Chapter 15 (1) Slope Stability 연세대학교 지반공학연구실

15.1 Introduction-Modes of Slope Failure Fall. This is the detachment of soil and/or rock fragments that fall down a slope (Figure 15.1). Figure 15.2 shows a fall in which a large amount of soil mass has slid down a slope. Topple. This is a forward rotation of soil and/or rock mass about an axis below the center of gravity of mass being displaced (Figure 15.3). Slide. This is the downward movement of a soil mass occurring on a surface of rupture (Figure 15.4) Spread. This is a form of slide (Figure 15.5) by translation. It occurs by “sudden movement of water-bearing seams of sands or silts overlain by clays or loaded by fills” (Cruden and Varnes, 1996). Flow. This is a downward movement of soil mass similar to a viscous fluid (Figure 15.6)

15.1 Introduction-Modes of Slope Failure The slope stability analysis involves determining and comparing the shear stress developed along the most likely rupture surface with the shear strength of the soil.

15.2 Factor of Safety (15.1) where factor of safety with respect to strength average shear strength of the soil average shear stress developed along the potential failure surface (15.2) where cohesion angle of friction normal stress on the potential failure surface

15.2 Factor of Safety (15.3) where and are the cohesion and the angle of friction that develop along the potential failure surface. (15.4) The factor of safety w.r.t cohesion (15.5) The factor of safety w.r.t friction (15.6)

15.2 Factor of Safety (15.7) : the slope is in a state of impending failure : the design of a stable slope

15.3 Stability of Infinite Slopes Assume : the pore water pressure is zero.

15.3 Stability of Infinite Slopes (Volume of soil element) (Unit weight of soil). (15.8) 1. Force perpendicular to the plane 2. Force parallel to the plane Note : This is the force that tends to cause the slip along the plane.

15.3 Stability of Infinite Slopes The effective normal stress, (15.9) The shear stress, (15.10) (Reaction to the weight) A normal component of A tangential component of

15.3 Stability of Infinite Slopes The resistive shear stress (15.13) Thus, Eq.(15.10) = Eq.(15.13) or (15.14)

15.3 Stability of Infinite Slopes From Eq.(15.7) and Substituting the and into Eq.(15.14), we obtain - The factor of safety (15.15) For granular soils (c=0), ( : stable slope)

15.3 Stability of Infinite Slopes The depth of the plane along which critical equilibrium occurs ( ), (15.16)

15.3 Stability of Infinite Slopes Stability with Seepage

15.5 Analysis of Slope with Plane Failure Surfaces (Culmann’s Method) Assume : The failure of a slope occurs along a plane when the average shearing stress tending to cause the slip is more than the shear strength of the soil. (15.18)

15.5 Analysis of Slope with Plane Failure Surfaces (Culmann’s Method)

15.5 Analysis of Slope with Plane Failure Surfaces (Culmann’s Method) normal component (15.19) tangential component (15.20) Average normal stress on the plane AC (15.21)

15.5 Analysis of Slope with Plane Failure Surfaces (Culmann’s Method) Average shear stress on the plane AC (15.22) Average effective resistive shearing stress (15.23)

15.5 Analysis of Slope with Plane Failure Surfaces (Culmann’s Method) (식15.22) = (식15.23) (15.24) Or (15.25) (15.26)

15.5 Analysis of Slope with Plane Failure Surfaces (Culmann’s Method) (15.27) (15.28) Substitute into Eq(14.36) (15.29) (15.30) where m = stability number

15.5 Analysis of Slope with Plane Failure Surfaces (Culmann’s Method) The Max. height of the slope by substituting & into Eq(13.40) (15.31)  Example 15.2

15.6 Analysis of Finite Slope with Circular Failure Surfaces - General - Modes of failures : a) Slope failure, b) Shallow slope failure c) Base failure - Types of stability analysis procedures 1. Mass procedures 2. Method of slices

15.6 Analysis of Finite Slope with Circular Failure Surfaces - General

Assume : The undrained shear strength of soil is constant with depth.   Assume : The undrained shear strength of soil is constant with depth. Choose a trial potential curve of sliding ( radius of trial potential curve, is the center of the circle)

 

- The weight of the soil above the curve as   - The weight of the soil above the curve as - The moment of the driving forces about (15.32) where, and

The moment of the resisting forces about (15.33) - For equilibrium, or   The moment of the resisting forces about (15.33) - For equilibrium, or (15.34) (15.35)

make a number of trials for different trial circles. Min obtained   make a number of trials for different trial circles. Min obtained from one of trial circles is the factor of safety against (Stability number) (15.36) The critical height ( ) of the slope by and in (15.37) Values of the stability number, , for various slope angle, , are given in Figure 15.13

 

 

- Limitation of using Figure 15.13 - Slopes of saturated clay   - Limitation of using Figure 15.13 - Slopes of saturated clay - Undrained conditions ( ) - In reference to Figure 15.13, the following must be pointed out :

1. For , the critical circle is always a toe circle.   1. For , the critical circle is always a toe circle. 2. For , the critical circle may be toe, slope, or midpoint circle, depending on the depth function, (15.38) 3. When the critical circle is a midpoint circle, Figure 15.15 shows the location of sliding circle. 4. Max. for failure at the midpoint circle is 0.181.

   Example 15.3, 15.4

  stability factor. (Fig. 14.12, 14.13 참조)