The external stability analysis is conducted using a modified Fellenius method, which assumes a circular failure surface passing through the base of the whole section of GRS-RW, including the facing. For sandy foundation, modified Fellenius method underestimates the safety, thus a simplified Bishop's analysis or bearing capacity analysis may be conducted. If the failure surface passes through the geosynthetic, the tensile resistance of the reinforcement has to be considered. The seismic coefficient method is used to account for earthquake loading.

For construction on a long slope, additional consideration is needed since loading by GRS-RW may lead to slope instability.

The factor of safety against external stability is determined from Equation 8.1. The required factor of safety under dead-load and earthquake conditions are 1.3 and 1.0, respectively.

  (8.1)

where

Mr,s	: resisting moment of soil mass
Mr,g	: resisting moment of geosynthetic reinforcement
Md,s	: driving moment of soil mass
Md,w	: driving moment of facing
Md,f	: driving moment of external load acting on the crest of facing

With reference to Figure 8.1, the components of moment are explained in following Sections:

  (8.2)

where

r	: radius of circular failure surface (m)
D W	: weight of soil slice per unit width (kN/m)
Ws	: surcharge load (kN)
b	: width of soil slice (m)
u	: pore water pressure per unit width (kN/m)
q	: angle of inclination of the base of soil slice (degree)
kh	: horizontal seismic coefficient
f	: internal friction angle of the soil (degree)

  (8.3)

where

Ti	: geosynthetic resisting force, see Eq. (6.6) (kN/m)
a i	: angle between the geosynthetic layer and failure surface (degree)
Li	: anchorage length of geosynthetic layer (m)
b	: width of soil slice (m)
s v	: vertical stress acting on geosynthetic layer (kPa)
Ff	: factor of safety against pullout (dead-load condition: 2.0, earthquake: 1.25)

  (8.4)

where

h1	: vertical distance from the center of circle to the center of soil mass (m)
h2	: vertical distance from the center of circle to the top of soil mass (m)

  (8.5)

where

Ww	: weight of facing (kN/m)
x	: horizontal distance from the center of circle to the center of gravity of facing (m)
y	: vertical distance from the center of circle to the center of gravity of facing (m)

  (8.6)

where

Pm	: moment (kN× m/m)
Pv	: vertical load (kN/m)
x'	: horizontal distance from the center of circle to the center of facing crest (m)
Ph	: horizontal load (kN/m)
y'	: vertical distance from the center of circle to the top of facing crest (m)

In addition to above-mentioned external stability analysis, the overall stability of reinforced zone against direct sliding has to be evaluated (Figure 8.2). The required factor of safety is referred to the Geosynthetic Design Manual of the PRWI. If R_a is extremely large, the reinforced soil mass may be modeled in several portions (Figure 8.3) to give the smallest factor of safety.

If the required factor of safety is not satisfied in the external stability analysis, the geosynthetic layers and/or their strength have to be altered to increase the resistance.