases, the seepage quantity decreases, and when core width decreases, the quantity of seepage increases.

When both upstream and downstream core base widths changed (increasing the upstream width while decreasing the downstream width simultaneously), there is no significant change on factor of safety except for the rapid draw down. From this result, it is seen that there is no significant loss of factor of safety and the inclination of upstream direction gives safe result. This result is the same with Khanna et al. (2015), which states that the factor of safety under rapid draw down remains high when the thickness of vertical core is less than 150% of height of dam. Because the pore pressure force is low as it dissipates easily as it drains the seeped water into the core and the dam remains stable.

When clay core width of upstream side increases as the downstream side decreases, the factor of safety slightly decreases and when downstream core width decreases as the upstream core remains the same, the factor of safety does not show significant change. This shows that the inclination of core to upstream direction may be done without affecting the stability of dam. However, when the core thickness is decreased too much, there is a probability of hydraulic fracturing (Nayebzadeh and Mohammadi 2011).

The base width of 23.2 (105% of dam height) has a good factor of safety and fulfills all design criterion except during sudden draw down over the other shape as shown in Table 3. Therefore, for this particular study, the 105% of dam height base width is the best core thickness. Khanna et al. (2017) and Nayebzadeh and Mohammadi (2011) added strength to this result, saying that the more stable core base width should be within 50% to 150% of dam height for zoned embankment dam. Therefore, in this comparison, the value between this is applicable.

Effect of clay core base shape

Having 1.8H:1V upstream and 1.5H:1V downstream side slope and core shape with base thickness 23.2 m, the further effect of clay core is checked by making the base of this shape nearly circular (arc) and the result is shown in Table 5. This base arc is done by inserting the clay core into the foundation about 3 m inside it and taking four different arcs and the different loading conditions are studied. This is done due to that the base straight core shape of stated above has low factor of safety during sudden draw down, and the deformation of base curved and base straight is done and compared.

Table 5 Effects of clay core shapes by changing base core to arc shape
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The arc radius was taken arbitrary along centerline of the core vertically that passes through the dam body at an elevation of 1204 m a.s.l, at a suitable position to make an arc. The sample of those shapes is displayed in Fig. 2.

This shows that when the radius of curvature increases, the factor of safety decreases and as the radius of curvature increases, there is increment of core thickness. As core thickness increases, the stability of dam decreases due to increment of pore water pressure and low shear strength parameter of core material. Almost all shapes in Table 5 fulfill the design requirements according to USACE (2003) and the base radius of 7 m is selected for this particular study as shown in Table 5. This shape is comparatively the best regarding to the factor of safety (Table 5) and consumes minimum fill material in comparison with other shapes.

The seepage quantity decreases as radius of curvature increases (Table 5); it is realized that when we reduce radius of curvature, the clay core width decreases and the seepage passes through the dam increases as the main objective of clay core is to reduce the seepage quantity.

(A) Effect of base shape of core on deformation.

The vertical and horizontal displacements increase as the base arc radius increases which shows that the base curved core is preferable than the base straight comparatively. This is due to that the higher radius of curvature has high clay core quantity and low radius consumes the low clay core quantity; so the clay core increment induces high pore water pressure that increases the dam deformation.

The Gidabo dam is categorized under the central clay core earth and rock fill dam, the maximum limit of the vertical deformations (settlement) and horizontal deformation (displacement) should less than 1.25% and 0.5% of dam height (Yaşar 2010). Taking the maximum limit, the Gidabo dam has 22 m height from bed level, the maximum settlement allowed for this dam is 0.275 m and maximum horizontal deformation should be less than 0.11 m.

The base circular core shape has the less stress distribution than the plain or base straight core shapes, so there is small displacement in comparison with straight base. The vertical and horizontal deformation at NPL is within acceptable limit. Hence, the base radius of 7 m is the most appropriate in all analysis (Table 5). This result is also better when it is compared to Ghafari et al. (2016), which shows the analysis done on Chenareh rock fill clay core dam of 120 m high; they obtained that the maximum settlement of 2.86 m occurs approximately at mid-height of the dam and is slightly more than 2% of the dam height.

(B) Effect of hydraulic fracturing.

The minimum total stress inside the core is well greater than the pore pressure as shown in Fig. 5, so there is no hydraulic fracturing problem for this dam. These show that the water or seepage quantity cannot form any piping inside the dam body that induces the crack. This result agree with the Talebi et al. (2013), and they state that hydraulic fracturing happens when pore water pressure exceeds the minimum total stress. A hydraulic fracture can occur when water pressure increases in the core, which further reduces effective stress (Mohsen and Faghihi 2008). According to Djarwadia et al. (2014), the hydraulic fracturing happens when total stress in the core is reduced.

Fig. 5
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Pore water pressure, maximum and minimum total stress of clay core at MWL

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The horizontal and vertical stresses are compared with pore water pressure, and the result obtained shows that both the horizontal and vertical stresses are above the pore water pressure, which shows that there is no crack problem induced in the clay core. This shows that the clay core has sufficient thickness and can be implemented. The result obtained in this analysis is in line with the finding of Nayebzadeh and Mohammadi (2011), which states horizontal and vertical core cracks happen when the respective total horizontal stress and total vertical stress are less than the pore water pressure.

Moreover, the healthiness of clay core is checking, in a way, whether the negative minimum total stress is happen inside the core, depending on this the minimum total stress observed in the core is from 40 to 160. This value is greater than negative, so there is no hydraulic fracturing in the core even at maximum pool level. This value is compromised with Nayebzadeh and Mohammadi (2011), which states that when negative minimum total stress occurs in the clay core, there is a probability of hydraulic fracturing inside the core, which induces the crack inside the core.

Dynamic analysis of selected shape

QUAKE/W is formulated for direct integration in the time domain, which means that the analyses are performed at many different moments in time and at certain time intervals. In this model, the integration follows a specified time stepping sequence. The horizontal and vertical ATH data have been produced for Gidabo embankment dam (for Kh = 0.20 and Kv = 0.10) from El Centro ATH of USA record. Because there is no acceleration time history data produced in Ethiopia and this USA ATH data are mostly used throughout the world (Dagne 2017). The consideration of dynamic analysis is due to the seismic reaction against strong vibration of the dams and earthquake (Nomiri and Khosrojerdi 2015).

The sensitivity analysis done on Bidvaz dam in China by Karbor-e-shyadeh and Soroush (2008) protects us that the inclined core is not stable for this particular site, they show that the dam with inclined core is generally less stable than the vertical core dam in seismic active region. During the earthquake, the dam was shaking in abnormal manner and the undrained shear strength of the dam decreased by the pore water pressure occurred (Tafti et al. 2008).

The computed minimum factor of safety of new shape after earthquake is 1.060 for downstream and 1.118 for upstream. This value is greater than the minimum requirement suggested by Melo and Sharma (2004) for unusual loading condition (i.e. FOS > 1) which ensures that the embankment is stable after earthquake. The stability of embankment dam during and after earthquake has been analyzed to evaluate the effect of the earthquake on stability. The earthquake stability analysis of post-earthquake is the most used in design; why because during earthquake case, there is a probability of restoring its initial stability and the dam may remain stable after earthquake happen.

Therefore, in particular for Gidabo embankment dam, the 1.8H:1V side slope (as shown in “Effect of side slopes on stability” section) and clay core shape with base thickness 23.2 m (as shown in “Effect of clay core by changing the size of base width” section) that has a base arc with arc radius 7 m (as shown in “Effect of clay core base shape” section) is selected section.

The base curve with radius of curvature of 7 m consumes less clay core material and induces the minimum settlement over the other. Also, this shape fulfills all design criterion even during sudden draw down the factor of safety is above allowable limit. During the base straight, the stability during sudden draw dawn is less than the minimum required safety factor, as it may have a probability of failure during sudden drawdown.

As the clay core thickness increases the factor of safety decrease, due to that the clay core has the tendency to capture the seeped water into the core. This absorbed water increases the pore water pressures; the pore water pressure is the destabilizing force that reduces the stability of the dam.

Conclusion

This study is carried out on the Gidabo rock fill dam, by studying the effect of dam side slope and clay core shape on the stability of embankment dam by introducing the new side slope and clay core shape taking Gidabo rock fill dam as case study. The selected side slope and clay core shape were chosen based on the shell material reduction without disturbing the stability of the dam.

Generally, the following conclusions are drawn: for rock fill dam, the steeper side slope is advisable without affecting the stability of the dam. Hence, the Gidabo dam is rock fill dam with low height; the steeper side slope is used and is safe in all loading condition and 1.8H:1V upstream and 1.5H:1V downstream side slope with base curve clay core shape is selected. As the side slope of the dam is changed from steeped to gentle, the factor of safety of the dam increases, when clay core shape remains unchanged. The selected side slope and clay core shape are analyzed for all loading conditions, and the finding under these conditions showed that all obtained values are within minimum safety factor requirement recommended by USACE (2003), Yaşar (2010) and Melo and Sharma (2004).

As it is shown in discussion part, there is no hydraulic fracturing occurred inside the newly introduced clay core shape; because pore water pressure is lower than the minimum total stress developed inside the clay core. Both the horizontal and vertical stress developed in the dam body are above the pore water pressure, which shows that there is no crack problem induced in the clay core. The vertical and horizontal deformations at normal pool level are 0.192 m and 0.023 m, respectively, which are safe. The upstream and the downstream slope stability of the embankment have been found stable after the earthquake. The computed minimum factor of safety for new dam after earthquake is 1.118 for upstream and 1.060 for downstream, which is safe as it is greater than recommended value (> 1).

Moreover, based on the material consumption, the new side slope consumes a less material compared to original. Even though the side slope is reduced, the dam is stable in all loading conditions.