DYNAMIC RESPONSE AND STABILITY ANALYSES OF AKOSOMBO DAM USING NUMERICAL ANALYSIS

Dams are very important in Ghana's economic development and environmental improvement. Although Ghana dams are seismically far from the active zone, accurately analysed dams should be evaluated since failure could severely impact the people in the flood environment and the region's economy on a large scale. This paper proposes a numerical procedure for the static, slope stability, and dynamic analysis of the Akosombo embankment dam. Nineteen horizontal acceleration time histories recorded data was used based on Maximum Design Earthquake (MDE), Maximum Credible Earthquake (MCE), Design Basis Earthquake (DBE) and Operating Basis Earthquake (OBE) data. The numerical results estimated showed that the Akosombo embankment dam is likely to experience moderate deformations during the different design earthquakes. The result also indicated that nonlinear analysis capable of capturing dominant non-linear mechanisms could be used to assess the stability of embankment dams. The factor of safety (FS) calculated was greater than 1.5 for high reservoir, rapid drawdown condition and low reservoir condition whereas, the FS values were found to be 1.42 for slow drawdown condition. Ambar using the non-linear dynamic time-history of Bingol and modal analysis The analysed under static conditions and dynamic analysis. The PGA responses caused by maximum design (MDE) core, foundation. The results obtained under the dynamic behaviour of the Akosombo dam provides an adequate basis for the deformations of the dam using different conditions of design earthquakes data. The results showed that deformations increased at the crest of the dam. The present study also aimed to numerically examine the slope stability of the Akosombo earth dam under the drawdown reduction method by Plaxis two-dimensional software. The strength for each load case combination of the dam is expressed through safety factors. Analysing the static stimulation of Akosombo dam using the drawdown principle, displacements and corresponding safety factors are obtained at the high reservoir, reservoir filling, and low water level conditions. The dam body and its foundation parameters used for the analysis are based on engineering properties determined from the literature. The total displacements are significant when studying most of the geotechnical problems. It is particularly recommended that laboratory tests be performed for the dam site conditions. The numerical results show that lower displacements occurred in the dam body and foundation through impounding. A factor of safety presents the primary key for slope stability analysis. The numerical results show that the drawdown reduction method used in the analyse effectively captures the progressive failure induced by reservoir dead load and water level fluctuations. Given the obtained results, when studying the problems related to slope stability in earth/rock-fill dams, it is recommended that inspections be carried out on the Akosombo dam during its life.

Dams are very important in Ghana's economic development and environmental improvement. Although Ghana dams are seismically far from the active zone, accurately analysed dams should be evaluated since failure could severely impact the people in the flood environment and the region's economy on a large scale. This paper proposes a numerical procedure for the static, slope stability, and dynamic analysis of the Akosombo embankment dam. Nineteen horizontal acceleration time histories recorded data was used based on Maximum Design Earthquake (MDE), Maximum Credible Earthquake (MCE), Design Basis Earthquake (DBE) and Operating Basis Earthquake (OBE) data. The numerical results estimated showed that the Akosombo embankment dam is likely to experience moderate deformations during the different design earthquakes. The result also indicated that nonlinear analysis capable of capturing dominant non-linear mechanisms could be used to assess the stability of embankment dams. The factor of safety (FS) calculated was greater than 1.5 for high reservoir, rapid drawdown condition and low reservoir condition whereas, the FS values were found to be 1.42 for slow drawdown condition.

…………………………………………………………………………………………………….... Introduction:-
Stability and crest displacements of embankment dams is a significant concern in every region. Seismic-induced deformations in a rockfill embankment dam may lead to overtopping and massive losses of built environments and people living along the dam paths. However, in recent years, the availability of seismic hazard maps and different design criteria have led to assessing the seismic safety of dams built without considering seismic-induced forces. Consequently, the adequately designed remedies have posed a challenging problem for geotechnical engineers. A standard manual on world register dams provided by the International Commission on Large Dams (ICOLD) has about 95 member countries, including Ghana, which defined dams with a measured height of more than 15 m or between 5 and 15 m whose reservoir capacities greater than 3 million m 3 as "large dams". Presently about 60,000 large dams have been registered (Wang et al., 2021), and 1,949 are in Africa. Skinner et al. (2009) report showed that West Africa has over 150 large dams constructed on their region's river.
Akosombo Dam is the largest dam in West Africa located on the Volta River in Ghana, with a wall height of 134 m (4th in Africa) and a capacity of 150 billion cubic metres (3rd in Africa). Akosombo dam is a rockfill embankment dam, about 82 km north of Accra city in the southeast of Ghana (Fig. 1). The dam has a crest length of 640 m, a crest width of 12.2 m, and a 114 m maximum structural height above the foundation level, completed in 1965. The ISSN: 2320-5407 Int. J. Adv. Res. 9(10), 639-655 640 reservoir is used for providing electricity for the host environment. The construction of embankment dams is more recognised globally with some advantages over other dams (Narita, 2000), i.e., the foundation does not require rigorous conditions. The embankment dams can be placed on alluvial deposits and pervious foundations. They can be constructed on the outskirts of the city area.
The Knowledge of different specialists (engineering, hydrology, geophysics, geology, and soil mechanics) is required for the construction of an earth-fill (embankment) dam that can provide safety and constant critical surveillance of dam reservoir and foundation during its lifetime (Ebrahimian, 2011). However, the highest responsibility belongs to the seismic designers. Dams' failure can lead to a severe loss of human and properties. The failures may be caused by structural deficiencies in the dam body due to poor design or construction, age of the dams, sliding of slope and instability, and overtopping (Shikhare et al., 2009).
However, a record shown considerable numbers of embankment dams have been damaged in different countries due to earthquakes (Gosschalk 1994). This call for a better method to enhance the stability of existing dams. The standard method used for the seismic design of earth dams was erroneous based on the assumption that dam bodies are fixed on a rigid foundation, thereby experiencing a uniform acceleration equal to the underlain-ground acceleration (Gazetas, 1985).
However, research has shown that the response of dams under earthquakes depends on the constructed materials, the geometry, and the base motion's nature. Therefore, many studies have been carried out to understand the seismic behaviour of earth and rockfill embankment dams. Newmark (1965) was the first to carry out the effects of earthquakes on dams and embankments. He used a sliding block method to evaluate the likely performance of the earth and the embankment dam. Lin and Whitman (1986) assess earthquake-induced permanent displacement using sliding blocks.
However, since the advent of more sophisticated and fast computer programmes, effective modelling, and testing, an increasing number of studies on earth (rockfill) dams using numerical methods such as finite element, finite difference, and boundary element methods with non-linear material models (Sengupta,  This study investigated the Ambar earth dam's dynamic response and earthquake resistance in the southeast part of Turkey using the non-linear dynamic time-history of Bingol (2003) earthquake and modal analysis methods. The dam was analysed under static conditions and dynamic analysis. The PGA responses caused by maximum design earthquake (MDE) applied to the dam body, impervious core, and foundation.
They showed that the Ambar dam might likely experience moderate deformations during the design earthquake but stable after the earthquake. Afiri and Gabi (2018); Afiri et al. (2018) evaluated the slope stability analysis of Souk Tleta dam in north Algeria using the shear reduction method. They showed that large displacements occurred in the dam body and foundation at the end of construction and lowered during the reservoir filling. Also, the result showed that the factor of safety in different conditions decreases when the reservoir water level increases. Finally, Jin and Chi (2019) conducted seismic fragility analysis on high earth-rockfill dams using various ground motion records. They used a program called DYNE3WAC in combination with the Pastor-Zienkiewicz-Chan model and Biot dynamic consolidation theory to determine the vertical deformation of the dams. This paper investigates the dynamic response and earthquake resistance of the Akosombo embankment dam located in Asuogyaman Province, Ghana, using non-linear dynamic time histories. The dam was first analysed under static conditions and then performed acceleration-time histories of 19 earthquakes.
The PGA responses caused by maximum design earthquake (MDE), Maximum Credible Earthquake (MCE), Design Basis Earthquake (DBE) and Operating Basis Earthquake (OBE) were applied to the dam body, impervious core, and foundation, and the factor of safety was calculated by drawdown reduction method. The drawdown reduction method was used by Athani et al. (2015) to determine seepage and stability analyses of earth dam using PLAXIS 3D Finite element method.

Geology of the Dam Site
The geology of the dam bodies' foundation, lithology, stratigraphy, and soil parameters need to be assessed during analysis. A high degree of judgment is required to evaluate the soil characteristics through comprehensive field observation and laboratory tests (Ozkan et al. 1996; Selçuk and Terzi, 2015). To construct the cofferdams for Akosombo Dam, the entire bedrock surface was stripped of a thick deposit of sand alluvium using machine at a depth of 200 feet below the water surface.
The upstream and downstream cofferdams formed by end dumping methods at depths varied from 30.48 m in the upstream to 60.96 m at the downstream. The clay core of Akosombo dam was compacted at moisture content slightly wet to 2 percent wet of optimum and compacted rockfill was sluiced at a water to cement ratio of 0.5 to 1.0. The field density of Akosombo core was put at 0.80 frequency of test at 764.555 m 3 (Wilson and Squier 1984). The shell is made of compacted or dumped rockfill, while filter materials are of fine and coarse materials.

Geometry of the Dam and soil Properties
When assessing the safety threshold value of any structure, the most critical factor is the deformation that occurs under seismic effects at which the accelerations change at various locations. Therefore, an accurately designed dam should detect the accelerations at the critical area of the dam under investigation (Selçuk and Terzi, 2015). The schematic cross-section of the Akosombo dam and the foundation layer used in this paper is shown in Fig. 2.
The geometrical features are provided in Table 1. The geotechnical parameters of the slope layers are determined using engineering experience obtained from the literature. The necessary parameters for the slope stability analysis and design are presented in Table 2. Only the geotechnical parameters and properties that concern the dam's slope stability analysis are specified in this study. The permeability (k) of dam materials used the standard values were taken from the engineering perspective.

Seismic activity in and around the dam site
Numerical estimation of permanent displacement of a proposed or existing earth/rockfill embankment dams requires an enormous task, mainly when information on field data is lacking. The seismic hazard assessment performed by probabilistic seismic hazard analysis (Cornell, 1968, andMcGuire, 1995) considers all possible earthquake scenarios affecting the site.
The seismic hazards estimated are represented by peak ground acceleration. Therefore, to assess the dynamic response of the Akosombo Dam, it is necessary to consider the seismic risk in and around the region.

Numerical Analysis
The dynamic performance of dams using numerical analysis to estimate the crest settlement requires a more sophisticated approach (Kan and Taiebat, 2011). For the seismic design of the dams and its appurtenant structures, the following design earthquakes were considered as recommended by Wieland (2012). 1. Operating Basis Earthquake (OBE): The OBE design is used where earthquake damage to a dam project is limited, where the mean value of ground motion is determined from a probabilistic seismic hazard analysis 644 (PSHA). According to ICOLD, 2010, the OBE should be designed at an average return period of 145 years (i.e., 50% probability of exceedance in 100 years). 2. Design Basis Earthquake (DBE): The DBE is designed for a return period of 475 years for dam and its appurtenant structures. The DBE mean value of ground motion parameters is estimated based on a PSHA. (i.e., the return period of the DBE usually determined based on the earthquake codes and regulations for buildings and bridges in any project region.). The ground motions for a 2% probability of exceedance within 50 years, which is equivalent to 2475 years of return period is also considered for the design earthquake in this study. 3. Maximum Credible Earthquake (MCE): The earthquake selected for dam structure whose return period is 2475 years. The earthquake that can reasonably expected to occur along a recognised fault or supported by known geologic and seismologic data. A hypothetical probabilistic earthquake is considered since the event is random, and its epicentral distance is determined mathematically by relationships of recurrence and magnitude for this study dam. Within all the frameworks of these assessments for the Akosombo seismic design considering the OBE, DBE, MCE and MDE, the peak ground acceleration earthquake coefficient was estimated as 0.03g, 0.08g, 0.21g and 0.39g respectively for 145, 475, 2475 and 10,000 years return periods. The input earthquake motions were compiled from a real accelerograms (  (Fig. 4) processed by Seism-Signal 2021, were used for the dynamic analysis using Plaxis 2D. The total displacement of the dam crest was chosen as Engineering Demand parameter (EDP). The response spectra estimated from the hard rock site conditions were compared with the 19 response spectra for the different return periods (Fig. 5).

Dynamic Analysis Results
Dynamic deformation analysis was considered incremental stresses as a driving force for permanent deformation based on stress redistribution. According to Rampello et al. (2009), permanent displacements have resulted from 647 plastic strains that accumulated during the earthquake because of progressive plastic loading, which are influenced by the duration of the strong motion. In the dynamic evaluations, the crest behaviour was selected as the parameter to represent earthquake-related deformations because it is the most frequently mentioned quantified measurement of damage presented in dam studies. The amount of crest settlement is related primarily to two factors: the peak ground acceleration at the dam site and the magnitude of the causative earthquake (Selçuk and Terzi, 2015). The computed total displacements along the dam body for MDE, DBE, MCE and OBE values are shown in Fig. (7-10).
As seen in Fig. (7-10), displacements increased with the increased height of the dam. When the dam section undergoes strong base excitation, a slump usually take place rather than failure along a discrete surface. Based on this study, permanent deformations are concentrated in the dam crest. In general, according to the literature, when earthquake shaking occurred in a dam site, the settlements at the crest of an embankment dam should not exceed 1 or 2% of the dam height. The dynamic analysis using nineteen values of PGA showed that the instability of the Akosombo dam took place along the crest where the maximum settlement occurred in the core of the dam. From the dynamic analysis, the analyses show the effect of deformation at the dam body. The estimated total displacements and displacement in horizontal directions of Akosombo dam are listed in Table 4.  The effects of different 19 earthquakes (Table 3) on the total displacements at the crest of Akosombo dam with different horizontal peak ground accelerations are shown in Fig. 11.

ISSN: 2320-5407
Int. J. Adv. Res. 9(10), 639-655 649 The peak ground acceleration varied with the displacement. The total displacements and peak ground acceleration increase at the dam crest. The horizontal peak ground accelerations and numerical calculated horizontal displacements are shown in Fig. 12. It can note that in (Fig.11-12), the maximum peak ground acceleration does not lead to an increase in permanent displacement in the dam body.
The total deformation is estimated larger (0.47 m) when the horizontal peak acceleration is 0.29 g for the Imperial Valley earthquake. Similarly, three earthquakes (Nahanni, Oroville, and Helena-Montana) are responsible for the large horizontal displacements in the numerical estimation of the Akosombo dam with the PGA values of 0.15 g, 0.08 g, and 0.034 g, respectively.

Slope Stability and Results
The safety factor Akosombo dam was assessed for the dam cross section of the greater height and computed using the 'φc reduction' procedure. For each phase condition, appropriate slope stability analysis is computed based on shear strength reduction method using FEM Plaxis 2D. The acceptable minimum value for safety for end of construction and multistage loading is around 1.3 . According to USBR (2019), if a static factor of safety against slope instability is greater than 1.5, it is regarded as less likely to damage deformation. (a) 652

Steady State Condition at High Reservoir
In this first stage, stability analysis was performed for the slopes of the dam for two dam points, as shown in Fig. 13, to optimize the volume of the dam body and materials. Gravity loading was used to calculate initial stresses and initial pressure of the dam under normal working condition. The slope analysis results under the steady state of high reservoir give a maximum safety factor of 1.72. For this study, the results of the finite element analyses are illustrated in Fig.14 (a-b). The dam body undergoes a maximum displacement of 2.2m due to the dead load of dam, and the settlement of different zones and foundation of the structure. The calculation of the displacements during this step is necessary because the imposed loads are very high which cause instability and even to a slope failure.

Rapid Drawdown Under the Maximum Water Level
Rapid drawdown condition was used to compute the stability of the dam when the reservoir water level was at the maximum of 84.73 m. The water pressure distribution in the dam is calculated using fully coupled flow-deformation analysis by assigning 5 days value for the Time interval parameter with a reduced head water of 50 m. The computed groundwater for the pore pressure distribution after the rapid drawdown of the reservoir as well the displacement at the dam maximum water level is illustrated in Fig. 15 (a-b). The slope analysis results under the rapid drawdown condition give a safety factor of 1.75.

Slow Drawdown Under the Maximum Water Level
Slow drawdown condition was used to determine the stability of the dam when the reservoir water level was at 84.73 m. The water pressure distribution in the dam is also calculated by fully coupled flow-deformation analysis by assigning 30 days value for the Time interval parameter when the head water reduced to 50 m. When the reservoir filling at the maximum level, the lowest factor of safety of 1.42 is observed. The groundwater computed for the pore pressure distribution under the slow drawdown condition of the reservoir and the deformation estimated are shown in Fig.16.

Low Water Level
A long term situated was considered to estimate the stability of the Akosombo dam when the reservoir water level was at 34.73m. The steady groundwater flow in the dam was calculated using plastic option. The numerical value under the water low level gives a safety factor of 1.74 for all the selected points. The groundwater computed for the pore pressure distribution under the low-level water reservoir and the maximum deformation experienced by the low level are illustrated in Fig.17. The behaviour of the Akosombo dam for all the conditions estimated, the displacements that occurred by water pressure in the dam body and foundation are observed. The maximum displacements are 2.2, 0.45, 2.2 and 0.24 for high reservoir under gravity loading, raid drawdown, slow drawdown, and lowest water level conditions, respectively. Factor of safety for all examined analysed conditions are shown in Fig.18. The results show that the safety factor of the dam decreased when the water level was in slow drawdown condition in the reservoir. The

Conclusions:-
A preliminary study of the dynamic response of the Akosombo dam was obtained by Plaxis 2D finite element analysis using 19 spectrum earthquake motions. According to the proposed seismic hazard map of southern Ghana, the site of Akosombo dam is situated in a moderate hazard.
The results obtained under the dynamic behaviour of the Akosombo dam provides an adequate basis for the deformations of the dam using different conditions of design earthquakes data. The results showed that deformations increased at the crest of the dam. The present study also aimed to numerically examine the slope stability of the Akosombo earth dam under the drawdown reduction method by Plaxis two-dimensional software. The strength for each load case combination of the dam is expressed through safety factors. Analysing the static stimulation of Akosombo dam using the drawdown principle, displacements and corresponding safety factors are obtained at the high reservoir, reservoir filling, and low water level conditions. The dam body and its foundation parameters used for the analysis are based on engineering properties determined from the literature. The total displacements are significant when studying most of the geotechnical problems. It is particularly recommended that laboratory tests be performed for the dam site conditions. The numerical results show that lower displacements occurred in the dam body and foundation through impounding. A factor of safety presents the primary key for slope stability analysis.
The numerical results show that the drawdown reduction method used in the analyse effectively captures the progressive failure induced by reservoir dead load and water level fluctuations. Given the obtained results, when studying the problems related to slope stability in earth/rock-fill dams, it is recommended that inspections be carried out on the Akosombo dam during its service life.