Objective

In the realm of geotechnical engineering

the evaluation of seismic slope stability is a very important research topic. It is known that the natural soils exhibit spatial variability

with the properties varying from point to point. This characteristic will have significiant effects on the slope stability

and it is necessary to investigate the slope stability by a statistical approach. The infinite slope model can evaluate the stability of long slopes running down a hillslide

and analyze the mechanics of shallow landslides. This study will focus on the reliability of infinite undrained slopes and cohesive-frictional soil slopes subjected to seismic loadings by the random field method.

Methods

The random field method is adopted to investigate the effect of horizontal and vertical seismic loadings on the reliability of infinite slopes. And the deterministic method is also used to verify the results by the random field method. For deterministic stability analyses of infinite undrained slopes with linearly increasing strength

the infinite slope equation is used to investigate the factor of safety FS and derive the analytical formula for the critical slope angle β

min

which leads to the least value of factor of safety FS. Then

an algorithm generating 1D non-stationary random fields of undrained strength is employed to investigate the probability of slope failure p

f

and the critical slope angle β

min

which leads to the maximum value of probability of slope failure p

f

. For deterministic analyses of infinite cohesive-frictional soil slope stability

the infinite slope equation is adopted to analyze the factor of safety FS

and the critical slope angle min is obtained by calculating the factor of safety FS at intervals of 0.01°. Then the random field method is used to compute the probability of slope failure p

f

and obtain the critical slope angle β

min

.

Results and Discussions

For the infinite undrained slopes subjected to horizontal and vertical seismic loadings

Fig. 2 shows that with the increasing of the slope angle β

the factor of safety FS firstly decreases and then increases

indicating that there exists a critical slope angle β

min

. Fig. 3 shows that with the increasing of the value of λ(ratio of the vertical seismic coefficient kv to the horizontal seismic coefficient k

h

)

the critical slope angle β

min

gradually increases

and the effect of the vertical seismic loading on the critical slope angle β

min

becomes more significant as the horizontal seismic coefficient k

h

increases. Fig. 5 shows that with the increasing of the value of λ

the probability of slope failure p

f

increases obviously

indicating that the effect of the vertical seismic loading on the reliability of infinite undrained slopes can not be ignored. It can also be seen that the probability of slope failure p

f

decreases as the nondimensional spatial correlation length Θ increases and eventually converges asymptotically on the first order second moment (FOSM) solution

indicating that the traditional reliability method will give unconservative results for infinite undrained slopes subjected to seismic loadings. Fig. 6 shows that there exists a critical slope angle β

min

which leads to the maximum value of the probability of slope failure p

f

. This phenomenon can also be verified by the deterministic method. For the infinite cohesive-frictional soil slopes subjected to horizontal and vertical seismic loadings

Figs. 8-10 show that with the increasing of the slope angle β

the value of FS/tanφ' (φ': internal frictional angle) firstly decreases and then increases

indicating that there exists a critical slope angle β

min

. The value of FS/tanφ' increases as the nondimensional parameter S = c'/(γHtanφ') (c': effective cohesion; γ: unit weight of soil; H: slope height) increases

while the critical slope angle β

min

decreases with the increasing of the nondimensional parameter S. When the value of horizontal seismic coefficient k

h

is relatively small

the effect of the vertical seismic loading on the stability of infinite cohesive-frictional soil slopes is not significant. With the increasing of the horizontal seismic coefficient k

h

the effect of the vertical seismic loading becomes gradually significant. Furthermore

the effect of the vertical seismic loading on the stability of the infinite cohesive-frictional soil slopes is affected by the horizontal seismic coefficient k

h

the slope angle and the nondimensional parameter S. Fig. 11 shows that the critical slope angle β

min

increases with the increasing of the value of λ

and the effect of the vertical seismic loading on the critical slope angle β

min

for infinite cohesive-frictional soil slopes becomes more obvious when the value of the horizontal seismic coefficient k

h

increases. Fig. 12 shows that the critical slope angle β

min

decreases with the increasing of the nondimensional parameter S

and eventually flatten out. It can also seen that the critical slope angle β

min

increases with the the increasing of the value of λ

and as the value of the horizontal seismic coefficient k

h

increases

the effect of the vertical seismic loading on the critical slope angle β

min

becomes gradually significant

especially for the relatively great value of the nondimensional parameter S. Fig. 13(a) shows that the probability of slope failure p

f

increases as the value of λ increases

while Fig. 13(b) shows that the probability of slope failure p

f

decreases as the value of λ increases. This phenomenon can also be verified by the deterministic method. Fig. 14 shows that there exists a critical slope angle β

min

which leads to the maximum value of the probability of slope failure p

f

and the value of the critical slope angle β

min

is consistent with the result shown in Fig. 11(b).

Conclusions

For the infinite slopes subjected to seismic loadings

the effect of the vertical seismic loading on the probability of slope failure p

f

is still significant even though the value of the horizontal seismic coefficient k

h

is small. Both horizontal and vertical seismic loadings can not be ignored when performing seismic reliability analyses of infinite slopes. There exists a critical slope angle β

min

which leads to the maximum probability of slope failure p

f

for infinite slopes. And the effect of the vertical seismic loading on the critical slope angle β

min

is gradually obvious as the horizontal seismic coefficient k

h

is increased.