Stability Analysis of Earth Slopes

The stability analysis of slopes plays a very important role in civil engineering. Stability analysis is used in the construction of transportation facilities such as highways, railroads, airports, and canals; the development of natural resources such as surface mining, refuse disposal, and earth dams; as well as many other human activities involving building construction and excavations. Failures of slopes in these applications are caused by movements within the human-created fill, in the natural slope, or a combination of both. These movement phenomena are usually studied from two different points of view. The geologists consider the moving phenomena as a natural process and study the cause of their origin, their courses, and the resulting surface forms. The engineers investigate the safety of construction based on the principles of soil mechanics and develop methods for a reliable assessment of the stability of slopes, as well as the controlling and corrective measures needed. The best result of stability studies can be achieved only by the combination of both these approaches. The quantitative determination of the stability of slopes by the methods of soil mechanics must be based on a knowledge of the geological structure of the area, the detailed composition and orientation of strata, and the geomorphological history of the land surface. On the other hand, geologists may obtain a clearer picture of the origin and character of movement process by checking their considerations against the results of engineering analyses based on soil mechanics For example, it is well known that one of the most favorable settings for landslides is the presence of permeable or soluble beds overlying or interbedded with relatively impervious beds. This geological phenomenon was explained by Henkel (1967) using the principles of soil mechanics.

The purpose of stability analysis is to determine the factor of safety of a potential failure surface. The factor of safety is defined as a ratio between the resisting force and the driving force, both applied along the failure surface. When the driving force due to weight is equal to the resisting force due to shear strength, the factor of safety is equal to 1 and failure is imminent. Figure 2.1 shows several types of failure surfaces.

The shear strength of soils can be determined by field or laboratory tests. No matter what tests are used, it is necessary to conduct an overall geologic appraisal of the site, followed by a planned subsurface investigation. The purpose of the subsurface investigation is to determine the nature and extent of each type of material that may have an effect on the stability of the slope. A detailed knowledge of the slope from toe to crest is essential. Fills situated over a deep layer of clays and silts may merit expensive drilling. Auger holes, pits, or trenches will suffice for smaller fills or those with bedrock only a short distance below the surface.

In the stability analysis of slopes, particularly those related to earth dams, it is necessary to estimate the location of the phreatic surface or the line of seepage. In the case of an existing slope, the phreatic surface can be determined from the subsurface investigation with adjustments for seasonal changes. If the slope has not been constructed and is quite complex in configuration, the easiest way to determine the phreatic surface is by drawing a flow net, as shown in Fig. 4.1. For a homogeneous and isotropic cross section, if the flow net satisfies the basic requirements that the flow lines and equipotential lines are perpendicular and form squares or rectangles of the same shape and that the vertical distance between equipotential lines along the phreatic surface are the same, the assumed phreatic surface is correct; otherwise, the phreatic surface must be changed until a satisfactory flow net is obtained. For an anisotropic cross section, a transformation based on the ratio between vertical and horizontal permeabilities must be made so that square flow nets can still be constructed. For a nonhomogeneous cross section, the flow nets must satisfy the continuity and interface conditions; as a result, the flow nets in some regions must be rectangular instead of square. Methods for constructing flow nets can be found in most textbooks in soil mechanics and also in Cedergren (1977).

The scope of field investigations should include topography, geology, water, weather, and history of slope changes. If a slide has occurred, the shape of sliding surface should also be determined.

The purpose of this chapter is to present some simple equations for determining the safety factor of slopes with plane failure surfaces. Only three simple cases will be considered: one involving an infinite slope with a failure plane parallel to the slope surface, one involving a triangular cross section with a single failure plane, and the other involving a trapezoidal cross section with two failure planes (Huang, 1977a, 1978b). For three failure planes, the computerized method presented in Chap. 8 should be used.

Since Taylor (1937) first published his stability charts, various charts have been successively presented by Bishop and Morgenstern (1960), Morgenstern (1963), and Spencer (1967). The application of these charts were reviewed by Hunter and Schuster (1971).

The SWASE (Sliding Wedge Analysis of Sidehill Embankments) computer program can be used to determine the factor of safety of a slope when some planes of weakness exist within the slope. These failure planes may exist at the bottom of an embankment or at any other locations. However, the maximum number of failure planes is limited to three because the program can only handle three blocks. If there are more than three planes, they must be approximated by three planes in order to use this program. If no planes of weakness exist, the cylindrical failure surface will be more critical and the REAME computer program, as presented in Chap. 9, should be used instead. Otherwise, both programs should be used to determine which is more critical.

The REAME (Rotational Equilibrium Analysis of Multilayered Embankments) computer program can be used to determine the factor of safety of a slope based on a cylindrical failure surface (Huang, 1981b). A major advantage of REAME over other comparable computer programs is that it requires very little computer time to run. This is made possible by an efficient method of numbering the boundary lines for different soils and controlling the number of circles. This program is particularly useful to those who have very little experience in stability analysis. Without worrying about the computing cost, a large region can be searched, and the minimum factor of safety determined. Features of this program can be described briefly as follows:

Both the simplified and the computerized methods presented in this book were initially developed for use in surface mining. The methods have been applied to three types of fills: bench fills, hollow fills, and refuse embankments.

The normal and the simplified Bishop methods presented so far are based on the method of slices. However, the friction circle method, originally proposed by Taylor (1937), considers the stability of the entire sliding mass as a whole. The disadvantage of the friction circle method is that it can only be applied to a homogeneous slope with a given angle of internal friction. Although this method is of limited utility, an understanding of it will give insight into the problem of stability analysis.

The application of earth pressure theory can be illustrated by the simple example shown in Fig. 12.1. By assuming the active force, P _A , and the passive force, P _p as horizontal, it can be easily proved by Rankine’s or Couloumb’s theory that the failure plane inclines at an angle of 45° + ø/2 for the active wedge and 45° − ø/2 for the passive wedge. From basic soil mechanics in which H _A and H _p are the height of active and passive wedges, respectively. The factor of safety can be determined by in which l is the length of failure surface at middle block, and W is the weight of middle block.