Assessments of Geotechnical Condition of Landslide Sites and Slope Stability Analysis Using Limit Equilibrium Method around Gundwin Town Area, Northwestern Ethiopia

: The study area is located in northwestern Ethiopia where landslide incidence is active. The landslide incidence in the area resulted in the devastation of 233.1 hectares cultivated and non-cultivated land, death of eight people, demolition of five houses, displaced 90 households, and 45 households are under risk. The slope failure in this area also caused tilting of the power line, tilting of two houses, cracking of three-houses floor, failed of bridge and blocking of streams as well as springs. The purpose of this research is to evaluate the cause, failure mechanism, landslide distribution, geotechnical condition of the site, slope stability analysis and factor of safety determination. Soil sampling, laboratory test, terrain characteristics, groundwater-surface manifestation characterization, groundwater depth determination, slope stability analysis and factor of safety calculation were the most important activities employed in this research work. Using disturbed and undisturbed soil samples of the selected slope section, Atterberg limit (liquid limit & plastic limit), natural soil moisture, unit weight, specific gravity, and shear strength parameters (cohesion & internal friction angle) test were carryout as ASTM standard. The most marginal factor of safety of the area is determined based on the general limit equilibrium method that encompasses different methods inside using slope/w in GeoStudio 2018 software package considering various groundwater conditions for all selected slope sections. The factor of safety for all selected slope sections of the various method under different groundwater conditions is less than one. Based on the finding of field observation and laboratory results, landslide types (rock/soil slides, rock/earth fall, debris/earth flow, & soil creeping) and landslide factors of the study area (slope angle, slope shape, slope modification, land use, groundwater, soil type, and rainfall) are determined. This research finds out that the soil has a great contribution to slope failure in the study area, besides the soil moisture and improper land use practice.


Introduction
The population growth rate around the world is alertly increasing from year to year. The demand for new lands for different purposes also increased in parallel. These bring slope geometry and environmental changes. The environmental and slope geometry changes also bring different natural hazards like slope instability, flooding, and drought. Among these, a landslide is one of the risky hazards that happens because of natural and manmade factors. Natural slope, which has been stable for many years, might befall due to change in slope geometry, loss shear strength of slope material, and an external [1]. The natural slope will also fall due to the combined effects of intense rainfall, steep topography, and soil condition [14]. Landslide is common in countries, which have fragile topography, complex geology, active gully and riverbank erosion, intense rainfall, and improper land utilization practice like Ethiopia. These conditions caused the country to have influenced by landslide incidence frequently. The study area is a part of northwestern Ethiopia, which has severely affected by landslide incidence. The landslide can cause damage in huge engineering structures, infrastructures, farmlands, villages, human beings, can block river channel, and road corridors. These all directly and indirectly retards the socio-economic growth of the countries around the world, particularly in developing countries like Ethiopia. In 2018, rainfall trigger landslide caused the death of 62 people, 30 people have injured, 5,091 households have displaced, damages of houses and wide cultivated farmland and non-cultivated land in a different part of the country. The landslide in the study area also caused damage in 233.1-hectare farmland, the death of eight people, one animal, destruction of five houses, block river channel, and springs. To minimize these damages due to a landslide, the various techniques have developed like qualitative (expert based/heuristic approach) and quantitative (statistical and deterministic/geotechnical approaches) that helps to identify the landslide-prone area in a given region. However, each technique has its own merit and demerit. The statistical approach is important to determine the spatial distribution of landslide and its relationship with different conditioning and triggering landslide factors. These methods are also important in areas, where geotechnical data-scarce and the area is relatively large. However, this method did not provide a factor of safety, which provide information about the slope material. This limitation can solve using geotechnical approaches. The geotechnical approach is best when the area is small and accessible. It provides a numerical value that explains the inherent condition of the slope material, unlike statistical approaches. However, it is expensive and time-consuming. Slope stability analysis using the limit equilibrium method is an important activity that helps us to check the slope stability condition by calculating the factor of safety from the ratio of resistance to driving force. Slope stability analysis can perform using limit equilibrium and finite element numerical methods. The limit equilibrium method is one of the oldest and the best well-known numerical methods that has been using routinely in geotechnical engineering work because of its simplistic and accuracy results ( [10]. However, it cannot help to determine the response of the ground under stress. For this purpose finite element method is preferable. Furthermore, limit equilibrium method is better when the analysis not expected material response under stress whereas the finite element method is appropriate when the analysis considers mechanical responses of the materials [10]. Hence the main objective of the present work is to characterize the geotechnical properties of soil and to calculate the factor of safety on failed slope section, general limit equilibrium method that encompasses various methods inside because of the assumption of inter slice force and the equation of statics have employed.

Description of the Study Area
Goncha Siso Eneses area is located in Northwestern Ethiopia and can access through Addis Ababa -Dejen -Gundeweyin -Mota asphalted road (Fig 1). However, it is important to use a gravel road to reach the exact landslide sites.
The area is bounded in between 37.9° E to 38.39° E longitude and 10.8° N to 11.06° N latitude. It has covered by scattering small bushes and a large tree. Goncha Siso Eneses area has characterized by tropical (<1,830m), subtropical (1,830 -2,440m) and cool (> 2,440m) climate zone. Annual rainfall varies from 762 mm -1,824mm. The annual rainfall distribution showed pronounced seasonality with the heaviest rainfall being in July and August. The mean temperature of the area is 18.50 0c with a mean minimum and maximum daily temperature of 11.40 0c and 25.50 0c respectively [3].

Satellite Image Interpretation
Satellite images of the study area were analyzed and interpreted to identify the spatial distribution of landslide in the area. This is performed using Google Earth Image analysis tools.

Landslide Inventory Mapping
The landslide inventory map of the study area is prepared using intensive fieldwork and detail Google Earth Image interpretation using the time slide series in the tool. Then the final landslide inventory map is prepared using GIS software.

Slope Stability Analysis
For the purpose of slope stability analysis, eight undisturbed soil samples were prepared and tested using direct shear strength test equipment.

IJSTR-0120-29607
The fourth unit is highly weathered basalt, which has aphanitic and porphyritic texture. The color of highly weathered basalt is brown, reddish, dark gray weathered color and black fresh sample color. Hence, the area covered by loose unconsolidated residual soil deposit; it is exposed only on a stream, gully erosion, road, and hillside.
This unit covered a large portion of the study area and contains rock fragments, fine and coarse soil particles formed by the surficial process. Red paleosol and unconsolidated tuff rock unit found associated with this rock unit. This unit is highly affected by the surficial process like weathering, and erosion. The springs are emanated at the contact of the paleosol and unconsolidated tuff rock unit.
The fifth unit is slightly weathered basalt that has aphanitic texture, brown, gray and dark color in weathered and fresh color respectively. This unit exposed at the cliff-forming topography and characterized by columnar joint and massiveness.
It covered by shallow soil mass and resulted in a shallow landslide in the area. The springs are emanated from the contact of this unit and unconsolidated tuff rock unit. This unit contains top detached rock blocks and failed rock fragments at the toe of the slope.
The six-unit is Tuff rock, which found in the northeast, southeast and central parts of the study area with a very small aerial extent. It is dark light and whitish weathered and fresh colors respectively. It is a highly weathered rock unit, which exposed at a road cut, stream erosion, and hillside.

Area
Ethiopia has a lot perineal and in perineal rivers that sourced from the mountain peak and has diversified lakes as well as springs in the rift,

Landslide Inventory
The Inventory data in the study area has collected using a detail field survey and Google Earth image

Landslide in Inegode Village
Inegode is one of the areas that has been severely affected by landslide incidence, especially along

Landslide in Angot Village
Angot is one of the areas that have severely affected by rockfall, debris and earthflow types of landslide incidence. This slide caused by heavy rainfall, spring, stream overflow, agricultural activities, river cut, slope shape and slope escarpment. Since the area is characterized by steep escarpment and highly concave upwards, rainwater can be impounded and infiltered into the sloping ground, which is then exposed at the slope toe.
The flowing of shallow groundwater inside the slope causes slope material saturation, piping and pore water pressure development. These all caused soil strength reduction and a slope material movement. Earthflow and debris flow are the common landslide incidence in the area but later the whole slope materials are developed tensional cracks, curved cracks, and uneven surface. The spring that was blocked by a landslide has been exposed at the slope toe and flows towards the river. This will also cause piping and slope toe erosion. The combination of all landslide caused damages in 120-hectare farmland that has covered by various crops and permanent fruits. The slowly moving ground was blocked the spring water and has been interrupted the irrigation activities.

Soil Moisture
This test is used to verify the natural moisture condition of the failure slope section in the study area. The moisture content test was performed for an undisturbed soil sample of DB03, DY03, and TM03 of the slope section for eight samples at various depth intervals. The average moisture content of the selected slope section ranges from 16% to 18% as can be seen in Table 3.

Specific Gravity of Soil
The specific gravity of soil in the selected slope section has been determined using a pycnometer with a specified temperature of distilled water.
This specific gravity also used for hydrometer analysis. Specific gravity can be calculated using  (Table 5).

Atterberg Limit Test
Atterberg limit test was performed for four-soil samples that have been taken from selected failed slope sections of DB03, DY03, TM03, and GS01 using Cone penetration and Casagrande rolling method for liquid limit and plastic limit according to ASTM D 4318 -00. The other driving limits (plasticity index and liquidity index) have been derived from the results of atterberg limit test.

Liquid Limit (LL)
The liquid limit test has been done for the selected failed slope section using a cone penetration method as the standard of the ASTM D 4318 for 500g soil fraction that passes through the sieve size of 0.425 mm. It was conducted for four-soil samples within three trials at a various moisture content of the soil. Using the moisture content and the cone penetration, d the flow curve has been plotted and the liquid limit is determined from the moisture content corresponding to d = 20mm.
The liquid limit of the soil in the study area ranges from 44 -59 % as indicated in  Table 4 Unit weight of soil

Plastic Limit (PL)
The plastic limit of the soil in the failed selected slope section of DB03, DY03, TM03, and GS01 is determined through repeated rolling of moist soil by hand on the ground glass plate until the soil crumbles as ASTM D 4318 standard and the result is presented in Table 7.

Plasticity Index (PI)
The plasticity index for the selected slope section is determined using the equation, PI = LL-PL.
Based on the [2], degree of soil plasticity classification as indicated in Table 6, the selected slope section falls under the medium to high plasticity classes.

Plasticity Chart
The plasticity chart is one of the most important relationships of the plasticity index and liquid limit which is developed by [4]. This chart helps us to separate silty soil from clay soil using the equation of A-line (PI = 0.73(LL-20)).
When the plasticity index and the liquid limit cross below A-line, the soil is inorganic silt or organic silt/clay with low, medium, high or very high plasticity and compressibility depending on the liquid limit value or when they cross each other above A-line, the soil is inorganic clay soil with low, intermediate, high or very high plasticity and compressibility [4].
He also states the zone of plasticity and compressibility based on the liquid limit of the Based on the Cassagrande's expression, the present soil plasticity index is fall below A-line of inorganic silty/organic clay soil with intermediate to high plasticity and compressibility (Fig 12). As a result of the liquid limit indicated in Table 7

Liquidity Index (LI)
Using liquid limit (LL), plastic limit (PL) and natural moisture content (w) result, the liquidity index of the soils for the selected failed slope section is calculated using the following formula.  Table 7, which is in a liquid state with very low strength.

Compression Index
The compressibility of soil is one of the engineering properties of soils that can be determined using the odometer test but it is timeconsuming, expensive and requires undisturbed soil samples. The compression index has a good relationship with a liquid limit, plasticity index, and shrinkage index [13; 16].
In this study, the compressibility condition of the soil was estimated using atterberg limit test. The compression index of the selected slope section of the study area was calculated using both the value of liquid limit and plasticity index values using the formula that has been used by [13; 16] i.e., Cc = 0.007 (LL-10) and Cc = 0.014 ( PI+3.6).
Using the relationship of compression index (Cc), liquid limit, and a plasticity index value, linear regression graphs have been plotted in Fig 11. The result of both liquid limit and plasticity index linear regression graph is indicated that both variables have a good relationship (Fig 11). As indicated in Table 7, the compression index is increased as the liquid limit and plasticity index values are increased. Therefore, from this relationship, we can conclude that the higher the liquid limit and plasticity index, the higher will be the compressibility  Note: PL-plastic limit, LLliquid limit, PIplasticity index, LIliquidity index, Aactivity and Cccompression index

Direct Shear Strength Test
In this study, shear strength parameters like cohesion and angle of internal friction in the selected failed slope sections have been determined from the direct shear strength test as shown in Table 8.

Slope Stability Analysis
The slope stability analysis in the selected slope section performed based on the input data (cohesion, internal friction angle, unit weight of soil, and groundwater condition using slope/w methods as can be seen in Fig. 23. For the calculation of factor of safety using slope/w software, the first task is to determine the input parameters followed by defining geometry, region/material, pore water pressure, and trial slip surface. These can be described in the following sections.

Geometry
Defining a working area with appropriate geometry, scale and unit are the most important activities to be done in slope stability analysis.
This is the process to define the physically admissible ideal slope geometry of the study area.
The geometry of an ideal slope was defined using points and polygons based on the scale of 1 to 2 and 15m slope height. If these points or polygons are not defined in the correct position, our model will be wrong. It needs great care to define this ideal geometry as illustrated in Fig 13.

Material
The material statement is one of the key elements in slope/w analysis. Various ways are available to define material in the slope stability analysis like Mohr's coulomb, undrained strength, and bedrock (impenetrable material) which depends information, the soil in the study area is more or less homogeneous. Therefore, the material of the region was assumed as a homogeneous.

Pore Water Pressure
Defining the pore water pressure is one of the key

Critical Slip Surface
In slope stability analysis, defining the critical potential slip surface is a very important step to get a minimum safety factor in a selected slope section using slope/w software. This can be performed by applying various searching options like entering and exiting, grid and radius and block specified searching options [6]. However, in present slope modeling, a critical slip surface is defined using enter and exit search options ( Fig   15A). Because it is suitable and can be controlled by the user to adjust the slip surface search until the most critical slip surface is found. The critical slip surface location, extent and shape can affect by the shear strength parameters.

Ordinary Method (OM)
As indicated in Table 10, this method was applied to calculate the factor of safety for selected failed slope sections under various groundwater conditions but it does not consider both normal and shear inter slice forces (Fig. 17), and not satisfy force in equilibrium (Fig. 22). Thus, it has not provided a factor of safety vs lambda graph because lambda is undefined (Fig. 22).
The ordinary method satisfies only the equation of moment in equilibrium (Fig. 22). The force polygon closure is not possible as can be seen in the free body diagram in Fig. 17  poor. This can help to conclude that an ordinary method will not satisfy the overall force equilibrium.
The factors of safety, calculated in this method, is unrealistic because the force polygon closure is so poor which means each slice is not in force equilibrium (Fig. 17).

Bishop Method (BM)
This method satisfies the overall moment equilibrium ( Fig. 22) but it does not satisfy the horizontal force equilibrium. It has inter slice normal force but not inter slice shear force ( Figure   18). The force polygon closure was examined under similar slice number, which is good unlike ordinary. The sliding masses are almost in horizontal force equilibrium (Fig. 22).
In the case of a factor of safety vs lambda graph, unlike ordinary-simplified method, Bishop's simplified method factor of safety falls in the moment equilibrium curve when lambda is zero (Fig. 22). IJSTR-0120-29607

Factors of Safety Computation Using Janbu Simplified Method (JM)
As indicated in Fig. 22, Janbu simplified method is the third limit equilibrium method that is satisfied only with the overall horizontal force in equilibrium. This method considers inter slice normal force like Bishop but it is ignored inter slice shear force (Fig. 19). As shown in Fig. 19, the force polygon closure in this method is better than the Bishop's simplified method. Thus, the slice of the slide mass is in horizontal force equilibrium.
As designated in Fig. 22 and Table 10, the factor of safety of Janbu is lower than the Bishop simplified method because the force in equilibrium in the Jambu method is sensitive to inter slice shear force. Its ignorance of the inter slice shear force is the cause for reduction of a factor of safety in the Janbu simplified method, however, Bishop's simplified method satisfied the overall moment in equilibrium and as a result, it is not sensitive for inter slice shear force in a circular slip surface

Spencer Method (SM)
This method satisfied both moment and force in equilibrium (Fig. 22). This method is considers both inter slice force (Fig. 20) and adopted the constant relationship between inter slice shear and normal force.
As indicated in Fig. 20, it has quite good force polygon closure. Therefore, all slices are in force equilibrium. Unlike Bishop and Janbu, the value of lambda is greater than zero (Fig. 22). Meaning, this method has both inter slice shear and normal force because lambda is the ratio of inter slice shear to the inter slice normal force. This method is used to calculate two factors of safety like the factor of safety with respect to moment and force equilibrium (Fig. 22).

Fig. 20 Free body diagram and force polygon closure in Spencer method
Inter slice normal force (E2) E 1 Fig. 19 Free body diagram and force polygon closure in Janbu Method IJSTR-0120-29607

Morgenstern Price Method (MPM)
This method satisfied the overall moment and force equilibrium (Fig. 22). This method has considered both inter slice force and has very good force polygon closure (Fig. 21). It is so important to calculate all possible factors of safety and to plot the factor of safety versus the lambda graph (Fig. 22). Unlike Spencer, this method is allowed various inter slice force functions.
Therefore, this method is the best of all the other limit equilibrium methods. This method satisfies all equations of statics and used to plot the factor of safety vs lambda graph that is so important to compare the factor of safety in each method (Fig.   22). The factor of safety for all failed selected slope sections was calculated using slope/w software.
As we know that factor of safety is the ratio of resistance force to driving force and it depends on the slope condition, material properties and slope angle. As the result indicated in Table 10 and Fig   22 a factor of safety for all failed selected slope sections is less than one.

Selected Slope Sections
The minimum factor of safety and critical slip surface of three selected slope sections are calculated and searched for different limit equilibrium methods by considering various groundwater condition as indicated in Figure 25.
All potential safety factors that are calculated at different groundwater conditions using various methods have been summarized in Table 10.

Rainfall
Slope failure has occurred in the middle, end of July, August, and September with intense and prolonged rainfall in the study area. As indicated in the bar graph of Fig. 24

Groundwater
The groundwater aquifer zone of the area ranges Therefore, groundwater in the study area has a great role in slope stability.

Land use/cover
Landslide in the study area has occurred in lands This confirms that land use/cover has a great role in slope instability.

Slope and modification
The slope gradient of Debre Yakob, Debre Birhan,

Monthly rainfall
Besides, the slope gradient, the orientation and the shape of the slope have also a great effect on slope stability problems in the study area. In the study area, landslides are common in concave and convex slope shape. This is because of the hydraulic and gravity effect of the concave and convex shape of the slope. The concave upward slope enhanced rainwater ponding and infiltration into the soil mass. This further enhances the reduction of shear strength of soil mass in a slope.

Discussion
Characterization of the physical properties of the soil is important to deduce the engineering properties of soil at various conditions. For this purpose, atterberg limit test was performed. The The liquidity index of the soil is greater than 1 (Table 7) which is in a liquid state and characterized by poor strength. These showed that the soils would have high swelling and shrinkage potential. This implies, when the slope section is exposed to excess water, the soil will behaves like a liquid and causes the slope instability problem.
Based on the information from fieldwork and laboratory result, we can conclude that the soil in the study area is highly susceptible to a landslide.
The compressibility index of a selected slope section was calculated using a simple linear regression relationship equation of the compression index with liquid limit and plasticity index. As the analysis in Figure 14 showed, the liquid limit and plasticity index has good linear regression with a compression index. Therefore, the higher liquid limit and plasticity index in a given soil mass will have a high settlement. This also leads to slope instability under internal settlements of slope material.
The factor of safety that has been calculated under various groundwater conditions of the selected slope section is less than one. This again confirms that the soil mass in the selected slope section is inherently unstable.
Soil moisture is another key factor that controls slope stability. As soil moisture results indicated in Table 3, it increases with depth. This is because of the infiltration of rainwater into the ground, which increases the groundwater  (Table 10).
As indicated in Fig. 25 and Table 10, the factor of safety of Janbu's simplified method (JM) is less than Bishop's method (BM). This is because JM is sensitive to inter slice shear force in circular slip surface but BM is not sensitive for inter slice shear force for circular slip surface.
When we compare the factor of safety of all methods, BM has more or less similar safety factor with SM/MPM ( Fig. 26 and Table 10). This is because it is not sensitive for inter slice force function in circular slip surface. Among all methods, MPM method is preferable in slope stability analysis because it provides a factor of safety with various user selected force function and it provides a factor of safety against lambda graph that helps us to compare factor of safety for different methods. Therefore, it is advisable to use MPM than the other limit equilibrium methods in slope stability analysis because it satisfies all equation of statics. shear -normal force assumption used to plot factor of safety vs lambda graph, and allows users to select a variety of interslice force function.

Recommendation
Landslide susceptibility analysis without any preventive and mitigation measure is senseless in the scientific world. It has known that landslide is the result of the combination of two or more landslide conditioning factors.