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SLOPE STABILITY ANALYSIS Different methods are used to calculate the Factor Of Safety of a potential slip surface depending on the geometry of the slip surface. For the simplified model of a circular surface, the Bishop’s Simplified Solution may be used. Bishop’s method uses the method of slices and limit equilibrium. In the method of slices, the soil mass lying above the trial failure surface is divided, by vertical planes, into a series of slices of equal width. Bishop (1954) outlines the process by which this method is undertaken. The calculated factor of safety is dependent upon: :W, the Weight of each slice; :α, the Angle between the Radius and the Vertical ; :c’, the cohesion coefficient; :b, the width of each slice; :ru, the pore Pressure ratio (given by u/gh); :φ’, the “angle of friction”. SHAPES IN SLOPES Looking at the shape or curve of a hillside can give clues to its past history and future stability. Concave parts of a hillslope indicate locations of past failure, a sign that future unsafe conditions. Convex slopes suggest that the slope formed above bedrock in the middle of the slope. The bedrock that helped form the concavity will not necessarily remain stable, however. THE USE OF PILES IN SLOPE STABILITY Slope stability has been the subject of a great number of different works. A useful Paper regarding the analysis of the stability of slopes is A.W. Bishop’s ''The Use of the Slip Circle in the Stability Analysis of Slopes''. This allows Calculations to be made for the stability of a slope for which the profile of the slip Surface is circular. Much work has been undertaken regarding the use of piles to transfer vertical axial loads to a firmer stratum of soil beneath ground level. However, relatively little work related to piles is focused on the issue of laterally loaded piles such as those required to stabilise slopes. C. Viggiani and B. Broms wrote the most useful and comprehensive papers on the subject of the latter. Viggiani’s ''Ultimate lateral load on piles used to stabilise landslides'' analyses a specific subject within Broms’s earlier ''Lateral Resistance of Piles in Cohesive Soils''. These papers consider the effects of lateral load on piles in order to ascertain what resistance piles can offer to the slope in order to stabilise them, and provides the necessary calculations to this effect. PILE DESIGN The design of the piles involves increasing the available shear force in an attempt to increase the factor of safety (''F'') from, say, 1.0 to 1.4 (i.e. on the verge of failure to a conservative value). The calculation of the strength of soil mobilised is already conservative, and applying ''F'' makes doubly sure. Once ''F'' has been acquired for the slope, the additional resistant shear force required to stabilise the slope should be acquired from limit equilibrium analysis of the soil mass above the slip surface. By adding this shear force, the moment caused by forces up the slope (shear force and friction) must exceed the moment caused by forces acting down the slope (the weight of the soil mass), about the pivotal point (i.e. the centre of the circle comprising the slip surface). It will therefore be necessary to find out the strength offered by a given pile in order to ascertain whether that pile will be able to resist the shear forces mobilised at the failure surface. This calculation applies a suitable F (e.g. 1.4) to the required strength (τf). If the available (mobilised) strength (τm) afforded by the pile matches or exceeds this, then the slope will be satisfactorily stabilised. The optimum design attempts to achieve a τm that only slightly exceeds τf (with F applied), according to the equation: :PY-available = PY-required / F This is because the calculations of F have already erred on the conservative side, and therefore the best design within these parameters is the most economically viable one. This not only takes into account materials, but also man-hours and any necessary plant hire. The ultimate lateral resistance (at working loads) of single piles and pile groups driven into cohesive soils occurs when tf is reached. τf can therefore be calculated by finding the shear force required to cause the first failure mechanism in a pile. This is known as ''Viggiani Shear'', and is calculated assuming failure takes place when either: :-One or two plastic hinges form along each individual pile; :-Lateral resistance of supporting soil is exceeded along total length of laterally loaded pile. The first mechanism of failure to occur is dependent on the values of cohesion coefficient, length of embedded strata and the ultimate moment the pile can resist. One of six different possible mechanisms result from when the ultimate lateral resistance is exceeded. :1) The pile-soil interaction reaches a yield value only in the firm stratum. The whole pile translates with the sliding soil, ripping the underlying firm stratum; :2) The pile rotates rigidly about a point on its axis within the embedded section; :3) The pile remains in place and the sliding soil ‘flows’ around it; :4) Plastic hinge forms in the soft statum; :5) Plastic hinges occur in both the soft and firm strata; :6) Plastic hinge occurs in the firm stratum. At low load levels, pile deflections are approximately linear to applied load. On approaching the τf, deflections increase very rapidly with increasing applied load. OTHER METHODS The other major method used to stabilise slopes is drainage of the slope to reduce pore water pressure. This increases effective stress within the slope, thus stabilizing the slope. However, this process is extremely slow for clay soils, and is therefore especially problematic for newly constructed slopes such as embankments. A total stress analysis of these slopes is necessary in these early stages in order to ascertain the stability; however, in the long term, an effective stress analysis may be used. Effective stress analyses are used with highly permeable slopes such as sands throughout its life, since the fully drained condition is reached rapidly. |
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