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5.1 The safety factors have to be estimated in all slope stability analysis problems, or even a rough estimate of the factor of safety may be sufficient for preliminary studies in some cases. Moreover, to establish the safety factor, it is required to obtain information about the slope characteristics and slope geometry as the slope material, configuration, and loading conditions.In general, the methods used for slope stability analysis can be divided into three broad categories. These categories are:1) Limit Equilibrium Method,2) Limit Analysis Method and3) Finite Element Method.Finite element method is the most reliable technique in determining the safety factor due to its versatility, robustness, and ability to model material and/or geometric nonlinearities. However, the finite element method could be time consuming, especially when dealing with complex geometry, or in case of nonlinear materials. A comprehensive investigation of the published slope stability analysis techniques is presented in Chapter (2).The objective of this research is to present a general equation to determine the factor of safety in slopes through assessment of a large number of factors that affect the slope stability. These factors include; slope geometry and configuration, soil properties, embankment loading and its extension, and the presence of water table in case of assessing the stability of waterways. The developed equation is an outcome of a total of about 15,000 analysis runs performed using the computer program PLAXIS to obtain the safety factors, and covering all the above mentioned slope and soil parameters. In addition, the effect of soil reinforcement on the stability of earth slopes is also presented and discussed. In this chapter, the research conclusions and the recommendations for further studies are outlined and discussed in the following sections. 5.2 CONCLUSIONS Based on the results obtained from finite element analysis by the use of the finite element code (PLAXIS), the following conclusions can be drawn:1- Soil Shear strength parameters (c,??) are directly proportional with the safety factor. If the shear strength parameters increased by 100%, an average increase of about 35 to 50% in the safety factor will be obtained.2- For low slope heights, H = 5 to 10 m, if the soil shear strength parameters are increased by 100%, an increase of the safety factor of about 100% would be obtained. Increasing the slope height from 5 to 10 meters, resulted in a reduction in the safety factor of about 35%, this reduction reached about 60% when increasing the slope height from 10 to 20 m. Therefore, slope height is an effective parameter in the slope stability problems and it is inversely proportional with the safety factor.3- Smaller slope angles resulted in higher slope safety factors. For gentle slopes, the effect of increasing the soil shear strength parameters is more pronounced. However, for steeper slopes, increasing the shear strength parameters has slight effect on the safety factors.4- The effect of the presence of surface loads on the safety factor is slight, that if the surface loads are increased by 10 times, a decrease in the safety factor of about 25% will be obtained. In the meantime, for very high loading values, the embankment bearing capacity should be checked along with the stability analysis. However, when the loads are applied at about 1.5 H away from the slope crest, the loading extension or intensity has no apparent effect on the factor of safety of that slope.5- The effect of increasing the soil angle of dilation (?) to be equal to the soil angle of internal friction (?) results in only 3% increase in the safety factor and this meets the results of Glamen et al., 2004 and Manzari and Nour 2000. On the other hand, the effect of the soil stress-strain modulus (E) is found to be negligible in the safety factor of slopes.6- The relation between the water level in the waterway and the safety factor is a nonlinear relation. The critical value of the safety factor is encountered when the slope is saturated and the waterway is empty (Rapid Drawdown case). On the other hand, for the highest water level, the increase in the factor of safety due to the presence of water in the water way is found to be about 100%.7- The shear band zone is strongly related to the presence of soil cohesion (c), the higher the soil cohesion is, the deeper and wider the shear band. In (?) slopes, the shear band is not clearly defined, only a failure wedge could be accurately observed. Keeping the soil angle of internal friction constant, while increasing the soil cohesion resulted in switching the failure surface from face failure to toe failure, then base failure. It should be noted that toe failure is the most common type of slope failure, assuring that the toe point is a stress concentration point, at which failure usually initiates.8- Based on the finite element method (FEM), through the finite element code (PLAXIS), a general equation for the assessment of the factor of safety in slope stability problems is obtained. The proposed equation contains most of the parameters affecting the stability of slopes. This general equation is presented as:F.S = eThe proposed equation has a coefficient of multiple determination R2 = 0.96543, which is satisfactory when fitting of the huge data volume obtained from PLAXIS results. The proposed equation is verified by comparing the calculated values obtained from that equation with PLAXIS results, and the maximum difference was about ±4%. Moreover, the results calculated from the proposed equation are compared with the results from Michalowski Charts (2002) and the maximum difference was about 7% in the conservative side, despite employing different analysis approaches.9- For most (c and c-?) slopes, arranging the reinforcement in the middle third of the embankment has a great influence on the safety factor. For (?) slopes, the reinforcement layers and grids should be condensed at the lower third. Generally, if the slope angle is smaller than (65o), the reinforcement layers should be arranged and condensed in the middle half of the slope height. The middle half in this case is that starts above the lower quarter and extends up to the lower edge of the upper quarter. For slope angles larger than (65o), the reinforcement layers should be condensed in the lower third of the slope.10- The safety factor is inversely proportional with the vertical distance between the reinforcement layers.5.3 RECOMMENDATIONS FOR FURTHER STUDIESDue to the importance and versatility of the slope stability analysis and assessment, further studies are always needed. These further studies include:1) Employing another finite element code to asses the developed equation. In addition to applying the two finite element codes in including the effect of soil reinforcement in the proposed equation.2) Extending the studies to include the effect of earthquakes of different magnitudes on the stability of slopes, either numerically or experimentally using the shaking table or centrifuge.3) Using finite element method to obtain a design charts for layered and reinforced earth slopes and including the effect of dynamic forces.4) Further research for the estimation of the slope soil bearing capacity will enhance understanding the soil behavior in such case, and will lead to more accurate estimation of the bearing capacity.5) More researches are required for the analysis of the shear band and the failure mechanism, and consequently the assessment of deformations that would occur in such slope.6) Three-dimensional analysis of slopes is always needed, mainly because the failure surface is usually limited to some extent in the third direction.7) Employing the neural network technique for the assessment of the stability of slopes problems.
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