Environmental Engineering Reference
In-Depth Information
25
Ground surface
Search boundary
t = 96 hours - F s = 1.122
t = 72 hours - F s = 1.286
t = 48 hours - F s = 1.450
t = 24 hours - F s = 1.620
t = 0 hours - F s = 1.828
20
15
10
Water table at t = 96 h
48 h
24 h
72 h
5
20
25
30
35
40
45
50
55
x -Coordinate, m
Figure 12.88 Simulation of rainfall
in combination with dynamic programming method
( μ
= 0 . 33).
of the dynamic programming technique opens the way for
analyzing more complex slope stability problems.
The computed factors of safety increase and are similar to
(or even greater than) the factors of safety computed from
the Morgenstern-Price (1965) method when a Poisson's ratio
of 0.48 was used in the stress analysis.
The dynamic programming method is able to locate a slip
surface shape that is slightly more efficient (in terms of min-
imizing the factor of safety function) than a circular shape,
even for a homogeneous soil slope.
The difference in results between the dynamic program-
ming procedure and limit equilibrium methods of slices is
relatively small for simple slopes. The dynamic program-
ming technique has increased analytical flexibility.
negative pore-water pressures (Fredlund, 1987a, 1989b;
Rahardjo and Fredlund, 1991). Nonlinear shear strength-
matric suction relationships can also be incorporated in the
slope stability analysis (Rahardjo et al., 1992).
The soil cohesion c is considered to increase as the matric
suction of the soil increases in the total cohesion method.
The cohesion due to matric suction is obtained by multi-
plying the average matric suction for a soil layer by tan φ b
[i.e., (u a
u w ) tan φ b ]. The increase in the factor of safety
due to negative pore-water pressures (or matric suction) is
illustrated in Fig. 12.89. The shear strength contribution from
matric suction is incorporated into the designation of the cohe-
sion of the soil [i.e., c
u w ) tan φ b ]. The factor of
safety of a slope can decrease significantly when the cohe-
sion due to matric suction is decreased during a prolonged
wet period.
c +
=
(u a
12.7 APPLICATION OF SLOPE STABILITY
ANALYSES
12.7.1 Examples Using Total Cohesion Method
The following two example problems illustrate the applica-
tion of the total cohesionmethod in analyzing slopes with neg-
ative pore-water pressures. The example problems involve
studies of steep slopes in Hong Kong. The soil stratigraphy
was determined from numerous borings. The shear strength
parameters (i.e., c , φ , and φ b ) were obtained by testing undis-
turbed soil samples in the laboratory. Negative pore-water
pressures were measured in situ using tensiometers. Slope sta-
bility analyses were performed to assess the effect of matric
suction changes on the factor of safety. Parametric slope sta-
bility analyses were also conducted using various percentages
of the hydrostatic negative pore-water pressures.
There are several ways that the shear strength of an unsat-
urated soil can be taken into account in a slope stability
analysis. The most logical way to accommodate unsaturated
soil shear strength is to modify computer codes such that
whenever the pore-water pressures are negative, the linear
or nonlinear unsaturated shear strength equation is used in
calculating the shear strength.
It is possible to also perform a slope stability taking the
shear strength of unsaturated soils into account even when
the computer code is not modified to accommodate unsat-
urated soil behavior. For example, it is possible to simply
subdivide the soil stratigraphy above the water table into
layers. The total cohesion in each layer can be computed to
reflect the sum of effective cohesion plus the cohesion due
to matric suction. This procedure is referred to as the “total
cohesion” method (Ching et al., 1984).
The second procedure involves rederiving the factor-of-
safety equations in order to accommodate both positive and
12.7.1.1 Example 1 (Slope behind Hospital and
Residential Buildings)
The site plan for example 1 is shown in Fig. 12.90. The site
consists of a row of residential buildings with a steep cut
slope at the back. The slope has an average inclination angle
 
Search WWH ::




Custom Search