Geotechnical Race Mesh and Incline Determination - Coursework Example

Advanced Geotechnics coursework Introduction Anisotropic soils are the type of soils that have different in the x, y and z directions and hence when considering a planer flow in which case the flow in the z-direction being neglected the flow can be represented by equation:  (1.0) The equation is not a Laplace equation as the flow is dependant on the ratios of horizontal and vertical permeabilities . As the equation is not a Laplace equation the solution of the equation using flownets does not have curvilinear squares and the crossings of flow and equipotential lines does not occur normally due to the fact that at the cross points the tangent to flow lines will not correspond the perpendicular line representing equipotential lines in contrast with the case of isotropic soils (Wooten et al, 1992).. To make the flow net in anisotropic soils be similar to that in isotropic soils it is necessary to choose to choose a coordinate system by creating an artificial domain (transformed section) where the representation of flow is Laplacian with the soil being isotropic. Stability The first step in the design of an embankment dam is assuring that the ground on which the dam is to be constructed is of desired stability. In many cases it is found that the embankment is supported by natural soil. Many problems that have been reported in embankments could easily have been preventable by early recognition of the problem and choosing the appropriate design. Stability problems have been found to be most common in situations where the embankment is resting on soft soils like low strength silts, peats and clays. The process of estimating the factor of safety involve soil profiling, establishing soils strength and establishing of ground water table through field explorations. If it is established that the embankment is unstable it is appropriate for measures to be taken to make the foundation soils stable. Infinite slope analysis This method is used where the extension of the slope is relatively over a long distance and the slope having a consistent subsurface profile. In such a case the failure plane is in parallel to the surface of the slope and this makes it possible for the limit equilibrium method to be applied readily. Infinite Slopes for dry cohesion less soils Figure I show a slice through a potential failure zone for a slope in a dry soil which is cohesionless like dry sand and the associated force polygon being as shown in figure 2. The weight of the slice whose width is b and its height being h and a unit dimension in the direction of page is given by h (1.1) In the equation  represents effective unit weight of the dry soil. Taking a slope with angle βas can be seen in figure 1 the normal and tangential force components of W can be determined by  and The shear strength along the failure plane can be given by The factor of safety abbreviated FS is the ratio of the available shear strength to the strength required so that stability can be maintained. Thus FS=  = =  =  As can be seen from the equation in case of an infinite slope analysis, the FS is not dependant on slope depth, h and is only dependant on internal friction of the soil and the slope angle, . The slope will be said to have reached limit equilibrium when FS=1.0. It is also clear that when FS=1.0 the maximum slope angle is restricted to the angle of internal friction. Infinite slope in cohesive soils and parallel seepage From the figure the pore water force that will act on the base of a typical slice that has a unit dimension in this page is expressed as Where h represents any depth that is equal or less than the depth of saturation and being a unit width. The friction strength, S, along the failure plane will be dependant on  and the effective normal force =N-U N being the total normal force. The equation for S is +(N-U)tan Thus the factor of safety will then be FS =  =  The calculation of seepage was governed by equation (1.1) which could be re-written to += 0 (1.2) In order to engender a simple Laplacian an adequate change of variable is used where the equation is re-written using  with c being a constant + = + (1.3) Or + = + (1.4) By comparing equation 1.2 and 1.4 the expression of c is identified as  (1.5) This is a clear indication of the flow being dependant on the ration of horizontal to vertical permeability with the associated flow net to the equation (1.2) has curvilinear quadrangles with side ration of  and this is seen in figure 1 where the length of 100 units in figure 2 corresponds to a length of approximately 58 units. The length of a 100 units has been found by considering that the full height of the embankment is 45m (35m +10m) as can seen from diagram appendix 1. Using the up stream slope the length along the base of the embankment at the boundary with the impermeable is calculated as  m as seen in figure 2. The length of 100m lies perpendicularly below the end point of the slope. The same length has been shortened in figure 1 by multiplying by  Thus the length of 100m is shortened to 100x = 58m as seen in figure 1. As observed from Figure 1 and Figure 2 transforming of the flow net makes the squares to be curvilinear. And after making the squares curvilinear it is now possible to apply the formula for seepage and the approximate amount of water that that is likely to seep through the embankment is established. While the untransformed flow net represent the real situation it is not useful in the calculation of the seepage. The other important aspect of the flow net is the establishing the squares of the flow net. This is an exercise that requires a lot of skills so as to have a flow net that can be used to predict the seepage with a small error. It is difficult to come up with a perfect flow net but the more modification is made so as to achieve curvilinear squares the higher the accuracy of predicting the seepage. The process of perfecting the flow net brings about the change in the number of equa-potential drops and flow channels which determine the ratio Nf/Nd and this in turn determine the seepage. Figure 1 Figure 2 Seepage calculations The quantity of seepage is given by Q =   is modified to  =   =   H is the head causing seepage and in this case it is taken as the height of the water level Q =  m3 Stability of slope Using infinite slopes (i)  (ii) (iii) Upstream slope stability Taking b and h to be unity and  and  and =24kpa Upstream slope angle is calculated as Thus  From equations (ii) and (iii) U = 8.96kn  From equation (i) =29.6kPa FS =  =  (iv) W= = 18.9kpa  = 3.84 Downstream slope stability Downstream slope angle is calculated as Taking b and h to be unity unit density of downstream soil and =9.6kPa Equation (i) will be modified to =  =14.18 Equation (iv) is modified to FS =  =  (iv) W is the unit weight of soil on downstream slope = 9.01  = 4.4 From the calculations it is clear that the upstream slope is much stable than the downstream slope. This stability has greatly been greatly been contributed by the angle of slope being higher at the upstream end. The effect of the angle could contribute to higher stability but the saturation of water in the upstream of the embankment makes it unstable. It should also be noted that while making the dam to be stables at the upstream through adjustment of the slope angle the cost of the building the embankment is put into consideration. Embankment with low slope is much stable but requires a huge amount of earthwork. The low slope will also increase seepage. Discussion In terms of stability of the embankment it is important to note that the water content of the soil at the time of compaction plays a vital role in the determination of its density, permeability, compressibility and the strength. This therefore means that the designing of an embankment is greatly influenced by the natural water content of the soil or the drying or wetting which can be done at the fill or before delivery to the fill. It is possible to reduce the natural water content to a certain extent in some instances the burrow soils may be excessively wet that it is not possible for them to be used in embankment without the lopes being flat. The amount of water in the soils also may affect the ability of the machinery used in hauling and compaction to operate to a satisfactory level. In designing and analysis of an embankment section it is required that shear strength and other properties of the soil be established at water content level and densities obtained during the construction process. in most projects the placement water contents will always fall in a range of 2% dry to 3%wet of optimum with a narrow range being required for soils having compaction curves with sharp peaks (Torrey, 1991). In the construction of embankment using water contents which are achievable in practice is a principal construction requirement but on the other hand the effect water has on the engineering properties of a compacted fill is a utmost importance in design. Soils whose compaction has been done when wet of optimum water content will have a tendency of exhibiting a plastic type of stress-strain behavior and there will be a likelihood having low strength in the construction stage with very high pore water pressure being experienced during this stage. On the other hand when compaction is done when the soils are dry of the optimum water content will tend to have a rigid stress strain bahaviour and will have high construction strength with very low porewater pressures at the stage of construction and will have less consolidation in comparison the soils which are compacted wet of optimum water content. However, in the case where compaction of soils is substantially dry of optimum water content there is high likelihood of occurrence undesirable when the soil is saturated. Cracks which occur in an embankment will be shallow and self healing for the case where compaction is on the wet side of the optimum water content as compared to the dry side. This is because of the low shear strength that is not able to support deep open cracks and as a result of the low deformation moduli. The stability of the earth dam during construction is highly determined by the Q strength (strength of embankment during construction). As it has been observed that the Q strength will be maximum in the cases where water contents is dry of optimum with a decrease with an increase in water content, the construction stability is highly determined by the level of water content when the soil is being compacted. This in other words means that porewater pressure is a major stability factor during the embankment construction. The Q strengths and pore-water pressures in the embankment construction stage are of major importance in high dams as compared to the low dams (U.S. Army Corps of Engineers, 1984). The stability of reservoir in the operating conditions is dictated by the R strength (strength of embankment at operating stage). As a result of R strength being highest at optimum water content, the shear strengths for fill water contents in both the wet and dry optimum case are to be established in order to determine the range that is allowable for placement of water contents (Sykora, D. W. et al.,1991).The limiting water content on the dry side of optimum also must be chosen so as to avoid occurrence of excessive settlement resulting from saturation with a preference of there being no settlement when saturation occurs. Use of geotextile and sand filled unit is another alternative is another alternative for providing stability of the slope as they can be utilized as matting so as to stabilize flow in stream channels. By use of geotextiles the soil strength can be improved at a much lower cost as compared to conventional nailing. Furthermore when geotextiles are used it is still possible to plant on steep slopes. Conclusions From the calculations it can be concluded that the earth dam is well designed in terms of stability with the down stream slope being slightly more stable than the upstream. The F.S. in both cases is higher than the recommended values and this makes it possible to use change soil parameters without the slopes reaching the unstable zone. The calculations for the seepage also indicate that there is no substantial loss of water through seepage. Overall the earth dam is well designed in terms of slope stability and seepage. Reference Sykora, D. W. et al. (1991). “Seismic Stability Evaluation of Ririe Dam and Reservoir Project, Report 1, Construction History and Field and Laboratory Studies, Vol I, Main Text,” Technical Report GL-91-22, U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS. Torrey, V. H., III, and Donaghe, R. T. (1991) “Compaction Characteristics of Earth-Rock Mixtures,”Miscellaneous Paper GL-91-16, U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS. Torrey, V. H., III, and Donaghe, R. T. 1991b (Aug). “Compaction Control of Earth-Rock Mixtures,” TechnicalReport GL-91-16, U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS. United States Committee on Large Dams. (1993). “General Guidelines and Current U.S. Practice in Automated Performance Monitoring of Dams,” Denver, CO. U.S. Army Corps of Engineers. (1984). “Shore Protection Manual,” 2 Vols, Washington, DC. Veesaert, C. J. (1990) . “Standardizing the Approach to Dam Safety Training,” Hydro Review, Vol 9, No. 3,pp 46-50. Walker, W. L. (1984). Earth Dams: Geotechnical Considerations in Design and Construction, Ph.D.Dissertation, Oklahoma State University, Stillwater, OK. Wooten, R. L., et al (1992). “Dams Going Safely Over the Top,” CivilEngineering, American Society of Civil Engineers, Vol 62, No. 1, pp 52-54. Appendix 1 Read More

The other important aspect of the flow net is the establishing the squares of the flow net. This is an exercise that requires a lot of skills so as to have a flow net that can be used to predict the seepage with a small error. It is difficult to come up with a perfect flow net but the more modification is made so as to achieve curvilinear squares the higher the accuracy of predicting the seepage. The process of perfecting the flow net brings about the change in the number of equa-potential drops and flow channels which determine the ratio Nf/Nd and this in turn determine the seepage.

Figure 1 Figure 2 Seepage calculations The quantity of seepage is given by Q =   is modified to  =   =   H is the head causing seepage and in this case it is taken as the height of the water level Q =  m3 Stability of slope Using infinite slopes (i)  (ii) (iii) Upstream slope stability Taking b and h to be unity and  and  and =24kpa Upstream slope angle is calculated as Thus  From equations (ii) and (iii) U = 8.96kn  From equation (i) =29.

6kPa FS =  =  (iv) W= = 18.9kpa  = 3.84 Downstream slope stability Downstream slope angle is calculated as Taking b and h to be unity unit density of downstream soil and =9.6kPa Equation (i) will be modified to =  =14.18 Equation (iv) is modified to FS =  =  (iv) W is the unit weight of soil on downstream slope = 9.01  = 4.4 From the calculations it is clear that the upstream slope is much stable than the downstream slope. This stability has greatly been greatly been contributed by the angle of slope being higher at the upstream end.

The effect of the angle could contribute to higher stability but the saturation of water in the upstream of the embankment makes it unstable. It should also be noted that while making the dam to be stables at the upstream through adjustment of the slope angle the cost of the building the embankment is put into consideration. Embankment with low slope is much stable but requires a huge amount of earthwork. The low slope will also increase seepage. Discussion In terms of stability of the embankment it is important to note that the water content of the soil at the time of compaction plays a vital role in the determination of its density, permeability, compressibility and the strength.

This therefore means that the designing of an embankment is greatly influenced by the natural water content of the soil or the drying or wetting which can be done at the fill or before delivery to the fill. It is possible to reduce the natural water content to a certain extent in some instances the burrow soils may be excessively wet that it is not possible for them to be used in embankment without the lopes being flat. The amount of water in the soils also may affect the ability of the machinery used in hauling and compaction to operate to a satisfactory level.

In designing and analysis of an embankment section it is required that shear strength and other properties of the soil be established at water content level and densities obtained during the construction process. in most projects the placement water contents will always fall in a range of 2% dry to 3%wet of optimum with a narrow range being required for soils having compaction curves with sharp peaks (Torrey, 1991). In the construction of embankment using water contents which are achievable in practice is a principal construction requirement but on the other hand the effect water has on the engineering properties of a compacted fill is a utmost importance in design.

Soils whose compaction has been done when wet of optimum water content will have a tendency of exhibiting a plastic type of stress-strain behavior and there will be a likelihood having low strength in the construction stage with very high pore water pressure being experienced during this stage. On the other hand when compaction is done when the soils are dry of the optimum water content will tend to have a rigid stress strain bahaviour and will have high construction strength with very low porewater pressures at the stage of construction and will have less consolidation in comparison the soils which are compacted wet of optimum water content.

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